Project_GDP.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('GDPCountry.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>Population</th>\n",
       "      <th>Area_sqm</th>\n",
       "      <th>Pop_Density_per sqm</th>\n",
       "      <th>Coastline (coast/area ratio)</th>\n",
       "      <th>Net migration</th>\n",
       "      <th>Infant mortality (per 1000 births)</th>\n",
       "      <th>GDP ($ per capita)</th>\n",
       "      <th>Literacy (%)</th>\n",
       "      <th>Phones (per 1000)</th>\n",
       "      <th>Arable (%)</th>\n",
       "      <th>Crops (%)</th>\n",
       "      <th>Other (%)</th>\n",
       "      <th>Climate</th>\n",
       "      <th>Birthrate</th>\n",
       "      <th>Deathrate</th>\n",
       "      <th>Agriculture</th>\n",
       "      <th>Industry</th>\n",
       "      <th>Service</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>31056997</td>\n",
       "      <td>647500</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>23.06</td>\n",
       "      <td>163.07</td>\n",
       "      <td>700.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>12.13</td>\n",
       "      <td>0.22</td>\n",
       "      <td>87.65</td>\n",
       "      <td>1.0</td>\n",
       "      <td>46.60</td>\n",
       "      <td>20.34</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.240</td>\n",
       "      <td>0.380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Albania</td>\n",
       "      <td>3581655</td>\n",
       "      <td>28748</td>\n",
       "      <td>124.6</td>\n",
       "      <td>1.26</td>\n",
       "      <td>-4.93</td>\n",
       "      <td>21.52</td>\n",
       "      <td>4500.0</td>\n",
       "      <td>86.5</td>\n",
       "      <td>71.2</td>\n",
       "      <td>21.09</td>\n",
       "      <td>4.42</td>\n",
       "      <td>74.49</td>\n",
       "      <td>3.0</td>\n",
       "      <td>15.11</td>\n",
       "      <td>5.22</td>\n",
       "      <td>0.232</td>\n",
       "      <td>0.188</td>\n",
       "      <td>0.579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>32930091</td>\n",
       "      <td>2381740</td>\n",
       "      <td>13.8</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>31.00</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>78.1</td>\n",
       "      <td>3.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>96.53</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.14</td>\n",
       "      <td>4.61</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.600</td>\n",
       "      <td>0.298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>American Samoa</td>\n",
       "      <td>57794</td>\n",
       "      <td>199</td>\n",
       "      <td>290.4</td>\n",
       "      <td>58.29</td>\n",
       "      <td>-20.71</td>\n",
       "      <td>9.27</td>\n",
       "      <td>8000.0</td>\n",
       "      <td>97.0</td>\n",
       "      <td>259.5</td>\n",
       "      <td>10.00</td>\n",
       "      <td>15.00</td>\n",
       "      <td>75.00</td>\n",
       "      <td>2.0</td>\n",
       "      <td>22.46</td>\n",
       "      <td>3.27</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Andorra</td>\n",
       "      <td>71201</td>\n",
       "      <td>468</td>\n",
       "      <td>152.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6.60</td>\n",
       "      <td>4.05</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>497.2</td>\n",
       "      <td>2.22</td>\n",
       "      <td>0.00</td>\n",
       "      <td>97.78</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.71</td>\n",
       "      <td>6.25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Country  Population  Area_sqm  Pop_Density_per sqm  \\\n",
       "0     Afghanistan    31056997    647500                 48.0   \n",
       "1         Albania     3581655     28748                124.6   \n",
       "2         Algeria    32930091   2381740                 13.8   \n",
       "3  American Samoa       57794       199                290.4   \n",
       "4         Andorra       71201       468                152.1   \n",
       "\n",
       "   Coastline (coast/area ratio)  Net migration  \\\n",
       "0                          0.00          23.06   \n",
       "1                          1.26          -4.93   \n",
       "2                          0.04          -0.39   \n",
       "3                         58.29         -20.71   \n",
       "4                          0.00           6.60   \n",
       "\n",
       "   Infant mortality (per 1000 births)  GDP ($ per capita)  Literacy (%)  \\\n",
       "0                              163.07               700.0          36.0   \n",
       "1                               21.52              4500.0          86.5   \n",
       "2                               31.00              6000.0          70.0   \n",
       "3                                9.27              8000.0          97.0   \n",
       "4                                4.05             19000.0         100.0   \n",
       "\n",
       "   Phones (per 1000)  Arable (%)  Crops (%)  Other (%)  Climate  Birthrate  \\\n",
       "0                3.2       12.13       0.22      87.65      1.0      46.60   \n",
       "1               71.2       21.09       4.42      74.49      3.0      15.11   \n",
       "2               78.1        3.22       0.25      96.53      1.0      17.14   \n",
       "3              259.5       10.00      15.00      75.00      2.0      22.46   \n",
       "4              497.2        2.22       0.00      97.78      3.0       8.71   \n",
       "\n",
       "   Deathrate  Agriculture  Industry  Service  \n",
       "0      20.34        0.380     0.240    0.380  \n",
       "1       5.22        0.232     0.188    0.579  \n",
       "2       4.61        0.101     0.600    0.298  \n",
       "3       3.27          NaN       NaN      NaN  \n",
       "4       6.25          NaN       NaN      NaN  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(227, 19)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 227 entries, 0 to 226\n",
      "Data columns (total 19 columns):\n",
      "Country                               227 non-null object\n",
      "Population                            227 non-null int64\n",
      "Area_sqm                              227 non-null int64\n",
      "Pop_Density_per sqm                   227 non-null float64\n",
      "Coastline (coast/area ratio)          227 non-null float64\n",
      "Net migration                         224 non-null float64\n",
      "Infant mortality (per 1000 births)    224 non-null float64\n",
      "GDP ($ per capita)                    226 non-null float64\n",
      "Literacy (%)                          209 non-null float64\n",
      "Phones (per 1000)                     223 non-null float64\n",
      "Arable (%)                            225 non-null float64\n",
      "Crops (%)                             225 non-null float64\n",
      "Other (%)                             225 non-null float64\n",
      "Climate                               205 non-null float64\n",
      "Birthrate                             224 non-null float64\n",
      "Deathrate                             223 non-null float64\n",
      "Agriculture                           212 non-null float64\n",
      "Industry                              211 non-null float64\n",
      "Service                               212 non-null float64\n",
      "dtypes: float64(16), int64(2), object(1)\n",
      "memory usage: 33.8+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "227"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df.Country.unique())\n",
    "# we are dropping country as it is unique for each row\n",
    "# or we can replace the country as index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population</th>\n",
       "      <th>Area_sqm</th>\n",
       "      <th>Pop_Density_per sqm</th>\n",
       "      <th>Coastline (coast/area ratio)</th>\n",
       "      <th>Net migration</th>\n",
       "      <th>Infant mortality (per 1000 births)</th>\n",
       "      <th>GDP ($ per capita)</th>\n",
       "      <th>Literacy (%)</th>\n",
       "      <th>Phones (per 1000)</th>\n",
       "      <th>Arable (%)</th>\n",
       "      <th>Crops (%)</th>\n",
       "      <th>Other (%)</th>\n",
       "      <th>Climate</th>\n",
       "      <th>Birthrate</th>\n",
       "      <th>Deathrate</th>\n",
       "      <th>Agriculture</th>\n",
       "      <th>Industry</th>\n",
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       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>31056997</td>\n",
       "      <td>647500</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>23.06</td>\n",
       "      <td>163.07</td>\n",
       "      <td>700.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>12.13</td>\n",
       "      <td>0.22</td>\n",
       "      <td>87.65</td>\n",
       "      <td>1.0</td>\n",
       "      <td>46.60</td>\n",
       "      <td>20.34</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.240</td>\n",
       "      <td>0.380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Albania</td>\n",
       "      <td>3581655</td>\n",
       "      <td>28748</td>\n",
       "      <td>124.6</td>\n",
       "      <td>1.26</td>\n",
       "      <td>-4.93</td>\n",
       "      <td>21.52</td>\n",
       "      <td>4500.0</td>\n",
       "      <td>86.5</td>\n",
       "      <td>71.2</td>\n",
       "      <td>21.09</td>\n",
       "      <td>4.42</td>\n",
       "      <td>74.49</td>\n",
       "      <td>3.0</td>\n",
       "      <td>15.11</td>\n",
       "      <td>5.22</td>\n",
       "      <td>0.232</td>\n",
       "      <td>0.188</td>\n",
       "      <td>0.579</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Population  Area_sqm  Pop_Density_per sqm  \\\n",
       "Country                                                  \n",
       "Afghanistan    31056997    647500                 48.0   \n",
       "Albania         3581655     28748                124.6   \n",
       "\n",
       "             Coastline (coast/area ratio)  Net migration  \\\n",
       "Country                                                    \n",
       "Afghanistan                          0.00          23.06   \n",
       "Albania                              1.26          -4.93   \n",
       "\n",
       "             Infant mortality (per 1000 births)  GDP ($ per capita)  \\\n",
       "Country                                                               \n",
       "Afghanistan                              163.07               700.0   \n",
       "Albania                                   21.52              4500.0   \n",
       "\n",
       "             Literacy (%)  Phones (per 1000)  Arable (%)  Crops (%)  \\\n",
       "Country                                                               \n",
       "Afghanistan          36.0                3.2       12.13       0.22   \n",
       "Albania              86.5               71.2       21.09       4.42   \n",
       "\n",
       "             Other (%)  Climate  Birthrate  Deathrate  Agriculture  Industry  \\\n",
       "Country                                                                        \n",
       "Afghanistan      87.65      1.0      46.60      20.34        0.380     0.240   \n",
       "Albania          74.49      3.0      15.11       5.22        0.232     0.188   \n",
       "\n",
       "             Service  \n",
       "Country               \n",
       "Afghanistan    0.380  \n",
       "Albania        0.579  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.set_index('Country')\n",
    "df.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MISSING VALUE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Population                             0\n",
       "Area_sqm                               0\n",
       "Pop_Density_per sqm                    0\n",
       "Coastline (coast/area ratio)           0\n",
       "Net migration                          3\n",
       "Infant mortality (per 1000 births)     3\n",
       "GDP ($ per capita)                     1\n",
       "Literacy (%)                          18\n",
       "Phones (per 1000)                      4\n",
       "Arable (%)                             2\n",
       "Crops (%)                              2\n",
       "Other (%)                              2\n",
       "Climate                               22\n",
       "Birthrate                              3\n",
       "Deathrate                              4\n",
       "Agriculture                           15\n",
       "Industry                              16\n",
       "Service                               15\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Population                            0.000000\n",
       "Area_sqm                              0.000000\n",
       "Pop_Density_per sqm                   0.000000\n",
       "Coastline (coast/area ratio)          0.000000\n",
       "Net migration                         1.321586\n",
       "Infant mortality (per 1000 births)    1.321586\n",
       "GDP ($ per capita)                    0.440529\n",
       "Literacy (%)                          7.929515\n",
       "Phones (per 1000)                     1.762115\n",
       "Arable (%)                            0.881057\n",
       "Crops (%)                             0.881057\n",
       "Other (%)                             0.881057\n",
       "Climate                               9.691630\n",
       "Birthrate                             1.321586\n",
       "Deathrate                             1.762115\n",
       "Agriculture                           6.607930\n",
       "Industry                              7.048458\n",
       "Service                               6.607930\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum() / len(df) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#! pip install missingpy\n",
    "from missingpy import KNNImputer\n",
    "#from sklearn.impute import KNNImputer\n",
    "\n",
    "impu = KNNImputer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:432: DeprecationWarning: 'warn_on_dtype' is deprecated in version 0.21 and will be removed in 0.23. Don't set `warn_on_dtype` to remove this warning.\n",
      "  DeprecationWarning)\n",
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:432: DeprecationWarning: 'warn_on_dtype' is deprecated in version 0.21 and will be removed in 0.23. Don't set `warn_on_dtype` to remove this warning.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
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       "      <th>Population</th>\n",
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       "      <th>Infant mortality (per 1000 births)</th>\n",
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       "      <th>Climate</th>\n",
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       "      <th>Service</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>31056997.0</td>\n",
       "      <td>647500.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>23.06</td>\n",
       "      <td>163.07</td>\n",
       "      <td>700.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>12.13</td>\n",
       "      <td>0.22</td>\n",
       "      <td>87.65</td>\n",
       "      <td>1.0</td>\n",
       "      <td>46.60</td>\n",
       "      <td>20.34</td>\n",
       "      <td>0.380</td>\n",
       "      <td>0.240</td>\n",
       "      <td>0.380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Albania</td>\n",
       "      <td>3581655.0</td>\n",
       "      <td>28748.0</td>\n",
       "      <td>124.6</td>\n",
       "      <td>1.26</td>\n",
       "      <td>-4.93</td>\n",
       "      <td>21.52</td>\n",
       "      <td>4500.0</td>\n",
       "      <td>86.5</td>\n",
       "      <td>71.2</td>\n",
       "      <td>21.09</td>\n",
       "      <td>4.42</td>\n",
       "      <td>74.49</td>\n",
       "      <td>3.0</td>\n",
       "      <td>15.11</td>\n",
       "      <td>5.22</td>\n",
       "      <td>0.232</td>\n",
       "      <td>0.188</td>\n",
       "      <td>0.579</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Population  Area_sqm  Pop_Density_per sqm  \\\n",
       "Country                                                  \n",
       "Afghanistan  31056997.0  647500.0                 48.0   \n",
       "Albania       3581655.0   28748.0                124.6   \n",
       "\n",
       "             Coastline (coast/area ratio)  Net migration  \\\n",
       "Country                                                    \n",
       "Afghanistan                          0.00          23.06   \n",
       "Albania                              1.26          -4.93   \n",
       "\n",
       "             Infant mortality (per 1000 births)  GDP ($ per capita)  \\\n",
       "Country                                                               \n",
       "Afghanistan                              163.07               700.0   \n",
       "Albania                                   21.52              4500.0   \n",
       "\n",
       "             Literacy (%)  Phones (per 1000)  Arable (%)  Crops (%)  \\\n",
       "Country                                                               \n",
       "Afghanistan          36.0                3.2       12.13       0.22   \n",
       "Albania              86.5               71.2       21.09       4.42   \n",
       "\n",
       "             Other (%)  Climate  Birthrate  Deathrate  Agriculture  Industry  \\\n",
       "Country                                                                        \n",
       "Afghanistan      87.65      1.0      46.60      20.34        0.380     0.240   \n",
       "Albania          74.49      3.0      15.11       5.22        0.232     0.188   \n",
       "\n",
       "             Service  \n",
       "Country               \n",
       "Afghanistan    0.380  \n",
       "Albania        0.579  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1 = impu.fit_transform(df)\n",
    "df_1 = pd.DataFrame(df_1, columns = df.columns, index = df.index)\n",
    "df_1.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Population                            0\n",
       "Area_sqm                              0\n",
       "Pop_Density_per sqm                   0\n",
       "Coastline (coast/area ratio)          0\n",
       "Net migration                         0\n",
       "Infant mortality (per 1000 births)    0\n",
       "GDP ($ per capita)                    0\n",
       "Literacy (%)                          0\n",
       "Phones (per 1000)                     0\n",
       "Arable (%)                            0\n",
       "Crops (%)                             0\n",
       "Other (%)                             0\n",
       "Climate                               0\n",
       "Birthrate                             0\n",
       "Deathrate                             0\n",
       "Agriculture                           0\n",
       "Industry                              0\n",
       "Service                               0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outlier Treatment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0gYr1CH4QEY+W/f9R0jUq5teqOF3SXeU6tsdJ2j1eZ9snS3p7RDxUNnWq+Kl8v3vLf7dJaq1YA2avOZJ+HBHnDr8hIn4o6bekgaD+eES8OtGdATOtfw743IhYG8VC5uMtwj/89/H924f15jF7whhjN0j6YkT8oqTfH6dfVf2r3h0RJyzHvIh4TdJu278tDfwZp/eX1xeVS8BK0p9K+upE90cAI8vDkn7D9gLbP6Nizqx/amBpuY6uVKyt+63yeo+k88rr/XNtw52s4q2f9Oaqe5L0fyqW5xyiPEN5ZdD87mckPTS8H45Ntr8m6TuS3mv7RdtXSbpc0lW2n5L0Pb35YduFkp6z/bykxZJumej++R8dKSLiv2zfoWJFPEm6PSKeKD8w2ylppe0vS3pB0j+UfW6S9BXbfybp8THu+kYV83N7VSy/+a6y/d8l3WP7Mo38CxUrJd1afti3S8XcNKCI+NQYN434alpE3KPiz6xVxmpoaChlAH+j/MoaMKsxBQEASTgDBoAknAEDQBICGACSEMAAkIQABoAkBDAAJPl/lafvgZKAcmoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qA1Q/7IMq3FcB/0n12ySmrmXdoDqWLS2aV0PTcS2q3yT94VLKA7N8/UyqH7RdvIAxfx04v5TyvjZNUyuUe8A6LkX1a+pHgQOzxRcO/a6vT0TEyQsYvhu48WjnKLkHLElJ3AOWpCQGWJKSGGBJSmKAJSmJAZakJP8PgdASYl2ZNqsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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omlPqOy/uBM4ppeyNiGdLKS/P3q6ZiIgvABeWUr6bvS3K5SEIzSmllD0073SY9X9/bSr1bXJXG1+Be8CSlMY9YElKYoAlKYkBlqQkBliSkhhgSUry/8kPSUVQ1ihlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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03AywFp32otxnZua/T/P25wLLM/OhTiemRccAS1IRzwFLUhEDLElFDLAkFTHAklTEAEtSkf8HD+yb6L5idJcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qS1fVHzGz0t+NM5LelF2ZwAUEMPLynKTrVtn/vbLnq93bsvKz8+7F+9Rer+Id2u6QVO0bZ3OSLq9sNLM3SXqHu39G0n5Jv6nib8D4pfSQy9PXApkjgJGXz0l6nZn9XqnBzN5hZr9Y5dgnJN1hZpvTu1PdKelL6b4fM7OfT5+/W9J/pPcm/mF3H5V0j4q/NqjSlKRClfYPqfjNN0nqVDHgz6t4bViS3qbiDXiAzBHAyIUX7/p0p6Rd6Y+hPSfpT1TlvrJe/JVHB1W8+9ZTkh5292fS3VOS9pjZs5K2SvqopC2SHk3bvijp3ipTeELStVZ253gzuzYdr9T3x1T8JuDP6sIq+mZJ/7a2qoHVcTc0bBjpr0B61N2vXuPrH5D0r+7+WB2veULS7VV+OgJoGCtgXEr+TBcuLVyUmW2TdIDwRbOwAgaAIKyAASAIAQwAQQhgAAhCAANAEAIYAIL8P/+E+3qRnusfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rm0J7rvVXAH9TSrm+vZNpoTLGWpAi4mrgZCnl4Vmu/7PAi6WU/e2dTAuVMZakBNxnLEkJGGNJSsAYS1ICxliSEjDGkpTA/wP+0Fy9oGPPwAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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S/5TzK0rPYO+Q1Gfpf6h6raQjkuTuM0qvEz9pZp+rcz/+VuldyCbK68vcKekTZvZDM7s4294HzWxK0lNKr1MDTcV3QQBAEM6AASAIAQaAIAQYAIIQYAAIQoABIAgBBoAgBBgAgvwaD9+4FeOMmPwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qXFIGzpQ1ClurjxM6A/iYhSwd4UxZkhLxhT5JSsRSlqRELGVJSsRSlqRELGVJSuT/Ac9gLF6D/W5HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df_1.columns:\n",
    "    sns.boxplot(df_1[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(227, 18)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in df_1.columns:\n",
    "    q1 = df_1[i].quantile(0.25)\n",
    "    q3 = df_1[i].quantile(0.75)\n",
    "    IQR  = q3-q1\n",
    "    ub = q3 + 1.5*IQR #upper bound\n",
    "    lb = q1 - 1.5*IQR #lower bound\n",
    "    uc = df_1[i].quantile(0.99) #upper cap\n",
    "    lc = df_1[i].quantile(0.01) #lower cap\n",
    "    for ind1 in df_1[i].index:\n",
    "        if df_1.loc[ind1,i]> ub:\n",
    "            df_1.loc[ind1,i] = uc\n",
    "        if df_1.loc[ind1,i]< lb:\n",
    "            df_1.loc[ind1,i] = lc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vBfaPiAPbbqdPoh5tRwxgAZCZ3wI+S7ds4krgssy8s919D3BmRKyl+0DDT07Q3efavuvo5nZPbsf4DvC3dB+Ls5bu44j2naCvj7YnptbR/ZG4a9T9XwKWDD8JN3x8uuUKr5ygb4ANEfENurnk97W2D9J9YOjadtwPTqKfQ4Db27TFBcA/ZOZPgbOBL0fErcBDk+hH2xGXo9S42isNVrQnlvpCRJwKnJyZfzDBfjcDf5WZq3pU13HteO/qxfG07XOeSa8oEbGM7pUdi6trkSbiCFgvSUQsB/Yf1fw3mVn7ES9jiIhP0H2e20gXZ+Zk5oilaWMAS1IRn4STpCIGsCQVMYAlqYgBLElF/h8enMqZ0zNdUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ym2LLvnTQCOUnXeZoXtt0X7uf/VZJ77a9zOXNyAtUXmE03mB+g8opHiwg8/ouNnonIsL2uZI+6/Klwc+r/IJeqhJsZ6jM9BeS/jAifmB7k6R/dfli3u2SdtWHO1nS1bZfUpmB7uK6foOkW23vjYizZtm/H9c3xT5n+yiV59pnVV4JNLtV5dxsw29K+lvbV9a+/LrKf7fMaz2Svibp35raXS/pq7b3SLpX5bxzK59XObVzfw3GKZWvWGrXl5l+Rk/b3qhy5L9bZVrghr+TdK3tA7X2xj57bV+uMoWmJd0SEY3pM0+TdG+88q0iWCCYPQ99Z/smlfB9tIdt3iHpwkg2Z/OhsH2Nyvn0O/vdF8wvghp9Z/utKt8FeE+/+zLIbH8sIjb2ux+YfwQ1ACTHm4kAkBxBDQDJEdQAkBxBDQDJEdQAkNz/ASCg+gd8B6kAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df_1.columns:\n",
    "    sns.boxplot(df_1[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input as X Output/ Target as Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_1.drop('GDP ($ per capita)', axis = 1)\n",
    "y = df_1['GDP ($ per capita)']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "xc = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>GDP ($ per capita)</td> <th>  R-squared:         </th> <td>   0.801</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                    <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.785</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>              <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   49.48</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 09 Mar 2021</td>  <th>  Prob (F-statistic):</th> <td>1.40e-63</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>10:28:23</td>      <th>  Log-Likelihood:    </th> <td> -2222.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>       <td>   227</td>       <th>  AIC:               </th> <td>   4482.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>           <td>   209</td>       <th>  BIC:               </th> <td>   4543.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>               <td>    17</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>       <td>nonrobust</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                   <td></td>                     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                              <td> 8642.6765</td> <td> 1.21e+04</td> <td>    0.715</td> <td> 0.475</td> <td>-1.52e+04</td> <td> 3.25e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Population</th>                         <td> 1.698e-06</td> <td> 3.89e-06</td> <td>    0.437</td> <td> 0.663</td> <td>-5.97e-06</td> <td> 9.36e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area_sqm</th>                           <td>-1.905e-05</td> <td>    0.000</td> <td>   -0.166</td> <td> 0.868</td> <td>   -0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Pop_Density_per sqm</th>                <td>    0.0281</td> <td>    0.188</td> <td>    0.150</td> <td> 0.881</td> <td>   -0.343</td> <td>    0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Coastline (coast/area ratio)</th>       <td>  -15.1276</td> <td>    3.853</td> <td>   -3.926</td> <td> 0.000</td> <td>  -22.723</td> <td>   -7.532</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Net migration</th>                      <td>  295.1782</td> <td>   45.856</td> <td>    6.437</td> <td> 0.000</td> <td>  204.779</td> <td>  385.577</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Infant mortality (per 1000 births)</th> <td>  -37.6590</td> <td>   26.997</td> <td>   -1.395</td> <td> 0.165</td> <td>  -90.881</td> <td>   15.563</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Literacy (%)</th>                       <td>   -0.4939</td> <td>   25.102</td> <td>   -0.020</td> <td> 0.984</td> <td>  -49.979</td> <td>   48.991</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Phones (per 1000)</th>                  <td>   32.2409</td> <td>    2.414</td> <td>   13.358</td> <td> 0.000</td> <td>   27.483</td> <td>   36.999</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Arable (%)</th>                         <td>  -75.8229</td> <td>   72.753</td> <td>   -1.042</td> <td> 0.299</td> <td> -219.247</td> <td>   67.601</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Crops (%)</th>                          <td>  -21.7611</td> <td>   39.638</td> <td>   -0.549</td> <td> 0.584</td> <td>  -99.903</td> <td>   56.381</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Other (%)</th>                          <td>  -34.6986</td> <td>   70.617</td> <td>   -0.491</td> <td> 0.624</td> <td> -173.912</td> <td>  104.515</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Climate</th>                            <td> -187.4946</td> <td>  561.108</td> <td>   -0.334</td> <td> 0.739</td> <td>-1293.652</td> <td>  918.663</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Birthrate</th>                          <td>  -30.8857</td> <td>   66.935</td> <td>   -0.461</td> <td> 0.645</td> <td> -162.839</td> <td>  101.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Deathrate</th>                          <td>  125.3649</td> <td>   80.701</td> <td>    1.553</td> <td> 0.122</td> <td>  -33.726</td> <td>  284.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Agriculture</th>                        <td>-4532.7267</td> <td> 9322.350</td> <td>   -0.486</td> <td> 0.627</td> <td>-2.29e+04</td> <td> 1.38e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industry</th>                           <td> 2115.0018</td> <td> 8947.628</td> <td>    0.236</td> <td> 0.813</td> <td>-1.55e+04</td> <td> 1.98e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Service</th>                            <td>-1155.9880</td> <td> 9240.786</td> <td>   -0.125</td> <td> 0.901</td> <td>-1.94e+04</td> <td> 1.71e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.555</td> <th>  Durbin-Watson:     </th> <td>   1.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.008</td> <th>  Jarque-Bera (JB):  </th> <td>  15.716</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.209</td> <th>  Prob(JB):          </th> <td>0.000387</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.220</td> <th>  Cond. No.          </th> <td>6.21e+09</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 6.21e+09. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:     GDP ($ per capita)   R-squared:                       0.801\n",
       "Model:                            OLS   Adj. R-squared:                  0.785\n",
       "Method:                 Least Squares   F-statistic:                     49.48\n",
       "Date:                Tue, 09 Mar 2021   Prob (F-statistic):           1.40e-63\n",
       "Time:                        10:28:23   Log-Likelihood:                -2222.8\n",
       "No. Observations:                 227   AIC:                             4482.\n",
       "Df Residuals:                     209   BIC:                             4543.\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================================\n",
       "                                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------------\n",
       "const                               8642.6765   1.21e+04      0.715      0.475   -1.52e+04    3.25e+04\n",
       "Population                          1.698e-06   3.89e-06      0.437      0.663   -5.97e-06    9.36e-06\n",
       "Area_sqm                           -1.905e-05      0.000     -0.166      0.868      -0.000       0.000\n",
       "Pop_Density_per sqm                    0.0281      0.188      0.150      0.881      -0.343       0.399\n",
       "Coastline (coast/area ratio)         -15.1276      3.853     -3.926      0.000     -22.723      -7.532\n",
       "Net migration                        295.1782     45.856      6.437      0.000     204.779     385.577\n",
       "Infant mortality (per 1000 births)   -37.6590     26.997     -1.395      0.165     -90.881      15.563\n",
       "Literacy (%)                          -0.4939     25.102     -0.020      0.984     -49.979      48.991\n",
       "Phones (per 1000)                     32.2409      2.414     13.358      0.000      27.483      36.999\n",
       "Arable (%)                           -75.8229     72.753     -1.042      0.299    -219.247      67.601\n",
       "Crops (%)                            -21.7611     39.638     -0.549      0.584     -99.903      56.381\n",
       "Other (%)                            -34.6986     70.617     -0.491      0.624    -173.912     104.515\n",
       "Climate                             -187.4946    561.108     -0.334      0.739   -1293.652     918.663\n",
       "Birthrate                            -30.8857     66.935     -0.461      0.645    -162.839     101.068\n",
       "Deathrate                            125.3649     80.701      1.553      0.122     -33.726     284.456\n",
       "Agriculture                        -4532.7267   9322.350     -0.486      0.627   -2.29e+04    1.38e+04\n",
       "Industry                            2115.0018   8947.628      0.236      0.813   -1.55e+04    1.98e+04\n",
       "Service                            -1155.9880   9240.786     -0.125      0.901   -1.94e+04    1.71e+04\n",
       "==============================================================================\n",
       "Omnibus:                        9.555   Durbin-Watson:                   1.855\n",
       "Prob(Omnibus):                  0.008   Jarque-Bera (JB):               15.716\n",
       "Skew:                           0.209   Prob(JB):                     0.000387\n",
       "Kurtosis:                       4.220   Cond. No.                     6.21e+09\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 6.21e+09. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = sm.OLS(y,xc).fit()\n",
    "ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fstat less than 0.05 model is significant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>GDP ($ per capita)</td> <th>  R-squared:         </th> <td>   0.801</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                    <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.785</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>              <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   49.48</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 09 Mar 2021</td>  <th>  Prob (F-statistic):</th> <td>1.40e-63</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>10:28:23</td>      <th>  Log-Likelihood:    </th> <td> -2222.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>       <td>   227</td>       <th>  AIC:               </th> <td>   4482.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>           <td>   209</td>       <th>  BIC:               </th> <td>   4543.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>               <td>    17</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>       <td>nonrobust</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                   <td></td>                     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                              <td> 9620.3348</td> <td>  299.480</td> <td>   32.123</td> <td> 0.000</td> <td> 9029.946</td> <td> 1.02e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Population</th>                         <td>  155.5794</td> <td>  356.182</td> <td>    0.437</td> <td> 0.663</td> <td> -546.590</td> <td>  857.749</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area_sqm</th>                           <td>  -59.3790</td> <td>  357.475</td> <td>   -0.166</td> <td> 0.868</td> <td> -764.099</td> <td>  645.341</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Pop_Density_per sqm</th>                <td>   51.8321</td> <td>  346.271</td> <td>    0.150</td> <td> 0.881</td> <td> -630.799</td> <td>  734.463</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Coastline (coast/area ratio)</th>       <td>-1581.3918</td> <td>  402.751</td> <td>   -3.926</td> <td> 0.000</td> <td>-2375.366</td> <td> -787.417</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Net migration</th>                      <td> 2115.4650</td> <td>  328.636</td> <td>    6.437</td> <td> 0.000</td> <td> 1467.598</td> <td> 2763.331</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Infant mortality (per 1000 births)</th> <td>-1287.6527</td> <td>  923.107</td> <td>   -1.395</td> <td> 0.165</td> <td>-3107.447</td> <td>  532.142</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Literacy (%)</th>                       <td>   -9.7969</td> <td>  497.915</td> <td>   -0.020</td> <td> 0.984</td> <td> -991.376</td> <td>  971.782</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Phones (per 1000)</th>                  <td> 7198.9293</td> <td>  538.933</td> <td>   13.358</td> <td> 0.000</td> <td> 6136.488</td> <td> 8261.371</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Arable (%)</th>                         <td>-1011.6755</td> <td>  970.714</td> <td>   -1.042</td> <td> 0.299</td> <td>-2925.321</td> <td>  901.970</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Crops (%)</th>                          <td> -321.7995</td> <td>  586.161</td> <td>   -0.549</td> <td> 0.584</td> <td>-1477.345</td> <td>  833.746</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Other (%)</th>                          <td> -553.4537</td> <td> 1126.368</td> <td>   -0.491</td> <td> 0.624</td> <td>-2773.953</td> <td> 1667.046</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Climate</th>                            <td> -126.8755</td> <td>  379.696</td> <td>   -0.334</td> <td> 0.739</td> <td> -875.400</td> <td>  621.649</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Birthrate</th>                          <td> -342.2609</td> <td>  741.738</td> <td>   -0.461</td> <td> 0.645</td> <td>-1804.507</td> <td> 1119.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Deathrate</th>                          <td>  737.4182</td> <td>  474.695</td> <td>    1.553</td> <td> 0.122</td> <td> -198.385</td> <td> 1673.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Agriculture</th>                        <td> -651.6274</td> <td> 1340.186</td> <td>   -0.486</td> <td> 0.627</td> <td>-3293.643</td> <td> 1990.389</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industry</th>                           <td>  287.9492</td> <td> 1218.184</td> <td>    0.236</td> <td> 0.813</td> <td>-2113.554</td> <td> 2689.453</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Service</th>                            <td> -189.3032</td> <td> 1513.260</td> <td>   -0.125</td> <td> 0.901</td> <td>-3172.512</td> <td> 2793.906</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.555</td> <th>  Durbin-Watson:     </th> <td>   1.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.008</td> <th>  Jarque-Bera (JB):  </th> <td>  15.716</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.209</td> <th>  Prob(JB):          </th> <td>0.000387</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.220</td> <th>  Cond. No.          </th> <td>    17.5</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:     GDP ($ per capita)   R-squared:                       0.801\n",
       "Model:                            OLS   Adj. R-squared:                  0.785\n",
       "Method:                 Least Squares   F-statistic:                     49.48\n",
       "Date:                Tue, 09 Mar 2021   Prob (F-statistic):           1.40e-63\n",
       "Time:                        10:28:23   Log-Likelihood:                -2222.8\n",
       "No. Observations:                 227   AIC:                             4482.\n",
       "Df Residuals:                     209   BIC:                             4543.\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================================\n",
       "                                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------------\n",
       "const                               9620.3348    299.480     32.123      0.000    9029.946    1.02e+04\n",
       "Population                           155.5794    356.182      0.437      0.663    -546.590     857.749\n",
       "Area_sqm                             -59.3790    357.475     -0.166      0.868    -764.099     645.341\n",
       "Pop_Density_per sqm                   51.8321    346.271      0.150      0.881    -630.799     734.463\n",
       "Coastline (coast/area ratio)       -1581.3918    402.751     -3.926      0.000   -2375.366    -787.417\n",
       "Net migration                       2115.4650    328.636      6.437      0.000    1467.598    2763.331\n",
       "Infant mortality (per 1000 births) -1287.6527    923.107     -1.395      0.165   -3107.447     532.142\n",
       "Literacy (%)                          -9.7969    497.915     -0.020      0.984    -991.376     971.782\n",
       "Phones (per 1000)                   7198.9293    538.933     13.358      0.000    6136.488    8261.371\n",
       "Arable (%)                         -1011.6755    970.714     -1.042      0.299   -2925.321     901.970\n",
       "Crops (%)                           -321.7995    586.161     -0.549      0.584   -1477.345     833.746\n",
       "Other (%)                           -553.4537   1126.368     -0.491      0.624   -2773.953    1667.046\n",
       "Climate                             -126.8755    379.696     -0.334      0.739    -875.400     621.649\n",
       "Birthrate                           -342.2609    741.738     -0.461      0.645   -1804.507    1119.985\n",
       "Deathrate                            737.4182    474.695      1.553      0.122    -198.385    1673.221\n",
       "Agriculture                         -651.6274   1340.186     -0.486      0.627   -3293.643    1990.389\n",
       "Industry                             287.9492   1218.184      0.236      0.813   -2113.554    2689.453\n",
       "Service                             -189.3032   1513.260     -0.125      0.901   -3172.512    2793.906\n",
       "==============================================================================\n",
       "Omnibus:                        9.555   Durbin-Watson:                   1.855\n",
       "Prob(Omnibus):                  0.008   Jarque-Bera (JB):               15.716\n",
       "Skew:                           0.209   Prob(JB):                     0.000387\n",
       "Kurtosis:                       4.220   Cond. No.                         17.5\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc= StandardScaler()\n",
    "\n",
    "X_scaled = sc.fit_transform(X)\n",
    "X_scaled = pd.DataFrame(X_scaled, columns = X.columns, index = X.index)\n",
    "xc_scaled = sm.add_constant(X_scaled)\n",
    "\n",
    "ols_scaled = sm.OLS(y,xc_scaled).fit()\n",
    "ols_scaled.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>Population</th>\n",
       "      <th>Area_sqm</th>\n",
       "      <th>Pop_Density_per sqm</th>\n",
       "      <th>Coastline (coast/area ratio)</th>\n",
       "      <th>Net migration</th>\n",
       "      <th>Infant mortality (per 1000 births)</th>\n",
       "      <th>Literacy (%)</th>\n",
       "      <th>Phones (per 1000)</th>\n",
       "      <th>Arable (%)</th>\n",
       "      <th>Crops (%)</th>\n",
       "      <th>Other (%)</th>\n",
       "      <th>Climate</th>\n",
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       "      <th>Agriculture</th>\n",
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       "    <tr>\n",
       "      <th>Country</th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>-0.115094</td>\n",
       "      <td>-0.220266</td>\n",
       "      <td>-0.347864</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>2.143829</td>\n",
       "      <td>3.079871</td>\n",
       "      <td>-2.537552</td>\n",
       "      <td>-1.041107</td>\n",
       "      <td>-0.132135</td>\n",
       "      <td>-0.502354</td>\n",
       "      <td>0.375437</td>\n",
       "      <td>-1.694570</td>\n",
       "      <td>2.210162</td>\n",
       "      <td>3.055247</td>\n",
       "      <td>1.612835</td>\n",
       "      <td>-0.263552</td>\n",
       "      <td>-1.201003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Albania</td>\n",
       "      <td>-0.414949</td>\n",
       "      <td>-0.418770</td>\n",
       "      <td>-0.306272</td>\n",
       "      <td>-0.458127</td>\n",
       "      <td>-1.993115</td>\n",
       "      <td>-0.393970</td>\n",
       "      <td>0.181254</td>\n",
       "      <td>-0.736564</td>\n",
       "      <td>0.539398</td>\n",
       "      <td>-0.218337</td>\n",
       "      <td>-0.449624</td>\n",
       "      <td>1.260999</td>\n",
       "      <td>-0.631504</td>\n",
       "      <td>-0.738826</td>\n",
       "      <td>0.583345</td>\n",
       "      <td>-0.645495</td>\n",
       "      <td>0.014199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Algeria</td>\n",
       "      <td>-0.094652</td>\n",
       "      <td>2.659029</td>\n",
       "      <td>-0.366433</td>\n",
       "      <td>-0.469797</td>\n",
       "      <td>-0.107041</td>\n",
       "      <td>-0.116716</td>\n",
       "      <td>-0.650571</td>\n",
       "      <td>-0.705662</td>\n",
       "      <td>-0.799921</td>\n",
       "      <td>-0.500325</td>\n",
       "      <td>0.932166</td>\n",
       "      <td>-1.694570</td>\n",
       "      <td>-0.448316</td>\n",
       "      <td>-0.842529</td>\n",
       "      <td>-0.327892</td>\n",
       "      <td>2.850162</td>\n",
       "      <td>-1.701740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>American Samoa</td>\n",
       "      <td>-0.453407</td>\n",
       "      <td>-0.427929</td>\n",
       "      <td>-0.216248</td>\n",
       "      <td>2.263057</td>\n",
       "      <td>-1.993115</td>\n",
       "      <td>-0.752237</td>\n",
       "      <td>0.710596</td>\n",
       "      <td>0.106750</td>\n",
       "      <td>-0.291774</td>\n",
       "      <td>2.527233</td>\n",
       "      <td>-0.417649</td>\n",
       "      <td>-0.216785</td>\n",
       "      <td>0.031762</td>\n",
       "      <td>-1.070336</td>\n",
       "      <td>-0.199902</td>\n",
       "      <td>-0.476559</td>\n",
       "      <td>0.568673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Andorra</td>\n",
       "      <td>-0.453260</td>\n",
       "      <td>-0.427843</td>\n",
       "      <td>-0.291340</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>2.143829</td>\n",
       "      <td>-0.904902</td>\n",
       "      <td>0.861837</td>\n",
       "      <td>1.171305</td>\n",
       "      <td>-0.874869</td>\n",
       "      <td>-0.517231</td>\n",
       "      <td>1.010534</td>\n",
       "      <td>1.260999</td>\n",
       "      <td>-1.209041</td>\n",
       "      <td>-0.563721</td>\n",
       "      <td>-0.670128</td>\n",
       "      <td>-0.394294</td>\n",
       "      <td>0.913082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Population  Area_sqm  Pop_Density_per sqm  \\\n",
       "Country                                                     \n",
       "Afghanistan      -0.115094 -0.220266            -0.347864   \n",
       "Albania          -0.414949 -0.418770            -0.306272   \n",
       "Algeria          -0.094652  2.659029            -0.366433   \n",
       "American Samoa   -0.453407 -0.427929            -0.216248   \n",
       "Andorra          -0.453260 -0.427843            -0.291340   \n",
       "\n",
       "                Coastline (coast/area ratio)  Net migration  \\\n",
       "Country                                                       \n",
       "Afghanistan                        -0.470180       2.143829   \n",
       "Albania                            -0.458127      -1.993115   \n",
       "Algeria                            -0.469797      -0.107041   \n",
       "American Samoa                      2.263057      -1.993115   \n",
       "Andorra                            -0.470180       2.143829   \n",
       "\n",
       "                Infant mortality (per 1000 births)  Literacy (%)  \\\n",
       "Country                                                            \n",
       "Afghanistan                               3.079871     -2.537552   \n",
       "Albania                                  -0.393970      0.181254   \n",
       "Algeria                                  -0.116716     -0.650571   \n",
       "American Samoa                           -0.752237      0.710596   \n",
       "Andorra                                  -0.904902      0.861837   \n",
       "\n",
       "                Phones (per 1000)  Arable (%)  Crops (%)  Other (%)   Climate  \\\n",
       "Country                                                                         \n",
       "Afghanistan             -1.041107   -0.132135  -0.502354   0.375437 -1.694570   \n",
       "Albania                 -0.736564    0.539398  -0.218337  -0.449624  1.260999   \n",
       "Algeria                 -0.705662   -0.799921  -0.500325   0.932166 -1.694570   \n",
       "American Samoa           0.106750   -0.291774   2.527233  -0.417649 -0.216785   \n",
       "Andorra                  1.171305   -0.874869  -0.517231   1.010534  1.260999   \n",
       "\n",
       "                Birthrate  Deathrate  Agriculture  Industry   Service  \n",
       "Country                                                                \n",
       "Afghanistan      2.210162   3.055247     1.612835 -0.263552 -1.201003  \n",
       "Albania         -0.631504  -0.738826     0.583345 -0.645495  0.014199  \n",
       "Algeria         -0.448316  -0.842529    -0.327892  2.850162 -1.701740  \n",
       "American Samoa   0.031762  -1.070336    -0.199902 -0.476559  0.568673  \n",
       "Andorra         -1.209041  -0.563721    -0.670128 -0.394294  0.913082  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### partial scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "## partial scaling\n",
    "\n",
    "X_partial_sc = X - X.mean()\n",
    "xp_sc = sm.add_constant(X_partial_sc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>GDP ($ per capita)</td> <th>  R-squared:         </th> <td>   0.801</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                    <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.785</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>              <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   49.48</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 09 Mar 2021</td>  <th>  Prob (F-statistic):</th> <td>1.40e-63</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>10:28:23</td>      <th>  Log-Likelihood:    </th> <td> -2222.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>       <td>   227</td>       <th>  AIC:               </th> <td>   4482.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>           <td>   209</td>       <th>  BIC:               </th> <td>   4543.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>               <td>    17</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>       <td>nonrobust</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                   <td></td>                     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                              <td> 9620.3348</td> <td>  299.480</td> <td>   32.123</td> <td> 0.000</td> <td> 9029.946</td> <td> 1.02e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Population</th>                         <td> 1.698e-06</td> <td> 3.89e-06</td> <td>    0.437</td> <td> 0.663</td> <td>-5.97e-06</td> <td> 9.36e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area_sqm</th>                           <td>-1.905e-05</td> <td>    0.000</td> <td>   -0.166</td> <td> 0.868</td> <td>   -0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Pop_Density_per sqm</th>                <td>    0.0281</td> <td>    0.188</td> <td>    0.150</td> <td> 0.881</td> <td>   -0.343</td> <td>    0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Coastline (coast/area ratio)</th>       <td>  -15.1276</td> <td>    3.853</td> <td>   -3.926</td> <td> 0.000</td> <td>  -22.723</td> <td>   -7.532</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Net migration</th>                      <td>  295.1782</td> <td>   45.856</td> <td>    6.437</td> <td> 0.000</td> <td>  204.779</td> <td>  385.577</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Infant mortality (per 1000 births)</th> <td>  -37.6590</td> <td>   26.997</td> <td>   -1.395</td> <td> 0.165</td> <td>  -90.881</td> <td>   15.563</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Literacy (%)</th>                       <td>   -0.4939</td> <td>   25.102</td> <td>   -0.020</td> <td> 0.984</td> <td>  -49.979</td> <td>   48.991</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Phones (per 1000)</th>                  <td>   32.2409</td> <td>    2.414</td> <td>   13.358</td> <td> 0.000</td> <td>   27.483</td> <td>   36.999</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Arable (%)</th>                         <td>  -75.8229</td> <td>   72.753</td> <td>   -1.042</td> <td> 0.299</td> <td> -219.247</td> <td>   67.601</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Crops (%)</th>                          <td>  -21.7611</td> <td>   39.638</td> <td>   -0.549</td> <td> 0.584</td> <td>  -99.903</td> <td>   56.381</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Other (%)</th>                          <td>  -34.6986</td> <td>   70.617</td> <td>   -0.491</td> <td> 0.624</td> <td> -173.912</td> <td>  104.515</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Climate</th>                            <td> -187.4946</td> <td>  561.108</td> <td>   -0.334</td> <td> 0.739</td> <td>-1293.652</td> <td>  918.663</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Birthrate</th>                          <td>  -30.8857</td> <td>   66.935</td> <td>   -0.461</td> <td> 0.645</td> <td> -162.839</td> <td>  101.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Deathrate</th>                          <td>  125.3649</td> <td>   80.701</td> <td>    1.553</td> <td> 0.122</td> <td>  -33.726</td> <td>  284.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Agriculture</th>                        <td>-4532.7267</td> <td> 9322.350</td> <td>   -0.486</td> <td> 0.627</td> <td>-2.29e+04</td> <td> 1.38e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industry</th>                           <td> 2115.0018</td> <td> 8947.628</td> <td>    0.236</td> <td> 0.813</td> <td>-1.55e+04</td> <td> 1.98e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Service</th>                            <td>-1155.9880</td> <td> 9240.786</td> <td>   -0.125</td> <td> 0.901</td> <td>-1.94e+04</td> <td> 1.71e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.555</td> <th>  Durbin-Watson:     </th> <td>   1.855</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.008</td> <th>  Jarque-Bera (JB):  </th> <td>  15.716</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.209</td> <th>  Prob(JB):          </th> <td>0.000387</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.220</td> <th>  Cond. No.          </th> <td>4.75e+09</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 4.75e+09. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:     GDP ($ per capita)   R-squared:                       0.801\n",
       "Model:                            OLS   Adj. R-squared:                  0.785\n",
       "Method:                 Least Squares   F-statistic:                     49.48\n",
       "Date:                Tue, 09 Mar 2021   Prob (F-statistic):           1.40e-63\n",
       "Time:                        10:28:23   Log-Likelihood:                -2222.8\n",
       "No. Observations:                 227   AIC:                             4482.\n",
       "Df Residuals:                     209   BIC:                             4543.\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================================\n",
       "                                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------------\n",
       "const                               9620.3348    299.480     32.123      0.000    9029.946    1.02e+04\n",
       "Population                          1.698e-06   3.89e-06      0.437      0.663   -5.97e-06    9.36e-06\n",
       "Area_sqm                           -1.905e-05      0.000     -0.166      0.868      -0.000       0.000\n",
       "Pop_Density_per sqm                    0.0281      0.188      0.150      0.881      -0.343       0.399\n",
       "Coastline (coast/area ratio)         -15.1276      3.853     -3.926      0.000     -22.723      -7.532\n",
       "Net migration                        295.1782     45.856      6.437      0.000     204.779     385.577\n",
       "Infant mortality (per 1000 births)   -37.6590     26.997     -1.395      0.165     -90.881      15.563\n",
       "Literacy (%)                          -0.4939     25.102     -0.020      0.984     -49.979      48.991\n",
       "Phones (per 1000)                     32.2409      2.414     13.358      0.000      27.483      36.999\n",
       "Arable (%)                           -75.8229     72.753     -1.042      0.299    -219.247      67.601\n",
       "Crops (%)                            -21.7611     39.638     -0.549      0.584     -99.903      56.381\n",
       "Other (%)                            -34.6986     70.617     -0.491      0.624    -173.912     104.515\n",
       "Climate                             -187.4946    561.108     -0.334      0.739   -1293.652     918.663\n",
       "Birthrate                            -30.8857     66.935     -0.461      0.645    -162.839     101.068\n",
       "Deathrate                            125.3649     80.701      1.553      0.122     -33.726     284.456\n",
       "Agriculture                        -4532.7267   9322.350     -0.486      0.627   -2.29e+04    1.38e+04\n",
       "Industry                            2115.0018   8947.628      0.236      0.813   -1.55e+04    1.98e+04\n",
       "Service                            -1155.9880   9240.786     -0.125      0.901   -1.94e+04    1.71e+04\n",
       "==============================================================================\n",
       "Omnibus:                        9.555   Durbin-Watson:                   1.855\n",
       "Prob(Omnibus):                  0.008   Jarque-Bera (JB):               15.716\n",
       "Skew:                           0.209   Prob(JB):                     0.000387\n",
       "Kurtosis:                       4.220   Cond. No.                     4.75e+09\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 4.75e+09. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols_partial_sc = sm.OLS(y,xp_sc).fit()\n",
    "ols_partial_sc.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ASSUMPTIONS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. MULTICOLLINEARITY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.outliers_influence import variance_inflation_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF</th>\n",
       "      <th>Feature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>25.532397</td>\n",
       "      <td>Service</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>20.026042</td>\n",
       "      <td>Agriculture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>16.545912</td>\n",
       "      <td>Industry</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>14.145739</td>\n",
       "      <td>Other (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>10.506242</td>\n",
       "      <td>Arable (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>9.500994</td>\n",
       "      <td>Infant mortality (per 1000 births)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>6.134302</td>\n",
       "      <td>Birthrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>3.830876</td>\n",
       "      <td>Crops (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>3.238427</td>\n",
       "      <td>Phones (per 1000)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>2.764233</td>\n",
       "      <td>Literacy (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>2.512426</td>\n",
       "      <td>Deathrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.808579</td>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>1.607444</td>\n",
       "      <td>Climate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.424810</td>\n",
       "      <td>Area_sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.414517</td>\n",
       "      <td>Population</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.336890</td>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.204191</td>\n",
       "      <td>Net migration</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          VIF                             Feature\n",
       "16  25.532397                             Service\n",
       "14  20.026042                         Agriculture\n",
       "15  16.545912                            Industry\n",
       "10  14.145739                           Other (%)\n",
       "8   10.506242                          Arable (%)\n",
       "5    9.500994  Infant mortality (per 1000 births)\n",
       "12   6.134302                           Birthrate\n",
       "9    3.830876                           Crops (%)\n",
       "7    3.238427                   Phones (per 1000)\n",
       "6    2.764233                        Literacy (%)\n",
       "13   2.512426                           Deathrate\n",
       "3    1.808579        Coastline (coast/area ratio)\n",
       "11   1.607444                             Climate\n",
       "1    1.424810                            Area_sqm\n",
       "0    1.414517                          Population\n",
       "2    1.336890                 Pop_Density_per sqm\n",
       "4    1.204191                       Net migration"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif = pd.DataFrame()\n",
    "vif['VIF'] = [variance_inflation_factor(X_partial_sc.values,i) for i in range(X_partial_sc.shape[1]) ]\n",
    "vif['Feature'] = X_partial_sc.columns\n",
    "vif.sort_values('VIF', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_partial_sc2 = X_partial_sc.drop('Service', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF</th>\n",
       "      <th>Feature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>14.141041</td>\n",
       "      <td>Other (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>10.504615</td>\n",
       "      <td>Arable (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>9.466748</td>\n",
       "      <td>Infant mortality (per 1000 births)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>6.134036</td>\n",
       "      <td>Birthrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>3.830859</td>\n",
       "      <td>Crops (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>3.252902</td>\n",
       "      <td>Agriculture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>3.212241</td>\n",
       "      <td>Phones (per 1000)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>2.740219</td>\n",
       "      <td>Literacy (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>2.508962</td>\n",
       "      <td>Deathrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.780749</td>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>1.714570</td>\n",
       "      <td>Industry</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>1.590360</td>\n",
       "      <td>Climate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.413954</td>\n",
       "      <td>Population</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.408147</td>\n",
       "      <td>Area_sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.331512</td>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.199117</td>\n",
       "      <td>Net migration</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          VIF                             Feature\n",
       "10  14.141041                           Other (%)\n",
       "8   10.504615                          Arable (%)\n",
       "5    9.466748  Infant mortality (per 1000 births)\n",
       "12   6.134036                           Birthrate\n",
       "9    3.830859                           Crops (%)\n",
       "14   3.252902                         Agriculture\n",
       "7    3.212241                   Phones (per 1000)\n",
       "6    2.740219                        Literacy (%)\n",
       "13   2.508962                           Deathrate\n",
       "3    1.780749        Coastline (coast/area ratio)\n",
       "15   1.714570                            Industry\n",
       "11   1.590360                             Climate\n",
       "0    1.413954                          Population\n",
       "1    1.408147                            Area_sqm\n",
       "2    1.331512                 Pop_Density_per sqm\n",
       "4    1.199117                       Net migration"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif2 = pd.DataFrame()\n",
    "vif2['VIF'] = [variance_inflation_factor(X_partial_sc2.values,i) for i in range(X_partial_sc2.shape[1]) ]\n",
    "vif2['Feature'] = X_partial_sc2.columns\n",
    "vif2.sort_values('VIF', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_partial_sc3 = X_partial_sc2.drop('Other (%)', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF</th>\n",
       "      <th>Feature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>9.437339</td>\n",
       "      <td>Infant mortality (per 1000 births)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>6.065702</td>\n",
       "      <td>Birthrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>3.252899</td>\n",
       "      <td>Agriculture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>3.201979</td>\n",
       "      <td>Phones (per 1000)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>2.718619</td>\n",
       "      <td>Literacy (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>2.508164</td>\n",
       "      <td>Deathrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.744867</td>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>1.713809</td>\n",
       "      <td>Industry</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>1.588994</td>\n",
       "      <td>Climate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>1.413931</td>\n",
       "      <td>Arable (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.398809</td>\n",
       "      <td>Area_sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.394332</td>\n",
       "      <td>Population</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>1.375567</td>\n",
       "      <td>Crops (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.324509</td>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.177433</td>\n",
       "      <td>Net migration</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         VIF                             Feature\n",
       "5   9.437339  Infant mortality (per 1000 births)\n",
       "11  6.065702                           Birthrate\n",
       "13  3.252899                         Agriculture\n",
       "7   3.201979                   Phones (per 1000)\n",
       "6   2.718619                        Literacy (%)\n",
       "12  2.508164                           Deathrate\n",
       "3   1.744867        Coastline (coast/area ratio)\n",
       "14  1.713809                            Industry\n",
       "10  1.588994                             Climate\n",
       "8   1.413931                          Arable (%)\n",
       "1   1.398809                            Area_sqm\n",
       "0   1.394332                          Population\n",
       "9   1.375567                           Crops (%)\n",
       "2   1.324509                 Pop_Density_per sqm\n",
       "4   1.177433                       Net migration"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif2 = pd.DataFrame()\n",
    "vif2['VIF'] = [variance_inflation_factor(X_partial_sc3.values,i) for i in range(X_partial_sc3.shape[1]) ]\n",
    "vif2['Feature'] = X_partial_sc3.columns\n",
    "vif2.sort_values('VIF', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_partial_sc4 = X_partial_sc3.drop('Infant mortality (per 1000 births)', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF</th>\n",
       "      <th>Feature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>4.484879</td>\n",
       "      <td>Birthrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>3.132257</td>\n",
       "      <td>Phones (per 1000)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>2.771160</td>\n",
       "      <td>Agriculture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>2.582218</td>\n",
       "      <td>Literacy (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.738336</td>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>1.665256</td>\n",
       "      <td>Industry</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>1.580450</td>\n",
       "      <td>Climate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>1.463293</td>\n",
       "      <td>Deathrate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>1.413394</td>\n",
       "      <td>Arable (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.397710</td>\n",
       "      <td>Area_sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.382396</td>\n",
       "      <td>Population</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>1.346897</td>\n",
       "      <td>Crops (%)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1.322850</td>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.176766</td>\n",
       "      <td>Net migration</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         VIF                       Feature\n",
       "10  4.484879                     Birthrate\n",
       "6   3.132257             Phones (per 1000)\n",
       "12  2.771160                   Agriculture\n",
       "5   2.582218                  Literacy (%)\n",
       "3   1.738336  Coastline (coast/area ratio)\n",
       "13  1.665256                      Industry\n",
       "9   1.580450                       Climate\n",
       "11  1.463293                     Deathrate\n",
       "7   1.413394                    Arable (%)\n",
       "1   1.397710                      Area_sqm\n",
       "0   1.382396                    Population\n",
       "8   1.346897                     Crops (%)\n",
       "2   1.322850           Pop_Density_per sqm\n",
       "4   1.176766                 Net migration"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif2 = pd.DataFrame()\n",
    "vif2['VIF'] = [variance_inflation_factor(X_partial_sc4.values,i) for i in range(X_partial_sc4.shape[1]) ]\n",
    "vif2['Feature'] = X_partial_sc4.columns\n",
    "vif2.sort_values('VIF', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>GDP ($ per capita)</td> <th>  R-squared:         </th> <td>   0.799</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                    <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.786</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>              <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   60.12</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 09 Mar 2021</td>  <th>  Prob (F-statistic):</th> <td>9.60e-66</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>10:28:24</td>      <th>  Log-Likelihood:    </th> <td> -2224.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>       <td>   227</td>       <th>  AIC:               </th> <td>   4478.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>           <td>   212</td>       <th>  BIC:               </th> <td>   4529.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>               <td>    14</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>       <td>nonrobust</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                <td></td>                  <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                        <td> 9620.3348</td> <td>  298.964</td> <td>   32.179</td> <td> 0.000</td> <td> 9031.013</td> <td> 1.02e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Population</th>                   <td> 1.405e-06</td> <td> 3.84e-06</td> <td>    0.366</td> <td> 0.714</td> <td>-6.16e-06</td> <td> 8.97e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area_sqm</th>                     <td>-2.966e-05</td> <td>    0.000</td> <td>   -0.262</td> <td> 0.794</td> <td>   -0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Pop_Density_per sqm</th>          <td>    0.0106</td> <td>    0.187</td> <td>    0.057</td> <td> 0.955</td> <td>   -0.357</td> <td>    0.379</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Coastline (coast/area ratio)</th> <td>  -15.2505</td> <td>    3.771</td> <td>   -4.045</td> <td> 0.000</td> <td>  -22.683</td> <td>   -7.818</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Net migration</th>                <td>  294.0734</td> <td>   45.252</td> <td>    6.499</td> <td> 0.000</td> <td>  204.871</td> <td>  383.276</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Literacy (%)</th>                 <td>    8.7987</td> <td>   24.219</td> <td>    0.363</td> <td> 0.717</td> <td>  -38.943</td> <td>   56.540</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Phones (per 1000)</th>            <td>   32.6500</td> <td>    2.370</td> <td>   13.778</td> <td> 0.000</td> <td>   27.979</td> <td>   37.321</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Arable (%)</th>                   <td>  -41.8676</td> <td>   26.638</td> <td>   -1.572</td> <td> 0.118</td> <td>  -94.378</td> <td>   10.643</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Crops (%)</th>                    <td>   -1.3818</td> <td>   23.463</td> <td>   -0.059</td> <td> 0.953</td> <td>  -47.632</td> <td>   44.869</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Climate</th>                      <td> -128.6667</td> <td>  555.418</td> <td>   -0.232</td> <td> 0.817</td> <td>-1223.515</td> <td>  966.182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Birthrate</th>                    <td>  -75.7142</td> <td>   57.134</td> <td>   -1.325</td> <td> 0.187</td> <td> -188.337</td> <td>   36.909</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Deathrate</th>                    <td>   50.4181</td> <td>   61.482</td> <td>    0.820</td> <td> 0.413</td> <td>  -70.776</td> <td>  171.612</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Agriculture</th>                  <td>-5516.0947</td> <td> 3461.857</td> <td>   -1.593</td> <td> 0.113</td> <td>-1.23e+04</td> <td> 1307.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industry</th>                     <td> 2457.0810</td> <td> 2833.698</td> <td>    0.867</td> <td> 0.387</td> <td>-3128.753</td> <td> 8042.915</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.500</td> <th>  Durbin-Watson:     </th> <td>   1.819</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.009</td> <th>  Jarque-Bera (JB):  </th> <td>  15.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.225</td> <th>  Prob(JB):          </th> <td>0.000542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.178</td> <th>  Cond. No.          </th> <td>1.20e+09</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.2e+09. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:     GDP ($ per capita)   R-squared:                       0.799\n",
       "Model:                            OLS   Adj. R-squared:                  0.786\n",
       "Method:                 Least Squares   F-statistic:                     60.12\n",
       "Date:                Tue, 09 Mar 2021   Prob (F-statistic):           9.60e-66\n",
       "Time:                        10:28:24   Log-Likelihood:                -2224.0\n",
       "No. Observations:                 227   AIC:                             4478.\n",
       "Df Residuals:                     212   BIC:                             4529.\n",
       "Df Model:                          14                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "================================================================================================\n",
       "                                   coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------\n",
       "const                         9620.3348    298.964     32.179      0.000    9031.013    1.02e+04\n",
       "Population                    1.405e-06   3.84e-06      0.366      0.714   -6.16e-06    8.97e-06\n",
       "Area_sqm                     -2.966e-05      0.000     -0.262      0.794      -0.000       0.000\n",
       "Pop_Density_per sqm              0.0106      0.187      0.057      0.955      -0.357       0.379\n",
       "Coastline (coast/area ratio)   -15.2505      3.771     -4.045      0.000     -22.683      -7.818\n",
       "Net migration                  294.0734     45.252      6.499      0.000     204.871     383.276\n",
       "Literacy (%)                     8.7987     24.219      0.363      0.717     -38.943      56.540\n",
       "Phones (per 1000)               32.6500      2.370     13.778      0.000      27.979      37.321\n",
       "Arable (%)                     -41.8676     26.638     -1.572      0.118     -94.378      10.643\n",
       "Crops (%)                       -1.3818     23.463     -0.059      0.953     -47.632      44.869\n",
       "Climate                       -128.6667    555.418     -0.232      0.817   -1223.515     966.182\n",
       "Birthrate                      -75.7142     57.134     -1.325      0.187    -188.337      36.909\n",
       "Deathrate                       50.4181     61.482      0.820      0.413     -70.776     171.612\n",
       "Agriculture                  -5516.0947   3461.857     -1.593      0.113   -1.23e+04    1307.978\n",
       "Industry                      2457.0810   2833.698      0.867      0.387   -3128.753    8042.915\n",
       "==============================================================================\n",
       "Omnibus:                        9.500   Durbin-Watson:                   1.819\n",
       "Prob(Omnibus):                  0.009   Jarque-Bera (JB):               15.039\n",
       "Skew:                           0.225   Prob(JB):                     0.000542\n",
       "Kurtosis:                       4.178   Cond. No.                     1.20e+09\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.2e+09. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model after removing \n",
    "xp_c = sm.add_constant(X_partial_sc4)\n",
    "\n",
    "ols_no_m = sm.OLS(y,xp_c).fit()\n",
    "ols_no_m.summary()\n",
    "\n",
    "\n",
    "# for partially scaled Conditional Number can be > 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. NORMALITY\n",
    "\n",
    "##### if data is not normal transform target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2268358813120028"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = ols_no_m.resid\n",
    "res.skew()\n",
    "#data is normal as skew is between -0.5 to 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(res)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(res, plot = plt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. LINEARITY\n",
    "\n",
    "##### errors must be random\n",
    "##### symmetric with 0 residue line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1f7bdcf2948>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(y, ols_no_m.predict())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rr3+As+dOG+T8XrluY9U5v8NWgDAMBPGZyoUfffa74KhpFhnwsx5OGEMf02dCc6Y1c+WpMxnQuEmlmHNIXIOwmRKGQlBMJtXkIwrjM+VHn/3OwTFhkUbiIQJ8U229HNFBf3jdN+KEkfV8Y9Esvn7/KyUxpYxritLT1x86U8JQyGV+KMd9UI2msDAmDZa6z34LTYknTVcf8+bN07a2toL2cT9EpR4Q8z2u+1gzJ4yks+dgYASIeyA7d83zgwa8YiI5+vtjbNm1l5XrNgZuACvlAJ5toAbKMoh37O3lrFueLen/z6geRGSja6G6JKZZuHDbk9s7e7j+sS1cu/hoPjpuBNHaCHURYXd3X8kHbS879o1PbuGfPnVkoAbPxEzonc79JTel1NZGOGry6MCZEko9C882++vY25u1bEqpBFZQTGFGuDAHt4v0h2jT9i4uvHMDCpy35nmO/7+/8aWaq9fDe/bcaUlBAcFyhPrlSAtSZnIivHXnnp6SO6QznWe2QbyUFYXDsvKiESxMWLiIiLCwdSKrl87l3hUnsHrpXBa2TqRjb6+vg7b74Z0zrZnVS+cyc+JIVp3ZypxpzcntgjL7C2P0SSG4c0oSWqYbv/4PmQZxESmpwKr2/5/hD2aGcojFFET5x1OP5LKfHTL93PKF42isizBnWjObtncB8Ye152C8tHgpZr+Jh9cr1+C6s2fzg8e3sGl7V2Bmf2GMPikEt1kwW9Z5qckUzVIjlFRgVfv/z/AH0ywcdnf30d0bSwoKiD+Ql//8Jdo7D3DpyTOS205taeSNXftKZo5KPLzf+ezRg3INrnrgFS49eUbes79yZQcHyWRUatzmoNueeYPrzp5dlll45gWVIiU3G3n9/yyz3MiGaRYOff0DGWdwI6I1jIrEL5V7tt+xr7dkESSRiKCqnsc/avKopJMz26Bc7pDISob7+nlsd3jrpu1d/ODxeKDDjIkjaazz9zy9winLsYZFNYbTGqXFhIVDtLaGmHrnVuzvG2BqSyO/+erfsHXXvqRZCCAWi9Gxtzc5aLU01g053LWuNuJ5/IZoTV4CqZwF1So5uPh97PTBuWNfL5PHNDC1ubEiA6eX2ailsa6kwjKMxfiM8mLCwmFcU5SOvQe47YK5XOryWdz498cwaUwDqqAKTdFDqv/C1om8392XEt562wVzuempP/DE5l0FD2K1EeGGJbNTcjtuWDKb2hIsQlRqKjm4+H3sINr03RqHH8Iy6OG0QU9aHQ6YsHCIRITaWqGhTrjzwvlEBGIKoxoidOw9mCJAbvnCcdREhDGNdZznSk5r7+zh0p9tZNWZrTyxeVfWQczr5u/pG+D6x7aw6sxWmhvr6Oo5yPWPbeFH58+BptznUM6CapUcXMpx7HJlBA9lEPRDWAa5GJ+ZyIKBObjdKHTs7eOLP32RT/7wP7n+sdc5cFCTggIOOb1H1NVw4GDMc9BqbqxL+Zw+iGUq911XG6FjXy8r123k3DXPs3LdRjr29eb9wJYzJLKSsfrVkieQq+x7JvwQlkELp3U729/98IAVXwwAJixc9ByMJU1AEE+Mc+dYJGjv7GHX3l62f7Dfc9Dq6jmY8tk9iMViyrsfHqC7tz+ZR5G4+WsjkvfaEl5RK5mjaUo/+ypkcCl1lE3QBrahMtQKtH4Iy3LeO7lIF6I7usqX62JkxsxQLgZiyoSR9Ukz0MRR9bz74QFP9fzgQIyGusggH8ctXziOH/1ma3K725fNoyYC73TupzFaw3sf9qao0+48ip6+gay28lhMeb+7l/29A7z1fjc3PbWVjn29KSp5ucwn+dr1/TAhBNGnMBSGqiH4FR0VlGJ86ULUvTRvgjBqkmHHCgm62LWnhzfe705xMN/498dQVxvhirs3JdtWXzCXg7EYV9y9iQkj67ny1JkcPm4EO7t6WP/yDk7/i8M4fOwIGusiHOiPJdfW/ukXP8Gqh18bdNOvOrOVax/ZnNHmHIspXT197Ow6wEqXYPIjhDdf8rW1V2PRulI5W4u5NtXs8H2ncz8Lrns6+XnOtGa+dtqslGRV81n4hxUSzIN+1RQzVHtnD1+573/4wTnHsOrMVsY1RRnbFGVkQy3ffujVFEf0db96nbPnTuO5N3dz1nFT2Nd7kFENjbz93j5+eM4xdPUcZPxI7zUbxjVFWXvRfBTlnc79KQ9/Ymb+7p4DKYImkbC36sxWVq7bWFaVvBBtYSiz5yAPhKXUlIrRECqhBZTr/5LubN+0vYu7nnuL+1aeiKoG7p4YLpiwcNEf806KGz8ySm1EGNsU5d4X32bZSdM9y3JMHz+CdRfN5/19fYxtitKxtzc5wE9taeTm849jYetEnti8K/n7U1samdIc93Msu+W5QQNQV08f7+45wEfHjfDs24wJTSxsnVhWlbyQaJxCo2yCGvniHihLFYkUJnNaOf8vXkL0K5+exeTRDYG8NsMFc3C7aKjzdhy+0dHNktt+x7I7XuT8E44A8CzLAUK0NsIR45uor6tJmowS23zp7pe4+vSjBjlm6+singNQwvS06uHX2Lprn2fftn/Qw5WnHkmLKwLLbwrRFgp1Rpdz2dF8He9+FhYMS9mUcv5fguRsNw4RGs1CRBYB/wbUAD9W1e+X+hhjG6ODHNYJvwDEHxABlEyF3WIcPnYEkYhkXPOhJiI8ePlJHOyPJWeSO/d4D0A9fQNJgZOoUeRVZLBjXy8PXn4SE0c1lPqSeFKItlDo7Llc+RuFzJQrVVgwSJQ7ryYoznbjEKEQFiJSA9wMfBpoBzaIyHpV3VzK43T2HOSmp/7AuovmE4kIb3Z0p5T2mNrSyIAqteJdluOt97tpqq9lwqj6jANqY7Rm0KCeadsBV62oRI2idRfNZ9feXrp6Dqb0bX/vALGm0lTBzUWhtvZCHvzEtZgwsp5LT55Bc2Md+/sGaIzmPxjnY1svxJTmVVgw3dkatrDdQgly0p5RHkIhLID5wDZVfRNARO4BFgMlFRZ9/QM8sXkXZ8+dxtgRURrq4klygONzmIMq1Ebg1gvmDipl/rPfvc2Rk0YCmQfU8U2DB81M2ybMYm6B8cfd+z0jqt56v5sR0RoODsQYUKWhrobxTf6YNfy0tSec/e99eGDQkrbNjbmPka/GUMhMuZKFBYNCOYoZGsEmFKGzIrIEWKSq/+B8Xgocr6pXZNpnKKGziVDGCSPrueazrQjwQfdBRkRriIjQEK3hMqecxwMbt3P23GnJaKgHNm7n8/M/ytFTxqTU8Mk0w03/zqsAIQxek3ntRfPpOTiQUo/qurNn8/Cmd1h64ke57OcvFeSADGLk0a69B/g7x9mfIN+Q0nzDUQsJWw2q073cBPFeMUpP2ENnve7IQVJORFYAKwAOP/zwgg/inj3d/fyfuOyUGTSPiBIRYSAW44KfvJgs5/HE5l0pUU0A3zyjlUhE+aC7l56+0iSqec3gu3r6uHbx0YyI1iTNUVeeOjMpKCC/KJ2gDoIH+73LqORjH89XYyhkphymqCU/MT/C8CYswqIdmOb6PBXYkb6Rqq4B1kBcsyj0IIlBYf0VC9jZdYCljnCY2tLIuovnJwehTE7Odzr3s/Qnr3LDktlc/1jc8bz2ovmMbKhNcWgXYi/3ekCbG6NMHtOQMtAdniG0NtsAG9Sy1JlKtdfV5g7ey9e2XqgAsIHSGO6ERVhsAGaKyHTgHeA84Hw/DhSJCAMxBoW9/vH9/clBKFtkUntnD1+/P54sd9szb/DehwdYdkeq7X3siLqiIkvSBzoR4f19vfz0i59Iahu3PfNGziKEQS1LXUyp9kI1BhMAhpEfoRAWqtovIlcAjxMPnb1DVX/v1/G8BtGbntrKrV84jst+/hKbtnfx2y3vcc+KExiIKX39MW7/7Zspa3Q3N9Zx6ckzBmWEX7K2jXtXnOA5+xUZmlmjvk6oEUlJALxhyWwmjW7I6oAMaoRLMaXazWRkGP4QCmEBoKqPAo/6fZxEYlb6INqxr5fRjXWsOrOV2VNG88H+g8m1LBKaxdZd+9i0vStZeba50VuDGIipp2ZSk2U8czsX0wsSptecSmg3D15+UtZBMqgRLtHammSp9gSFCLGwaAzmMDbCRGiERTlIOHxvfHKL52De1z9AtCbCgJKMRoLUOk3XPrI56bO48tSZLGydOChqqiYi/HbLeykz57uee4vvnTU7a78yCYcR0RpPoXSwP5b1fIM6C88kxFoa61KWsHXXzwrboBvU4ALDyIQJCxduh29zY5SffvET1ESE2poIv9m8k1EN41j18Gv88JxjPAfnoyaP4sHLT6I2Ivzo/Dk01dcwYdSRg0qYr33uLT5z7NRBy6/mWwIjXTgUk1WcmIUnBtyde3oqPuB6CbHmhlp27ImvI7K7u48HNm7nK5+excwJI9nasS/Qg66XMAtqcIFhZMKEhYuEr2LOtGYWz5nChXduSA5AibW1s5V8aIzWHnrQm+Kx/F6r7K06s5VLf7aR+1aeyDWfyV1FM92Hkn782555Y5BDuBBzktcsd/XSuYxvihKJRCoyg09fc/r1dz8clFty45Nb+M5njw70oJtJgyg2yMEwyo0VEnSRcPheevKMQYUCL/3ZRs6eG4/eTURD5SqOlynaKOHLUNW8Csilr4yWEA6Jto59vUwa3cCDl5/Es1edwoOXn8Sk0fXs3NOTUiAvU+E8r1nuynUbebl9T3Kpz/7+2JCWAC0Fu7v7PM1+Z8+dRv/A0HMySr2CX6a+ewmzAaXkq90VQjnOvVJU87lVEtMsXCRs5d29/Z4DUEIY5Cr5kJiBw2BHecL5XcjAkG7DdwsHd/6Ge/2L9JlsNnNNLqF2ydo27lt5YsVm8Jn6N64pSm2Nd04GxDW7TNpPuXwGmfquqhULLqhmf0k1n1ulMc3CRcJWftiYBs9Z3/iR9Smz+cljGpja3JiiGbjLWV9x96YUDSBhPnlg4/bkwJDPLMirZPMR45qYOKphkGaSaSa7a1+vZ/u7Hx5IJsGln+/YpmhyjfCDRczgiyXTmtMTR9UzcWT9oBLoNyyZzRV3b8qq/ZSr5Ha29bIrVYa7nOXGy001n1ulMc0ijUhEqI2IZzTUwYEBblgym8ljGhCEGmcmDyRt+SLCjU/Gk/PaO3u4/rGEBtJEbSRCjcB3Pns0NQJdPX2D1uTONAvKNxw0FoulRFnd9swbbNrelXGw39HVw1iP6KPrzp7NDY//L187bRZ3PfcWdRlm8OUwm3hFR61eOpePjGmktjaSHHR7Dg7wxq59XP/YoWq8+VSSdV+PUgu/bOHJlQrxDWoyZimo5nOrNCYsPIhEItz13FuDQlsvXDCdmJJSBmTN0rm0jKjjna4DySid5SdNp2NvH5u2d7FpexcX3rmBZ686hcmjG7KGwBZr2onFlPe7+7j2kc0pg362wX53dx9fvvdl1l+xgPtWnsiOrh52d/cly59v3rmXu//h+OQMvhJmk1whvolB953O/Vx454aUfTMNFOVKSBxqeLKfwQRBTcYsBUE5tzCGc+fChIUH45qifOXTswbNtAdiytUPvpoyuK9Yt5FrFx/NhXduSBmcLz15RjKpLHGz5gqBTfzmUGdBmRzBmQZ7d4mSnr74MZfc9rtB/UEqn5ORzyw800DhVVOqnAmJhWoQftvdh3LuYRn8gpBoWq1+ExMWaSQeirEj6pILxA/ElO/+cjMX/+XHPAf3Ec7CPO7kvISpZFxTlImj6mlprOO9vQdKlh/hRSYVvCYiSXONl/bgPqZXf97Y1U137wCzJo0qmdnEj8HHa6C4Ycls9h3oZ3zawlCVFn7Z8DsHo9BzD9PgF4T/a7Xm0JiwcJEtkui7Z/0FfQdjGaObErR39jB5dAMoKeag+OI9tSXNj0gnfWY9Z1ozV546kwHVZGTQ5NEN7Ok5yJfvfdnzmJm0j459vSW72f0afCIRYdLo+pTy7Ynqv/lW9A0CbqE/Z1pzcsXAvv4BYrHSrIZYyLmHbfCr9P+1Wv0mJixcZHsoJo5qoL8/xuqlc1OSwxKlPRJMbWlk3Mhosm6U+3d+cM4xKY7zjn29TBhV7xkCOxTcM+sJI+v5xqJZgwTRrEmjkjOvWCzGgIJqfJY/rinKrEmjuHfFCbR39gxaurVUN7ufg09P39zIzWgAABQRSURBVMAgvwWUru/lwL207NdOmzVoCddyz+irdfDzi6D4TUqNCQsX6Q9FYla3v6+fjr3xwfioyaMPlQYHdu3rTVt69ThqBM+HS4AfPJ5aTXVUfe2gNbmHSroKfq6HwEoMyOOaohln99HaGr76i//x7Wb3c/Cphgc1IfTf3XNgUHJoJWb01XBNy0kQ/CZ+YHkWLtwx8XOmNfO102Zx7SOb+ZsbnknG7ANMGFXPlJYR1NXWcMvT21h1Ziv3rjiBVWe2cvPTW1HEM7Z+f98Am7Z3sXLdRs5d8zzXPrKZSKS0/wK3Cp5tQM4Wj5642XNlqA+VbLkHxeJ338tBQujPmNgUiBl9NVzTcuKVFxVE/06hmGbhwj0j8Cr5kT6r84qaun3ZvIxhpvWuFeD8fuByzQazze79dhL6OfMKgoOzFEQiQmNdbSBm9NVyTctJpf0mfiCq1Vk3Zd68edrW1lbwfokonf19/fzNDc8M+v7Zq05hSsuIQdvnUzYbKFv4YS4ncsfeXs665dlBA1G5TBylioYKS0jnUAhaFFI1X2vjECKyUVXnDWo3YeFNpQfTfMn2AOf6LkgDUS4yCd8wncNQCMoAHbb7xRg6JiwKJAwPR7F9LHYgKtdAluk8x42M8ne3PBd4gV4N+DV5CoowNA6RSViYzyIDYbDTFhuCWoxdtZzCNNN53n3J8YFwAFeKcg60fkSwhWFCZhzCoqGykBhM81lzohJ4hfquOrPVCfX1t45/Oat7ZsxMF++os+EQ0umublyO9UX8iGCzCrHhwoRFGmFaOCWfUF+/+l/ORK1MA1VjtGbYhnSWe6D1I3zWkv3ChZmhXIRNLS401LeUlDNRK1OobXNjlObGaKBNhX5R7oHWD7OsJfuFC9MsXIRNLXY/wH8+eVRZB49yJmplS3IKuqnQL/xMbMxEqa+1JfuFC9MsXIRRLU48wB17vSvGlnrwcDtVJ40urK5VMQ7ZakxyKoZqKCkRhiAS4xAmLFyEWS0ux+BRjJkufd+FrRP59t+2UhMRGySGQLUMtDYJCA+WZ+EibD6LdPwOpSwm1t69b8IZX+lqqoZhDMbyLPIg7LM1v2dpxZjp3PuW2xlvGEbx+ObgFpHviMg7IvKy8zrD9d03RWSbiGwRkdNc7Yuctm0icrWrfbqIvCAiW0XkXhHxzTA7XB2m+VCMU9W9b3NjXeh8Q4Yx3PE7GupGVT3WeT0KICKtwHnAx4FFwC0iUiMiNcDNwOlAK/B5Z1uA65zfmgl0Ahf73G/Dg2KiV9z7JpaTdRMW35BhDFcqYYZaDNyjqr3AWyKyDZjvfLdNVd8EEJF7gMUi8jrwSeB8Z5u7gO8At5a110ZRZjr3vrHY4BUHwxbJY5QHqx0VHPwWFleIyDKgDfiqqnYCU4DnXdu0O20A29PajwfGAV2q2u+xfQoisgJYAXD44YeX6hwMF8X4Rdz7ThjVkBQ6dbURaiPCzj09NiAYScIecFJtFGWGEpFfi8hrHq/FxGf+M4BjgZ3ADxO7efyUDqF9cKPqGlWdp6rzJkyYUPD5GP7iLqWSWJHvsDGN7N7Xx9UPvMJrOz7k7d3dtHfup78/NuTfTpRpCVPpFmMwYUuSrXaK0ixU9VP5bCcitwOPOB/bgWmur6cCO5z3Xu3vA80iUutoF+7tjZCQaZY4aXQ9Nz65heUnTU8JpV29dC5HTR6dd6l1r9+ur42w7I4XbVYaUsKYJOsXQTDH+RkNdZjr41nAa8779cB5IlIvItOBmcCLwAZgphP5FCXuBF+v8USQp4Elzv7LgYf96rfhD5lmiT19A5w9d9qgUNqV6zbmPYPM9Ntv795vs9IQU4mSJkGk3BWGM+FnNNT1IvKqiLwCnAJ8BUBVfw/cB2wGHgO+pKoDjtZwBfA48Dpwn7MtwFXA/3Gc4eOAn/jYb8ODYk06mWaJAxqPlCpmBpnpt0dEawa1DcdZaVix2lFxgmKO883BrapLs3z3PeB7Hu2PAo96tL/JoYgpo8yUYkW+gZh6llJpqIswcVR9zjIr2dTwTGVa9velCoZqmJUGwRxRLsKeJFsqgmKOs6qzVYYfTt1iZza7u/v47i83c93Zs1NmiauXzmV8Uz0fGRN/n2kGmUsNzzQD/ei4EVU1Kw2KOaKcWJJscMxxVhuqivBrTe53Ovez4LqnB23/7FWnMKVlRM7fTew/Z1ozl548g+bGOrp6DnLs1DFMGtOY9diQX00qr/2BqpqF+7UOthFsyh1CbLWhhgHFrMmd7YYsthpvYv9N27tYuW5jcv+HLl+Q3Madg5E+8OejhmfK/6imQTQo5gijvATFHGdmqCqimMEkm6mpWEdjIft7mVoS/g431eB/KJSgmCOM8hMEc5xpFlVEMRpANkFT7MymkP29hNZ3f7nZyoNQHQseDScHfbVhwqKKKGYwySVoii1/nu/+XkLric27uHbx0RVXw7NRjkEwKOaIoWLlO8KNCYsqopjBJCiz1kxCKxKJBNb/UM5BMMwryxXjUzMqjwmLADOU2epQB5OgzFqDIrQKwQbB/DAHfbgxYRFQKqGyl3PWmkkQBkVoFYINgvkR5jXuDYuGCixBSfH3g1zJZUGI/CgEi1LKDyvfEW5Mswgo1TxbrTazTRhNZ5UgjFqjcQgTFgGl2lR2t9kJYMLI+pRzC7MgtEEwf8LsoB/umBkqoFSTyp5udjp3zfN8Y9Es5kxrTm4TZkEI4TOdGUahWG2oAFOpBKZSHzdTTaNrFx/NhXdusHh7wwgQVhsqhFRCZfcjCiuT/2XGxJE8e9UpKQKpEEFl2cBGNRCW+9iEhZFCqZzP7gdARFjYOpEnNu9Kfj+1pZHGupqU3yxEUFk2sFENhOk+Np+FkUIporDSfRR/v/p3XHnqkSxsnQhk9r8UEi5czaHFxvAhTPexaRZGCqWIwvJ6AC792UbuW3ki13xGM6rahQiqag4tNoYPYbqPTbMwUihFFFamB0BVs0YLFZLcZolwRjUQpvvYhIWRgjtn4NmrTuGhyxcUbD8d6gNQiKCqptBiY/gSpvvYQmeNklOM086ioYzhRtDuYwudNcpGMRnNhYQL+xFaHLQH16h+wpLVbsLC8IWwPABuwhTGaBjlxnwWhuFQiTDGWEzp2NvLO5376djbm6y8axhBwzQLw3AodxijaTJGmDDNwjAcyh3GGKaELMMoSliIyDki8nsRiYnIvLTvviki20Rki4ic5mpf5LRtE5GrXe3TReQFEdkqIveKSNRpr3c+b3O+P6KYPhtGJsodxhimhCzDKNYM9Rrwd8Bqd6OItALnAR8HPgL8WkSOdL6+Gfg00A5sEJH1qroZuA64UVXvEZHbgIuBW52/nar6ZyJynrPduUX22wgB5Y5MKve6FNW2ZonfWKRaZSlKs1DV11V1i8dXi4F7VLVXVd8CtgHzndc2VX1TVfuAe4DFIiLAJ4H7nf3vAj7n+q27nPf3A6c62xtVTK6lV/2inOtShCkhq9JU6n4wDuGXz2IKsN31ud1py9Q+DuhS1f609pTfcr7f42w/CBFZISJtItLW0dFRolMxKsFwsOeXIlt+uDAc7oegk9MMJSK/BiZ7fPUtVX04024ebYq3cNIs22f7rcGNqmuANRDP4M7QNyMEDBd7fhjzUSrBcLkfgkxOYaGqnxrC77YD01yfpwI7nPde7e8DzSJS62gP7u0Tv9UuIrXAGOCDIfTJCBHDwZ5vNvj8GQ73Q9Dxywy1HjjPiWSaDswEXgQ2ADOdyKcocSf4eo0XqHoaWOLsvxx42PVby533S4DfaLUWtDKSVLs932zwhVHt90MYKKqQoIicBfw/YALQBbysqqc5330LuAjoB76sqr9y2s8A/hWoAe5Q1e857R8j7vAeC2wCLlDVXhFpANYBc4hrFOep6pu5+maFBMNPNc+8M61LXuiKhMOJar4fgoQvhQRV9SHgoQzffQ/4nkf7o8CjHu1vEo+WSm8/AJxTTD+NcFLN9nyzwRdONd8PhVApoWnlPgyjApgN3hgKlSwRY+U+DKMCmA3eGAqVDCE2zcIwKkC5s8WN6qCS5ksTFoZRIcwGbxRKJc2XZoYyDMMICZU0X5pmYRiGERIqab40YWEYhhEiKmW+NDOUYRiGkRMTFoZhGEZOTFgYhmEYOTFhYRiGYeTEhIVhGIaRk6KqzgYZEekA3i7T4cYTX5PDiGPXIxW7HqnY9ThEEK/FR1V1Qnpj1QqLciIibV4lfYcrdj1SseuRil2PQ4TpWpgZyjAMw8iJCQvDMAwjJyYsSsOaSncgYNj1SMWuRyp2PQ4RmmthPgvDMAwjJ6ZZGIZhGDkxYWEYhmHkxIRFgYjIDSLyvyLyiog8JCLNru++KSLbRGSLiJzmal/ktG0Tkasr03P/GS7n6UZEponI0yLyuoj8XkT+yWkfKyJPishW52+L0y4icpNzjV4RkeMqewb+ICI1IrJJRB5xPk8XkRec63GviESd9nrn8zbn+yMq2W8/EJFmEbnfGTdeF5ETw3h/mLAonCeBo1V1NvAH4JsAItIKnAd8HFgE3OI8MDXAzcDpQCvweWfbqmK4nKcH/cBXVfUo4ATgS855Xw08paozgaeczxC/PjOd1wrg1vJ3uSz8E/C66/N1wI3O9egELnbaLwY6VfXPgBud7aqNfwMeU9U/B44hfl1Cd3+YsCgQVX1CVfudj88DU533i4F7VLVXVd8CtgHzndc2VX1TVfuAe5xtq43hcp4pqOpOVX3Jeb+X+EAwhfi53+VsdhfwOef9YmCtxnkeaBaRw8rcbV8RkanA3wI/dj4L8EngfmeT9OuRuE73A6c621cFIjIa+GvgJwCq2qeqXYTw/jBhURwXAb9y3k8Btru+a3faMrVXG8PlPDPimFDmAC8Ak1R1J8QFCjDR2Ww4XKd/Bb4BxJzP44Au1yTLfc7J6+F8v8fZvlr4GNAB/NQxy/1YRJoI4f1hwsIDEfm1iLzm8Vrs2uZbxE0QP080efyUZmmvNobLeXoiIiOBB4Avq+qH2Tb1aKua6yQiZwK7VHWju9ljU83ju2qgFjgOuFVV5wDdHDI5eRHY62HLqnqgqp/K9r2ILAfOBE7VQ4kq7cA012ZTgR3O+0zt1US2869qRKSOuKD4uao+6DS/JyKHqepOx4ywy2mv9uu0APisiJwBNACjiWsazSJS62gP7nNOXI92EakFxgAflL/bvtEOtKvqC87n+4kLi9DdH6ZZFIiILAKuAj6rqvtdX60HznOiO6YTd1C9CGwAZjrRIFHiTvD15e53GRgu55mCY1//CfC6qv6L66v1wHLn/XLgYVf7Mifq5QRgT8IcUQ2o6jdVdaqqHkH8HviNqn4BeBpY4myWfj0S12mJs30gZtKlQFXfBbaLyCyn6VRgM2G8P1TVXgW8iDuutwMvO6/bXN99C3gD2AKc7mo/g3jk1BvAtyp9Dj5em2Fxnmnn/JfEzQSvuO6JM4jb3Z8Ctjp/xzrbC/GosTeAV4F5lT4HH6/NycAjzvuPEZ88bQN+AdQ77Q3O523O9x+rdL99uA7HAm3OPfIfQEsY7w8r92EYhmHkxMxQhmEYRk5MWBiGYRg5MWFhGIZh5MSEhWEYhpETExaGYRhGTkxYGKFGRAZE5GUnw/4XIjJCRI4Qkdcq3TcAp9rox3z43XFOtdt9IvKjtO/misirTuXSmxK1lgqtdCoiE0TksVL33QgnJiyMsNOjqseq6tFAH3BppTuUQEQ+DtSo6psl+K30agsHgFXA1zw2v5V4xdJE9dJFTntBlU5VtQPYKSILiu2/EX5MWBjVxH8Bf+a8rxGR2yW+xsQTItIIICLHisjzcmg9ksTs+hkRuU5EXhSRP4jIXzntNRJfw2SDs89Kp/0wEfmtS6v5K4/+fIFDmbk4WsAPReQlEXlKRCY47TNE5DER2Sgi/yUif+603yki/yIiT5NWultVu1X1v4kLDVzHOAwYraq/03gS1Vq8K7zmW+n0P5zzMIY5JiyMqsCZeZ9OPOsV4rPkm1X140AXcLbTvha4SuPrkbwKXOP6mVpVnQ982dV+MfGSC58APgFc4pRzOR94XFWPJb5Gwcse3VoAuAvqNQEvqepxwH+6jrEG+EdVnUtcU7jFtc+RwKdU9at5XoopxOsLJXBXLR1KpdM2wEsQGsMMKyRohJ1GEUkM1P9FvE7TR4C3VDXRvhE4QkTGAM2q+p9O+13ES00keNC9vfN+ITBbRBJ1jcYQF0QbgDucIoL/4TqWm8OIl6dOEAPudd7/DHjQqVZ7EvALObSMQ71rn1+o6kCW809nKFVLs+2zi/j1NIY5JiyMsNPjzO6TOINur6tpAGjM47cS+wxw6NkQ4rP+x9M3FpG/Jr7IzzoRuUFV16b3jXjto0woce2+K/0cXHTn0W837RxakAtSq5YOpdJpA/HzMIY5ZoYyhg2qugfodPkXlhI3B2XjceAyR4NARI4UkSYR+SjxdRtuJ67NeK2V/DqHfCgQf94SGsr5wH9rfO2Lt0TkHOf3RUSOGcLpAUnz0l4ROcGJglqGd4XXfCudHgkEIrLMqCymWRjDjeXAbSIyAngTuDDH9j8mbpJ6yRl8O4g7hk8Gvi4iB4F9xAfldH7pbPdr53M38HER2Uh8RbhznfYvALeKyLeBOuJL0v5PrhMRkT8SXy8iKiKfAxaq6mbgMuBO4trUrzi0muP3gftE5GLgT8A5TvujxCvlbgP2k3pNTnHOwxjmWNVZw/AJJwLraWCBqg6IyD5VHVnpfhWCiPwWWKyqnZXui1FZzAxlGD6hqj3EI54CsYZyoTihvf9igsIA0ywMwzCMPDDNwjAMw8iJCQvDMAwjJyYsDMMwjJyYsDAMwzByYsLCMAzDyMn/B6k6gmcI1XhUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ocxErgiOeSU0hrH04eWO0DlenwW0kTEk5cYsxu8zF2a8+n/xTjHFIVxZZUk6hgoU+lyqB686anlBc6bqzpnsa7pcLAz4Z3Ioxu8xl4C9ln49fKcY4pCuLHCinUMH4c2muD7K9b9CzkOBAIMDdL7zLwjPaeWD+MSw8o527X3iXQMD5Z1jojKbDw2FGwsYXGW6LMbvMJftvOa3GKxmJbJouPzo7O83q1auLLUZBsHM4AiXnhMz2GMVwjG7e2c81K9emlped08GEhiCBQKCkVpKFjjLK9TvRaKj84uW9ISJdcYXqPmlXZeFvnH40tdWBlOiddD+knt0DnHnr856F4kUHi3A4zHDYMBI2VFcFaG2opbrafmXhJNPDlxyHIJ4MPO9v7+MLNzzHjMmNXHzCIbSOrWV8qIZf/OEN/rhum0byoAN/KeDl/eqkLNQMVWRGa2Zxcji+v31vyTgh4zNkzvy3P/HNZS+xqTcyg9/Qs8fxnJ1k2jsw4lm2zZqqAJOaQryyaScL7uli2+4B5t3xV/64blvs+JW+e7uczLB+pRhBA6osPCSTIshHmmGnH82YpG3/bp2Q8djZonNRbnYZMq98aA1ndUxOGXjjP19EOLW9NeGzJjWFePejvqxTb7iVu7WhliVzPqkWWMi65IrilmJUjtRoqDzg5DPIZFPMJf48+VjRmXDycnTvYOJg5tYJmW4zWy520nDYsHfAXqE1hmoSBl67z18ypwMgZgJaOqeDq//v2pTPSjd4ZyN3dXWAz0wcy4oFxzI8EqYqYJ+wrdSc3UplUYxsv6osRonTQNTcEMyoCJxWBf1DI3zQuzfFHmx3rLsuPIrF5xzOFStei7UtPudwmuqDsUEu0w8pqoDG1VWzYsGxVAm2jtxclNv2vkHe/ajPdsDd2T+UMPDaff7F93axYsGx/PSrhmB1FVUB6NkzkHAMp8E7XrFmI3d1dYADG0Oxzyj0Tak+ASUTxQidVWUxSpwG0Pu+NzOj+cIp/vztbXu48K5VKTNgu2NdcOcqbpg9nYVntNMYqmFn/xD/6/E3WTLnyLzna8rFTjo4PMLNz2yw3V9x9wvvJgy8Tp9vjOGgpjExed0M3vHnddPZh+dsSkq+KUWEKol873bXdLQD/WiiXFTJVBaFLqilymKUOA1wTvnm42fAdkvJG2ZP5/on1sc+J34G7HSsmqpArNBQ9DiBQCDv+Zpqqu1NXjUO0UwQUYg9ewa48cn1LDyjndaxtTQ3BKkS4eoz2qmrqUroa/f5IpKw0nIzo4o/r+gKJldTUiAgNNcHMw7i4bDhve19vL99bywT6KeaxzClud71oJ1ragzNv6R4jSqLUeI0wIWCVRlnwMmzVoDL7nslVo4UEmfATsdqHVvr2uSUTDarheqAcMt5M9jRNxQbDPerr6E6zWDUFKrhvotmsm33ANv7BnntHzs48bP7s+XjfWzvG+Shrk1ccco0pk0ca6s8l8zp4JqVa1PCVlvG1sZm0lt29acojfjzWvLc2ykrm2xNSW4G8Z39g2z9eB8LH12boPwbx9TQGAq6mvXnGuWi+ZcUr1FlMUqcHE2NoSCNoWDGGXD8UrJn90Bae7zTsQ4YV8eKBccyNBKmxtq74NZkET2Gm1n30HCYfUPhhMHwprMPZ2jYvpRjOGzY0LMnJu+p7a1cftKhfPvXLyeYoxY/tZ6fnzmdlrG1KSafqKKAxAGwKVTD5l39MSUUr3QgkofqwYuPZXvfIEuee5sbn1zPolmHcUhrA6Ga7E008YN4dA9GY6iGoeERdvQN0D84ggF+9OCahAH7Rw+u4aGLj3W1KtneN8iIMdx5wVHc/MyG2KTBzSqo1PIvqUnMewp9jVVZjJJMjqZsZnWZIhzsjtUUqkkYkN1GKEUHr+M+3cyt3z6SS377t4yz7hED//K71xIGw3/53WusWHCs7XGSZ7tndUzm4nu7UkJoF57RHhvU4pXnB717Y4oiSnQAXL9tHwvu6UpROtee+Xm27xlMuB5R/8j+4+uYZDmuM91k8TeiiFBtRUW1NNTyw9OmJaxSoqbDGxx8I0Nhk3bWb2dCin5mz54BV6ugUsq/pCYx7ynGNVZlkQfy5WhyE+GQfKye3al7GNxEKH1v+WpaGmqZNeMgfvWnDSw8o53m+iCtY2s5cHzI9gdnjHF0QNuRPBs/pKXe9v3N9UFEhHDYJBw3OgC2NNTGZvJ7B0diPho7pbNvKGy7p2PFgmPZf1wdYB/S3NbSQG//UKx+xZ59wwk74G86+/CYCS6qKKKf/6MHI8f+cFe/7YAdDttft6iCtDMh/ejBNTww/xjb34DdjLIYoZROqEnMe4pxjVVZlBjZKp5cI5S6e/tZeEY7Vz60hpaGyPFGwoa3e/poqKtmv+pUGZwGb6e6v/H9f3jaNDbtsB9M96sPcs3KtTEzUnRgbK4Psvw7R7P1430x886kphBL53bQ0lCb8DktDbUcOrEBYwwLz2hnyXNvx8w4UYUWCIitcl381Hp+cPKhCSuVG2ZPjx0juoL6xTc+z+T9xthe70Na6ln2n+9w09mHx1Zfk5pC3D63M5aa3WnW7/QdQurKNN2MslSyIZeaSawc0eJHStZka34Ih03Mnt84psbWrLJ0TgeNodSBxmnwjvpo7PrfPq+TD3ftiymlZEfzLecdyZLn3uaP67axbsvuhJlRICA01FUz747EmfyCe7pYNOswLrxrFRBZtfz49GnM/c0nK4HrzprOjU+u55VNOzMOzGd1TE5ZqURXC9Eos2jU2ds9e2yv96Yd/cyacRB/euNDViw4FmM+2Rdy1UNrUs576dyO2Kzf6TusqQ6krCIM6U1apTBzLyWTWLlSjGusysLnOJkfmkI19OweSLur/M4LjuLyk9pSzCoL7u2yXc46Dd7Jy9/4Aa65IUjjmOrYDD0aQtvW2sCGbXu4ZuXrCSuA5JnR0HDYdgY1dUJ97Ga5/KS2BMdyS0Mtg8Nhbjh7Opt29POp5kj69XhFGXV8v7Jpp2NKjwPH17F0bkdsBRU2hoe6NrF0bkeKv+TGJyP+hfsumsn+4+piijPqd+nZPZiwF2ZC3KzfKYR6YGgkZRVx73cz798pNqVkEitXdAe3kjXZOL0njqtNmJXe/MwGbjzHecOanW3cafBOl7Jj6dwOTm1v5Y/rtsUS9N15wVEsemxdxpmR0wxqTG1V7JxH4nwpMyY3pqyUbp/XmRKZFV3VPL7mg4TQ42ik06SmEMYQkzG6M/6qL32Wg5vG8MD8Y+ju7SdsIhl0r/rSZ9jZP0RtdcDW7xI976j8j1xyfMJ3OHFcLYtmHcaYYBU7+4e4/on1XH5SWyzyLHqdnXbDp9vrMlqyjboppwJhpYoWP1JyIjkLaG//kK2pon8w0QTzyqadbNnZb5uQLCDCe9v7EpIcvvHhx4j1enL/dCk7FtzTxdVfaY+9b1JTiE81j3FVEMepcM6E+trYOYdqqmOvX3zCISkrpe8tX822Pam+ikvv+xvnHTOFA8bVcfu8Tk5tb+WHp02LKYjkyK0rVrxGQ1011dUBgtVV/OYv7xA2cNXDf+eby15i0WPr+KhvMCFJodvCP/2DI1x41yq+uewlFtzTxSubdjImWJWimG9+ZgO3ffvIhM+7Yfb0tHtdRkOuyS41M633FPoa+2ZlISKnA78EqoBfG2N+UWSRShYn59eISd1TsfzF91LMKjfMns623fsAEpy8C+7p4obZ07lh9vQEn8WSOR00hWrSHrsqICmzIMDVPpRMM6j4JXk0OWHy8YdG7FdEPbsHGBOsZtrEsVzztcM4Z+mLdPf2O3+OtaekKVTDT77SHtszEn19wT1dKX4XNzNAuxXU3sGRlLaePQPsGRhOMGld/8R6fnXeDKgn72hkkxLFF8pCRKqAW4BTgG5glYisNMasK65kpYmT6aauJpBi57zilGm0jgsmmEAe+dsHfOnzBzB5vzFcP3s6P35wDa9s2kl3bz8BEX7xhzdZNOswJu8X4u2ePm5+5q3Yprp0jje7wcXNgJMpQix5QLY10zhk593eN8gB4yM+hvjQ4HQpQsJhwz969wLYKpRk/4GbCDc7G3R09ZVs0vvl028l7D/x0rFZSpFNutGvuPhCWQBHAxuNMe8AiMj9wCxAlYUNTs6vCfW1TKivTZnlbtnVnxBZlGzzj3fg7uwf4pVNO7nwrlU8MP+YmB3+p18dSXtsu0R/+bzxowOyU6LB1oZaW8f03S+8y5EHTwcSlaxdipClczqoCsDH+yJpPfYNhfMWkeK0AgFS/FFXnDKNdVt2F8SxmSnqplADuG70Kz6+KKsqIrOB040xF1nP5wIzjTGXOb2nUsqqOpHNTRxfonHp3A5bx/OiWYcRrA4khKNGQ0ujDlu7aCinTWVe3vhO9UU+3jfIrv5hemxShAQCkiLXqe2tXP2VdgzwTk8fNz+zgZ49A/z2opl8+9cv24YdF2IAK+QMO913BZlrtuRLbq/L/iqf4Osa3CJyNnBakrI42hjzP5L6zQfmAxx88MEd77//fsFl9SPJ6by/ueyllD7/+aMT+Pnv18US+iWno8hmgHS68eP3J+RzAIw/v5aGWi4/qY0pE+qprRLqglUJe0SSB7SqAHztV4my/v7y/xrzawxZBZICIhzUFHLc/e5nnAb5bAZwJ0VcFRBX3/cHvXs5/rpnU9qfv/LEWPp6JT84KQu/mKG6gclxzycBm5M7GWOWAcsgsrIojGj+J2oCefiS4xgctjethIJV/PzM6fz0q5F0GNUB4VfnzchpYHeyg2/e2c/sJS/mfYYe76Tt7u3n5mc2cPlJbUzeL8T6rXsS0ogn+xc+6N2bIOuMyY0Mj5iEkNrrzprOnc+/w7Vnft5zRVEMu72TzyUbf0b8dzBjciPnHzeV8+ISSmb6vnWjXyqF/i34JXR2FdAmIlNFJAicC6wsskxlRSAgtI6t48DxoZRQz6VzO9gvFIyF6bWOrWO/eueQvUz1rp3qB0ez4EYjbjLV1XZLco6qH542jYWPruXk//1nFj66lq0f72Nnv/2xkmW9+IRDuPS+vyVEB1350Bqu/ko7E+q9NYfko2Z7PsmmDnT8d+AU3pzu+3YbglwpFOO34AtlYYwZBi4DngTeAFYYY14vrlTlSSAgtLU0cN9FM3nw4mNZeEY7v3z6LTb07HH1Q3TzI7a78a87azpLnns71iefETfxg5rdQPWjB9cwNBy2VXDJsjrt9q6yViVe4hTGmi+lmi3ZDODx34FTWPLg8IjjJCM+AOD5K0/kkUuOr2jndjF+C34xQ2GMeRx4vNhy5JNSDAUMhw3b9gzETARRkvM2OeEmLt+uVOk1K9cmFH3Kp4kh0z6MloZaevYMxjbhJZtFkmXNhzkkl+++lMJYIbtdxPHfgVNY8kjYxHwgdqapQpcRLWUGh0doaahN2G+z5Lm3Pf0t+GJlUY54vYzMZApKJ9Pmnf05D0puB7T43af7j6vjilOm2c5QczmPZOIHtUlNoRTTyeUntaXs1o6fpSXLamemi25KdEOu3302Zp984/Q9uN1FHP8dHDFpPEvndqRcw2t/v65kVk2lTihYxY9Pj2QbiGYP+PHp0xwzQOcD36wsyg0vd8bmGpoalWnhGe05z55zcURGB5KVlx1P/2Ak11NdTZVtPqdcHd/RQW14OJyy32LqhE/qbMRXwYvmx0o+Vm11ILaJce/gCMMjYf7Ru9d1re1cv/tiJejLV6hz/MqgZWxdwookHA47FrpSUhkOG+58/t2ElcWdz7/LtWd+3rNjqrIoEl6aFHIdjKIyjaZm9WgGtK0fDyS8776LZuZVoUaVzy+ffiuh2FNdTWLdjXT7Jrb3DcaKIkWJ7kMZW1eTUa5w2NA/NJzTd1+sBH1eTGziFUc4bPjw430a7ZQFJmw4/7ipKZtnjYcOblUWRcLLUMBcFVF8htRoKvHm+iAHNoYS0m4nk2x/b2tpyHpAsxuQtu0eyOo8MvkB4o8RncWe2t7KtV//PEvndLBt94BtlE78oOh0bccEqzJe3+gM/cNduQ+MyXb7qHnIS+Xh5cQmek0WP7U+5wlKJTJiSPmtRitCeoUqiyLhpUkhV0UUL9Mrm3ay6LF13D6vM6OiyIeJwm5A2t436Po83OexcaIAABXGSURBVMiRfIxovP83bnuBloZaxxra8YOi07XdOziS8frGl7PNx8BYqBQYXqb8iFfg0ZofbiYolU62JY7zgSqLIuGlSSFXRZSLTLmaKJIHmIBNlNFDXZtYOqeDBUlRSnbnkSxHS0MtH+7aR31tFaGaaprrgymDXnwYbXdvv2MVvJGwifkunAoVTRxXl/H6RpVVd+8nRaAaQzVMagpxQA47vwuVETbd72m0CitegcfX/Hj+yhNVUaShpto+MaaXdU1UWRQRr0IBR6OIvK4BHg4bdvYPsmXnvgQlcNeFR3Hbt4/k+7/9W6ztwuOncvcL77Fo1mFMnVDPmNoqJtTXxvI4xSubcPiTFOROBZDaWhoSlE/yngk7X811Z03n2t+vi2XVjd/tvm8oTJVEIlPsysomn3dylb74vFq5DIyFCqVN93uyq2mejcLSndm5UR2QlFIBXtY1AVUWGSnFvRBuyJciynT+2dzs8Tb75ApwF9y5isXnHMHCM9o5pKWeTTv6uf6JSNLCFV3dCYNqpmp8TjuEH77kOA5orItFMo23ZvXxM9u7X3iXOy84ih19g+zsH4olToxm1Y1e29axdVldw2R5oxlvrzhlWs6mx0IOtLmk/HBz72gJ1tzoHxzh+ifWF6yuCaiySEulp0V2c/7Z3OxRs8lNDr6BsDEsuKeLB+YfE0uZHv96dMbsVI3vvotmsm7LbscdwvuGwkxqDLH/+LqY7yB5dvaDkw/lhiffTKkXUVMdyNmRbCfvlQ+t4eHvHwcCW3b15zQRiV77xU+t56yOybHormz2fIwWJ4UVCla5une0BGtuBKur6NkzEDPbgfcrMlUWaaiUKmFOM8BcdmOnu9mjs9DkHbwzJjdy+UltNFs1J8LGpJ0xZ6rGN+BQAKlKUuUNBat4+JLjGBoOp60XsWffcCxkdjR2+SgtDbX07B5IMMUtndvBtNaxVLu0O0dTs/zg5EMT9o0UckLjNFkYDhvX947uzM6e5vogy79zNO9v3xvb7/Op5jGershUWaSh1NIreEG61UO2u7EzEZ2FxvsGWhpq+fHp0xJm9zedfTi3nDeDS+97JZZSfOqEegwRR3Omanw7+gZs7bnR3a2Z5E1WfslpyvNhl7/8pLaYooh+ZnR1NKlpjOuBvrd/KKYokmVrrg96bkJ1mixs2ZV7FgAlM+GwYe/gSMycO6kpUt7YbhNpvtB0H2koZnqFQpEuIVm+zz86C+3ZM8CNT65n0azD+PdvzYgN6tHj/8vvXqN1bB2PXnYc1379MBY+upYTbnyOb9z6Auu37qYpVJM2gV1jKMjEcRHfxAPzj2HRrMOYOK6OxpC7WVdyCov+wdFNGuwS7k2ZMMb2M7dZhZnckk6hFyorqV3Kj0q4d4rJtj0DKSlqLr63i217Bjw7pq4s0lCKzrd8O9zTDTYHWOnK83X+drNQp+OHjSEcDqTMvqOz5nSmr0BAmNJcz9i6mrxcp9E6kuMz+UaVwdaPB2w/M1oTfLSyiUhRTaileO+UE0MjYdv7Zngk7NkxVVmkodScb1443NMNhF6cf7IJqGe3/aCZTpEMDo9kNCXl0w6ej4Gvt38oIZPvjMmNKaay5Jrgo5GtSiiqGajU7p1yo6bKfp9FdZV3xiJflFXNhXKswe1FHeJiR3ylO/72vsGSqbs82hWdXVnQGZMb+fdvzeDDj/fZ1gQfjWyldO2U/DM8HObNrbsT0uovmdPBZya6D5Bwwtc1uHOhHJWFV3WIi7mXJLpJL5JtFupqAgkb73JVZKW2P8ZJ0T98yXEIknc5iz0JULxneDjMtj0DDI+Eqa4K0NpQO2pFAf6vwa3g3SasYoUuOg1o0fKkuZoyij1Q2ikqJ3NR8o70XPdcJKNmoPKnujrAgY2hzB3zhK4sfESxB8FscDOz98Ks5uXnuiHddwTYXhMvvtdSW1kp/kFXFiXAaG9gv8wW3Q5+Xu1jKeb+mEwbGe2UVb43f/ppUqH4B91nUSDyVUbVbRnLYuK2mLxXsfjFjPHPRVHlW7m5vf75KFmrVA6qLAqE2xu4HHA7+NltVnMTkpppkMv1c/NBLooq38rNzfX3uga8Un6oGapAVELqkChuHfG5mNXcmFiKaa7LZU9Gvjewubn+lZL3TMkfqiwKRCXl7c9m8Ms2EsvtIFesCK9cFFW+lZub619JkxclP6iyKBCVlP7Ay5l9sQc5uyAFSI1yylZR5VO5ubn+lTR5UfKDKosC4ZdIpnzh1cy+kINcsmJoCtWwoWdPgsJf/p2jGRgOl1zkUabrX0mTFyU/6D4LxVcUKizUqRrfL59+K6Ew0p0XHJVQ9Q/8k1ZD92Iodug+C6UsKNQKzaka38Iz2hOUxZhglW9t/1p0SMkGz0JnReQaEflARF61/r4c99q/ishGEVkvIqfFtZ9utW0Ukavi2qeKyMsiskFEHhARXStXMIXYa+LkG0k20+wdHNG6DUpF4PU+i8XGmCOsv8cBRKQdOBf4HHA6cKuIVIlIFXAL8CWgHfiW1RfgOuuz2oBe4Lsey61UOE57H1rH1ibs3/hU85ii7elQlEJSDDPULOB+Y8wA8K6IbASOtl7baIx5B0BE7gdmicgbwBeB86w+dwPXALcVVGqfo/bp7HByAB84PpRiAgMqJnBBqVy8VhaXicg8YDXwL8aYXuAg4KW4Pt1WG8CmpPaZQDOw0xgzbNM/ARGZD8wHOPjgg/N1Dr5HcwVlTzrfiJ2d38+2f51IKG4YlRlKRJ4WkbU2f7OIzPwPAY4AtgA3Rd9m81Emh/bURmOWGWM6jTGdLS0tWZ9PuZIp1YjmCLInEBCa64Oxqn3b+waLcm28/H5yTfuhv5nKY1QrC2PMyW76icjtwGPW025gctzLk4DN1mO79o+ARhGptlYX8f0VF6TbyJbLqqNSZqKlsCLzWoZc0n6UwnVRCo+X0VAHxD09E1hrPV4JnCsitSIyFWgD/gqsAtqsyKcgESf4ShPZCPIsMNt6//nAo17JXY6kS1SXbYLDSkpAVwrJH72WIZcd8aVwXZTC42U01PUi8ncRWQOcCFwBYIx5HVgBrAOeAC41xoxYq4bLgCeBN4AVVl+AK4F/tpzhzcBvPJS77EiXhTXbwSKfA4VbU0axTB7FTi1SCBlyyXhbCtdFKTyeObiNMXPTvPZz4Oc27Y8Dj9u0v8MnEVNKlqRz1mabPiPXgcJN6ozb53XS1tJAb/9Qxn6FMHmUQv4kr2XIJe1HKVwXpfBouo8KJ1v7cy4lS92mzpjUFOK+i2Zy3q9fjvWLf+72eNmcezrfSynY5gshQ7Y+qFK4Lop3OKX7UGWhZDVY5DJQOCmYhWe0s+CeroS+D158LLOXvOj4PMrzV57IQU1jcjndrM6jFJz5+ZIhn+dSCtdF8QbNDVUGeHWDZpMjKJfcTG5TZ0xqCqX4Prb3DXpi8ij1uhjx5EOGfK8GSuG6KIVFy6r6hFKKQso2N5Pb1BlL53bwUNemhH4PdW1i6dyOvKfTqDQnrUYwKaNFVxY+wc9lMN2mzmgK1XDFKdNYt2V3rN8Vp0yjraUh69KrmVZgleakrTTlqOQfVRY+wc83ezapM7JJsWGHW3NLrsV//GqrrzTlqOQfVRY+we83u9sBf7S28Gx8Edn6XvwcBaSV8ZTRosrCJ+jN7o5sVmDxisnNisHPpsBKK+ur5B9VFj5Bb3Z35LICc7ti8LMpEAofweRXk51ij0ZD+YhCVIjzO+lSmzjhNlIol9QYlUopRe8p+UFXFkpZkc99IMkrBjUFusfPJjvFHlUWii1+NiFka25xa7pSU6B7/G6yU1JRM5SSQqWZELIxXakp0B1qsis/NDeUkkIuyQK9olArHD+vpEoRP4cZVzqaG6pMKMSgViomhGwHnNFcm1wihVTBOKMmu/JDlYWPKNRsrVQ2AGbjJM312uQ64OvMOTOabLC8UJ+FjyhUMrhcwk+9IJsVTi7XZjS+GU3Mp1QaurLwEYUyD5WKCSGbFU4+a0m78c2UiqlOUQqFrix8RCEjTEoh6iebFU6ha0lrtI9Saaiy8BGlYh4qFPErnOevPJFHLjne0SeQy7UZzYBfad+FomjorM/QCBxnCl1LWr8LpRzR0NkywS8RJsUYSLO9NqP1zfjlu1CUfKDKQsk7fgor1QFfUdyhPgslK8JhQ8/uAT7o3UvP7gHbMFMNK1WU8kNXFoprKqXug6IoqejKQnGN1n1QlMplVMpCRM4WkddFJCwinUmv/auIbBSR9SJyWlz76VbbRhG5Kq59qoi8LCIbROQBEQla7bXW843W61NGI7OSO9nWfdCwUkUpH0ZrhloLfANYGt8oIu3AucDngAOBp0XkUOvlW4BTgG5glYisNMasA64DFhtj7heRJcB3gdus/73GmP8iIuda/b45SrmVOIaHw2zbM8DQSJiaqgCtDbVUV6fOI7Tug6JULqNaWRhj3jDGrLd5aRZwvzFmwBjzLrARONr622iMeccYMwjcD8wSEQG+CDxovf9u4Otxn3W39fhB4CSrv5IHhofDvLl1N+csfZEv3PAc5yx9kTe37mZ4OJzSV+s+KErl4pWD+yDgpbjn3VYbwKak9plAM7DTGDNs0/+g6HuMMcMissvq/1HyQUVkPjAf4OCDD87LiZQ72/YMcPG9XQl+iIvv7WLFgmM5sDHR76ArBkWpXDIqCxF5Gtjf5qWfGGMedXqbTZvBfiVj0vRP91mpjcYsA5ZBZAe3g2xKHEMjYVs/xPBI6soCdF+ColQqGZWFMebkHD63G5gc93wSsNl6bNf+EdAoItXW6iK+f/SzukWkGhgP7MhBJsWGmqqArR+iusq9hVLTXihK+eNV6OxK4Fwrkmkq0Ab8FVgFtFmRT0EiTvCVJpKg6llgtvX+84FH4z7rfOvxbOBPplwTWhWB1oZalszpSPBDLJnTQWuDu9VDpdXrVpRKZVSJBEXkTODfgRZgJ/CqMeY067WfAN8BhoF/Msb8wWr/MvB/gCrgDmPMz632TxNxeO8HvALMMcYMiEgdcA8wg8iK4lxjzDuZZCvXRIJeEI2GGh4JU50mGsqOUqrXrSjK6HFKJKhZZ5VR8UHvXo6/7lkAZkxu5OITDqExVMOkphAHjA+pOUpRfIZmnVU8Ibr3oqWhlh+eNo0rH1pT8skDFUXJHk33oYyK6N6Ly09qiykK0OSBilJu6MpCGRXRvRf1tVWaPFBRyhhdWSijJhAQQjXVmjxQUcoYVRZKXtDkgYpS3qgZSskLmgpEUcobVRZK3tBUIIpSvqgZSlEURcmIKgtFURQlI6osFEVRlIyoslAURVEyospCURRFyUjZJhIUkR7g/WLLkSUTsKkA6ANU7sKichcWP8o9Gpk/ZYxpSW4sW2XhR0RktV22x1JH5S4sKndh8aPcXsisZihFURQlI6osFEVRlIyosigtlhVbgBxRuQuLyl1Y/Ch33mVWn4WiKIqSEV1ZKIqiKBlRZaEoiqJkRJVFERGR/UTkKRHZYP1vsulzhIi8KCKvi8gaEflmMWRNkimj3Fa/J0Rkp4g8VmgZk+Q4XUTWi8hGEbnK5vVaEXnAev1lEZlSeClTcSH3fxeRv4nIsIjMLoaMybiQ+Z9FZJ31W35GRD5VDDmTcSH3xSLydxF5VUT+IiLtxZAzmUxyx/WbLSJGRHIPpzXG6F+R/oDrgausx1cB19n0ORRosx4fCGwBGktdbuu1k4CvAo8VUdYq4G3g00AQeA1oT+pzCbDEenwu8EAJ/DbcyD0FmA4sB2b7ROYTgTHW4+/76FqPi3v8NeAJP8ht9RsL/Bl4CejM9Xi6sigus4C7rcd3A19P7mCMecsYs8F6vBnYBqTsriwwGeUGMMY8A+wulFAOHA1sNMa8Y4wZBO4nIn888efzIHCSiBS7alNGuY0x7xlj1gDhYghogxuZnzXG7LWevgRMKrCMdriR++O4p/VAKUQGufltAywiMsHbN5qDqbIoLhONMVsArP+t6TqLyNFEZhBvF0C2dGQld5E5CNgU97zbarPtY4wZBnYBzQWRzhk3cpca2cr8XeAPnkrkDldyi8ilIvI2kYH38gLJlo6McovIDGCyMWbUpmCtlOcxIvI0sL/NSz/J8nMOAO4BzjfGeD6TzJfcJYDdCiF5VuimT6EpRZky4VpmEZkDdAJf8FQid7iS2xhzC3CLiJwHXA2c77VgGUgrt4gEgMXABfk4mCoLjzHGnOz0mohsFZEDjDFbLGWwzaHfOOD3wNXGmJc8EjWBfMhdInQDk+OeTwI2O/TpFpFqYDywozDiOeJG7lLDlcwicjKRSccXjDEDBZItHdle6/uB2zyVyB2Z5B4LHAY8Z1lV9wdWisjXjDGrsz2YmqGKy0o+mZ2cDzya3EFEgsAjwHJjzO8KKFs6MspdQqwC2kRkqnUtzyUifzzx5zMb+JOxPINFxI3cpUZGmS2zyFLga8aYUplkuJG7Le7pV4ANBZTPibRyG2N2GWMmGGOmGGOmEPER5aQooh+of8WLZmgGniHyw3sG2M9q7wR+bT2eAwwBr8b9HVHqclvP/x/QA/QTmQWdViR5vwy8RcTX8xOr7WfWjQNQB/wO2Aj8Ffh0sX8bLuU+yrqufcB24HUfyPw0sDXut7yy2DK7lPuXwOuWzM8Cnyu2zG7kTur7HKOIhtJ0H4qiKEpG1AylKIqiZESVhaIoipIRVRaKoihKRlRZKIqiKBlRZaEoiqJkRJWForhARPZk2f+EXLPtisg/iciYXN6rKF6hykJRSo9/AmyVhYhUFVgWRQFUWShKVlgrhudE5EEReVNEfhvNUGvVFnhTRP4CfCPuPdeIyA/jnq8VkSkiUi8ivxeR16y2b4rI5URS0T8rIs9a/feIyM9E5GXgahF5JO6zThGRhwt1/krlormhFCV7ZgCfI5KH53ngeBFZDdwOfJHITvAHXHzO6cBmY8xXAERkvDFml4j8M3CiMeYjq189sNYY8z8txfSGiLQYY3qAC4E783lyimKHriwUJXv+aozpNpHsv68SKUL0GeBdY8wGE0mLcK+Lz/k7cLKIXCci/80Ys8uh3wjwEID12fcAc0SkETiW0kjzrZQ5qiwUJXviM6WO8MkK3Sl3zjCJ91odRApbAR1ElMa/icj/dHj/PmPMSNzzO4nkDPsW8DsTqcGhKJ6iykJR8sObwFQROcR6/q24194DjgQQkSOBqdbjA4G9xph7gRujfYhUFxzrdCATqZi4mUhNhbvydgaKkgb1WShKHjDG7BOR+cDvReQj4C9EaglAxIQ0T0ReJZJW+i2r/fPADSISJpJZ+PtW+zLgDyKyxRhzosMhfwu0GGPWeXA6ipKCZp1VFB8iIr8CXjHG/KbYsiiVgSoLRfEZItJFpIbFKaY0Ks0pFYAqC0VRFCUj6uBWFEVRMqLKQlEURcmIKgtFURQlI6osFEVRlIyoslAURVEy8v8BvZWCoXyrj2YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in X_partial_sc4.columns:\n",
    "    sns.scatterplot(X_partial_sc4[i], ols_no_m.resid)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8285773037282241, 0.8338424695118343)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.diagnostic import linear_rainbow\n",
    "\n",
    "linear_rainbow(res = ols_no_m, frac = 0.5)\n",
    "#fraction is how much data\n",
    "#here we consider 50% of the data\n",
    "#stats,pval. pval > 0.05 so null hypothesis\n",
    "#hence data is linear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. HOMOSCEDACITY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(ols_no_m.predict(),ols_no_m.resid)\n",
    "plt.show()\n",
    "\n",
    "#not a perfect homo but also not a hetero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stat Value:  0.7124269225010615\n",
      "PValue:  0.9537219755464738\n",
      "Arangemnet:  increasing\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.api import het_goldfeldquandt\n",
    "\n",
    "stat, pval, arrangemnet = het_goldfeldquandt(ols_no_m.resid, X_partial_sc4)\n",
    "print('Stat Value: ', stat)\n",
    "print('PValue: ', pval)\n",
    "print('Arangemnet: ', arrangemnet)\n",
    "\n",
    "#pval is greater than 0.05 \n",
    "#hence the data is homoscedacitic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. AUTO CORRELATION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- ACCEPTABLE 1.5 - 2.5\n",
    "- NO AUTO CORRELATION = 2\n",
    "- -VE AUTO CORRELATION < 1.5\n",
    "- +VE AUTO CORRELATION > 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>GDP ($ per capita)</td> <th>  R-squared:         </th> <td>   0.799</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                    <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.786</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>              <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   60.12</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Tue, 09 Mar 2021</td>  <th>  Prob (F-statistic):</th> <td>9.60e-66</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>10:28:27</td>      <th>  Log-Likelihood:    </th> <td> -2224.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>       <td>   227</td>       <th>  AIC:               </th> <td>   4478.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>           <td>   212</td>       <th>  BIC:               </th> <td>   4529.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>               <td>    14</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>       <td>nonrobust</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                <td></td>                  <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                        <td> 9620.3348</td> <td>  298.964</td> <td>   32.179</td> <td> 0.000</td> <td> 9031.013</td> <td> 1.02e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Population</th>                   <td> 1.405e-06</td> <td> 3.84e-06</td> <td>    0.366</td> <td> 0.714</td> <td>-6.16e-06</td> <td> 8.97e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area_sqm</th>                     <td>-2.966e-05</td> <td>    0.000</td> <td>   -0.262</td> <td> 0.794</td> <td>   -0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Pop_Density_per sqm</th>          <td>    0.0106</td> <td>    0.187</td> <td>    0.057</td> <td> 0.955</td> <td>   -0.357</td> <td>    0.379</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Coastline (coast/area ratio)</th> <td>  -15.2505</td> <td>    3.771</td> <td>   -4.045</td> <td> 0.000</td> <td>  -22.683</td> <td>   -7.818</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Net migration</th>                <td>  294.0734</td> <td>   45.252</td> <td>    6.499</td> <td> 0.000</td> <td>  204.871</td> <td>  383.276</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Literacy (%)</th>                 <td>    8.7987</td> <td>   24.219</td> <td>    0.363</td> <td> 0.717</td> <td>  -38.943</td> <td>   56.540</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Phones (per 1000)</th>            <td>   32.6500</td> <td>    2.370</td> <td>   13.778</td> <td> 0.000</td> <td>   27.979</td> <td>   37.321</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Arable (%)</th>                   <td>  -41.8676</td> <td>   26.638</td> <td>   -1.572</td> <td> 0.118</td> <td>  -94.378</td> <td>   10.643</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Crops (%)</th>                    <td>   -1.3818</td> <td>   23.463</td> <td>   -0.059</td> <td> 0.953</td> <td>  -47.632</td> <td>   44.869</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Climate</th>                      <td> -128.6667</td> <td>  555.418</td> <td>   -0.232</td> <td> 0.817</td> <td>-1223.515</td> <td>  966.182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Birthrate</th>                    <td>  -75.7142</td> <td>   57.134</td> <td>   -1.325</td> <td> 0.187</td> <td> -188.337</td> <td>   36.909</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Deathrate</th>                    <td>   50.4181</td> <td>   61.482</td> <td>    0.820</td> <td> 0.413</td> <td>  -70.776</td> <td>  171.612</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Agriculture</th>                  <td>-5516.0947</td> <td> 3461.857</td> <td>   -1.593</td> <td> 0.113</td> <td>-1.23e+04</td> <td> 1307.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industry</th>                     <td> 2457.0810</td> <td> 2833.698</td> <td>    0.867</td> <td> 0.387</td> <td>-3128.753</td> <td> 8042.915</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.500</td> <th>  Durbin-Watson:     </th> <td>   1.819</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.009</td> <th>  Jarque-Bera (JB):  </th> <td>  15.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.225</td> <th>  Prob(JB):          </th> <td>0.000542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.178</td> <th>  Cond. No.          </th> <td>1.20e+09</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.2e+09. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:     GDP ($ per capita)   R-squared:                       0.799\n",
       "Model:                            OLS   Adj. R-squared:                  0.786\n",
       "Method:                 Least Squares   F-statistic:                     60.12\n",
       "Date:                Tue, 09 Mar 2021   Prob (F-statistic):           9.60e-66\n",
       "Time:                        10:28:27   Log-Likelihood:                -2224.0\n",
       "No. Observations:                 227   AIC:                             4478.\n",
       "Df Residuals:                     212   BIC:                             4529.\n",
       "Df Model:                          14                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "================================================================================================\n",
       "                                   coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------\n",
       "const                         9620.3348    298.964     32.179      0.000    9031.013    1.02e+04\n",
       "Population                    1.405e-06   3.84e-06      0.366      0.714   -6.16e-06    8.97e-06\n",
       "Area_sqm                     -2.966e-05      0.000     -0.262      0.794      -0.000       0.000\n",
       "Pop_Density_per sqm              0.0106      0.187      0.057      0.955      -0.357       0.379\n",
       "Coastline (coast/area ratio)   -15.2505      3.771     -4.045      0.000     -22.683      -7.818\n",
       "Net migration                  294.0734     45.252      6.499      0.000     204.871     383.276\n",
       "Literacy (%)                     8.7987     24.219      0.363      0.717     -38.943      56.540\n",
       "Phones (per 1000)               32.6500      2.370     13.778      0.000      27.979      37.321\n",
       "Arable (%)                     -41.8676     26.638     -1.572      0.118     -94.378      10.643\n",
       "Crops (%)                       -1.3818     23.463     -0.059      0.953     -47.632      44.869\n",
       "Climate                       -128.6667    555.418     -0.232      0.817   -1223.515     966.182\n",
       "Birthrate                      -75.7142     57.134     -1.325      0.187    -188.337      36.909\n",
       "Deathrate                       50.4181     61.482      0.820      0.413     -70.776     171.612\n",
       "Agriculture                  -5516.0947   3461.857     -1.593      0.113   -1.23e+04    1307.978\n",
       "Industry                      2457.0810   2833.698      0.867      0.387   -3128.753    8042.915\n",
       "==============================================================================\n",
       "Omnibus:                        9.500   Durbin-Watson:                   1.819\n",
       "Prob(Omnibus):                  0.009   Jarque-Bera (JB):               15.039\n",
       "Skew:                           0.225   Prob(JB):                     0.000542\n",
       "Kurtosis:                       4.178   Cond. No.                     1.20e+09\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.2e+09. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xp_c = sm.add_constant(X_partial_sc4)\n",
    "\n",
    "ols_no_m = sm.OLS(y,xp_c).fit()\n",
    "ols_no_m.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TRAIN TEST SPLIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xtrain shape: (158, 14)\n",
      "ytrain shape: (158,)\n",
      "xtest shape: (69, 14)\n",
      "ytest shape: (69,)\n"
     ]
    }
   ],
   "source": [
    "xtrain, xtest, ytrain, ytest = train_test_split(X_partial_sc4, y, random_state = 48, test_size = 0.3)\n",
    "\n",
    "print('xtrain shape:', xtrain.shape)\n",
    "print('ytrain shape:', ytrain.shape)\n",
    "print('xtest shape:', xtest.shape)\n",
    "print('ytest shape:', ytest.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lr = LinearRegression()\n",
    "\n",
    "lr.fit(xtrain,ytrain)\n",
    "ypred_train = lr.predict(xtrain)\n",
    "ypred_test = lr.predict(xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score, mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tools.eval_measures import rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8100429697509695"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_train_lr = r2_score(ytrain, ypred_train)\n",
    "r2_train_lr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7279555483928396"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_test_lr = r2_score(ytest, ypred_test)\n",
    "r2_test_lr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FEATURE ENGINEERING"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#! pip install mlxtend\n",
    "from mlxtend.feature_selection import SequentialFeatureSelector as sfs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backward Elimination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr_backward = sfs(estimator=lr, k_features=6,scoring='r2', forward = False)\n",
    "y = df_1['GDP ($ per capita)']\n",
    "sfs_backward = lr_backward.fit(X_partial_sc4, y)\n",
    "sfs_backward.k_feature_names_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7737304006688333"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfs_backward.k_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_backward = sfs(estimator=lr, k_features=(4,10),scoring='r2', forward = False)\n",
    "y = df_1['GDP ($ per capita)']\n",
    "sfs_backward = lr_backward.fit(X_partial_sc4, y)\n",
    "sfs_backward.k_feature_names_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7737304006688333"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfs_backward.k_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture')"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_backward = sfs(estimator=lr, k_features='best',scoring='r2', forward = False)\n",
    "y = df_1['GDP ($ per capita)']\n",
    "sfs_backward = lr_backward.fit(X_partial_sc4, y)\n",
    "sfs_backward.k_feature_names_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7737304006688333"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfs_backward.k_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture']"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_backward = list(sfs_backward.k_feature_names_)\n",
    "feature_backward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr_forward = sfs(estimator=lr, k_features='best',scoring='r2', forward = True)\n",
    "y = df_1['GDP ($ per capita)']\n",
    "sfs_forward = lr_backward.fit(X_partial_sc4, y)\n",
    "sfs_forward.k_feature_names_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7737304006688333"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfs_forward.k_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture']"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_forward = list(sfs_forward.k_feature_names_)\n",
    "feature_forward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recursive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import RFE, RFECV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_split.py:1978: FutureWarning: The default value of cv will change from 3 to 5 in version 0.22. Specify it explicitly to silence this warning.\n",
      "  warnings.warn(CV_WARNING, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "y = df_1['GDP ($ per capita)']\n",
    "rfe = RFECV(estimator=lr)\n",
    "rfecv_model = rfe.fit(X_partial_sc4,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 5, 4, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfecv_model.ranking_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature</th>\n",
       "      <th>Rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Net migration</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>Phones (per 1000)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>Arable (%)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>Climate</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>Birthrate</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>Deathrate</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>Agriculture</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>Industry</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>Literacy (%)</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>Crops (%)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Area_sqm</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Population</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Feature  Rank\n",
       "3   Coastline (coast/area ratio)     1\n",
       "4                  Net migration     1\n",
       "6              Phones (per 1000)     1\n",
       "7                     Arable (%)     1\n",
       "9                        Climate     1\n",
       "10                     Birthrate     1\n",
       "11                     Deathrate     1\n",
       "12                   Agriculture     1\n",
       "13                      Industry     1\n",
       "5                   Literacy (%)     2\n",
       "8                      Crops (%)     3\n",
       "2            Pop_Density_per sqm     4\n",
       "1                       Area_sqm     5\n",
       "0                     Population     6"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rank = pd.DataFrame()\n",
    "rank['Feature'] = X_partial_sc4.columns\n",
    "rank['Rank'] = rfecv_model.ranking_\n",
    "rank.sort_values('Rank')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3     Coastline (coast/area ratio)\n",
       "4                    Net migration\n",
       "5                     Literacy (%)\n",
       "6                Phones (per 1000)\n",
       "7                       Arable (%)\n",
       "8                        Crops (%)\n",
       "9                          Climate\n",
       "10                       Birthrate\n",
       "11                       Deathrate\n",
       "12                     Agriculture\n",
       "13                        Industry\n",
       "Name: Feature, dtype: object"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_rfecv = rank[rank['Rank']<4]['Feature']\n",
    "# should be ==1 to be in alignment with class I used < 4\n",
    "feature_rfecv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Literacy (%)',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Crops (%)',\n",
       " 'Climate',\n",
       " 'Birthrate',\n",
       " 'Deathrate',\n",
       " 'Agriculture',\n",
       " 'Industry']"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_rfecv = list(feature_rfecv)\n",
    "feature_rfecv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## building model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score, mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "xtrain, xtest, ytrain, ytest = train_test_split(X_partial_sc4, y, test_size = 0.3, random_state = 48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 train & R2 test:  0.8087081833017111 0.7299176337596316\n",
      "MSE train & MSE test:  19618576.739286043 20092496.50345691\n",
      "RMSE train & RMSE test:  4429.286256191402 4482.465449220653\n"
     ]
    }
   ],
   "source": [
    "### BACKWARD\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(xtrain[feature_backward], ytrain)\n",
    "ypred_train = lr.predict(xtrain[feature_backward])\n",
    "ypred_test = lr.predict(xtest[feature_backward])\n",
    "\n",
    "r2_train = r2_score(ytrain, ypred_train)\n",
    "r2_test = r2_score(ytest, ypred_test)\n",
    "\n",
    "print('R2 train & R2 test: ', r2_train, r2_test)\n",
    "\n",
    "mse_train = mean_squared_error(ytrain, ypred_train)\n",
    "mse_test = mean_squared_error(ytest, ypred_test)\n",
    "\n",
    "print('MSE train & MSE test: ', mse_train, mse_test)\n",
    "\n",
    "rmse_train = np.sqrt(mse_train)\n",
    "rmse_test = np.sqrt(mse_test)\n",
    "\n",
    "print('RMSE train & RMSE test: ', rmse_train, rmse_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8087081833017111, 0.7299176337596316, 4429.286256191402, 4482.465449220653)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_backward = (r2_train,r2_test,rmse_train,rmse_test)\n",
    "result_backward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 train & R2 test:  0.8087081833017111 0.7299176337596316\n",
      "MSE train & MSE test:  19618576.739286043 20092496.50345691\n",
      "RMSE train & RMSE test:  4429.286256191402 4482.465449220653\n"
     ]
    }
   ],
   "source": [
    "### FORWARD\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(xtrain[feature_forward], ytrain)\n",
    "ypred_train = lr.predict(xtrain[feature_forward])\n",
    "ypred_test = lr.predict(xtest[feature_forward])\n",
    "\n",
    "r2_train = r2_score(ytrain, ypred_train)\n",
    "r2_test = r2_score(ytest, ypred_test)\n",
    "\n",
    "print('R2 train & R2 test: ', r2_train, r2_test)\n",
    "\n",
    "mse_train = mean_squared_error(ytrain, ypred_train)\n",
    "mse_test = mean_squared_error(ytest, ypred_test)\n",
    "\n",
    "print('MSE train & MSE test: ', mse_train, mse_test)\n",
    "\n",
    "rmse_train = np.sqrt(mse_train)\n",
    "rmse_test = np.sqrt(mse_test)\n",
    "\n",
    "print('RMSE train & RMSE test: ', rmse_train, rmse_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8087081833017111, 0.7299176337596316, 4429.286256191402, 4482.465449220653)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_forward = (r2_train,r2_test,rmse_train,rmse_test)\n",
    "result_forward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 train & R2 test:  0.8098124085472707 0.728759598655256\n",
      "MSE train & MSE test:  19505329.199002434 20178647.31962993\n",
      "RMSE train & RMSE test:  4416.4838049066175 4492.064928251809\n"
     ]
    }
   ],
   "source": [
    "### RECURSIVE CV\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(xtrain[feature_rfecv], ytrain)\n",
    "ypred_train = lr.predict(xtrain[feature_rfecv])\n",
    "ypred_test = lr.predict(xtest[feature_rfecv])\n",
    "\n",
    "r2_train = r2_score(ytrain, ypred_train)\n",
    "r2_test = r2_score(ytest, ypred_test)\n",
    "\n",
    "print('R2 train & R2 test: ', r2_train, r2_test)\n",
    "\n",
    "mse_train = mean_squared_error(ytrain, ypred_train)\n",
    "mse_test = mean_squared_error(ytest, ypred_test)\n",
    "\n",
    "print('MSE train & MSE test: ', mse_train, mse_test)\n",
    "\n",
    "rmse_train = np.sqrt(mse_train)\n",
    "rmse_test = np.sqrt(mse_test)\n",
    "\n",
    "print('RMSE train & RMSE test: ', rmse_train, rmse_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8098124085472707, 0.728759598655256, 4416.4838049066175, 4492.064928251809)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_rfecv = (r2_train,r2_test,rmse_train,rmse_test)\n",
    "result_rfecv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "result_feature  =pd.DataFrame()\n",
    "result_feature['Backward'] = result_backward\n",
    "result_feature['Forward'] = result_forward\n",
    "result_feature['RFECV'] = result_rfecv\n",
    "\n",
    "result_feature.index = ['R2 Train','R2 Test', 'RMSE Train','RMSE  Test']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Backward</th>\n",
       "      <th>Forward</th>\n",
       "      <th>RFECV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>R2 Train</td>\n",
       "      <td>0.808708</td>\n",
       "      <td>0.808708</td>\n",
       "      <td>0.809812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>R2 Test</td>\n",
       "      <td>0.729918</td>\n",
       "      <td>0.729918</td>\n",
       "      <td>0.728760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>RMSE Train</td>\n",
       "      <td>4429.286256</td>\n",
       "      <td>4429.286256</td>\n",
       "      <td>4416.483805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>RMSE  Test</td>\n",
       "      <td>4482.465449</td>\n",
       "      <td>4482.465449</td>\n",
       "      <td>4492.064928</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Backward      Forward        RFECV\n",
       "R2 Train       0.808708     0.808708     0.809812\n",
       "R2 Test        0.729918     0.729918     0.728760\n",
       "RMSE Train  4429.286256  4429.286256  4416.483805\n",
       "RMSE  Test  4482.465449  4482.465449  4492.064928"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# with 6 features backward and forward perform better so we proceed with either one of them\n",
    "#RMSE is also similar\n",
    "# RFECV we have 11 features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CROSS VALIDATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "cv_score = cross_val_score(lr, X_partial_sc4, y, cv = 5, scoring = 'r2')\n",
    "\n",
    "avg_score = np.mean(cv_score)\n",
    "var_error = np.std(cv_score)\n",
    "\n",
    "coeff_var = var_error/avg_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7535360846057294, 0.11345166875800274, 0.15055903901053888)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Coastline (coast/area ratio)',\n",
       " 'Net migration',\n",
       " 'Phones (per 1000)',\n",
       " 'Arable (%)',\n",
       " 'Birthrate',\n",
       " 'Agriculture']"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_backward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7737304006688333, 0.10445033994791436, 0.134995781292327)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## features backward\n",
    "\n",
    "lr = LinearRegression()\n",
    "cv_score = cross_val_score(lr, X_partial_sc4[feature_backward], y, cv = 5, scoring = 'r2')\n",
    "\n",
    "avg_score = np.mean(cv_score)\n",
    "var_error = np.std(cv_score)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4434.862920643043, 966.1786176772686, 0.21785986060132276)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "lr = LinearRegression()\n",
    "cv_score = cross_val_score(lr, X_partial_sc4[feature_backward], y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "#both for first model and second the coeff is high for both\n",
    "# so we regularize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## REGULARISATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge,Lasso,ElasticNet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "cv_score = cross_val_score(lr, X_partial_sc4[feature_backward], y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_lr = avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RIDGE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "ridge_model = Ridge(normalize=True)\n",
    "cv_score = cross_val_score(ridge_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_ridge=avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "ridge_model = Ridge(alpha=0.57\n",
    "                    ,normalize=True)\n",
    "cv_score = cross_val_score(ridge_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_ridge_5=avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "#for alpha 0.5 the permissable error given by client 5300 is statisfied"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LASSO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso_model = Lasso(normalize=True)\n",
    "cv_score = cross_val_score(lasso_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_lasso=avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso_model = Lasso(alpha=126.8,normalize=True)\n",
    "cv_score = cross_val_score(lasso_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_lasso_126= avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ELASTIC NET"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_model = ElasticNet(normalize=True)\n",
    "cv_score = cross_val_score(en_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_en=avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_model = ElasticNet(alpha=0.00632,normalize=True)\n",
    "cv_score = cross_val_score(en_model, X_partial_sc4, y, cv = 5, scoring = 'neg_mean_squared_error')\n",
    "rmse = np.sqrt(abs(cv_score))\n",
    "avg_score = np.mean(rmse)\n",
    "var_error = np.std(rmse)\n",
    "\n",
    "coeff_var = var_error/avg_score\n",
    "\n",
    "result_en_6=avg_score, var_error, coeff_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "score_card = pd.DataFrame()\n",
    "score_card['Linear'] = result_lr\n",
    "score_card['Ridge alpha = 1'] = result_ridge\n",
    "score_card['Ridge alpha = 0.5'] = result_ridge_5\n",
    "score_card['Lasso alpha = 1']= result_lasso\n",
    "score_card['Lasso alpha = 126.8']= result_lasso_126\n",
    "score_card['Elastic Net alpha = 1'] = result_en\n",
    "score_card['Elastic Net alpha = 0.00632'] = result_en_6\n",
    "\n",
    "score_card.index = ['Model Bias Error','Variance Error','Coeff of Variance Error']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear</th>\n",
       "      <th>Ridge alpha = 1</th>\n",
       "      <th>Ridge alpha = 0.5</th>\n",
       "      <th>Lasso alpha = 1</th>\n",
       "      <th>Lasso alpha = 126.8</th>\n",
       "      <th>Elastic Net alpha = 1</th>\n",
       "      <th>Elastic Net alpha = 0.00632</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Model Bias Error</td>\n",
       "      <td>4434.862921</td>\n",
       "      <td>5682.751452</td>\n",
       "      <td>5294.786650</td>\n",
       "      <td>4613.220849</td>\n",
       "      <td>5299.416270</td>\n",
       "      <td>9479.429619</td>\n",
       "      <td>5299.192809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Variance Error</td>\n",
       "      <td>966.178618</td>\n",
       "      <td>356.526277</td>\n",
       "      <td>484.820291</td>\n",
       "      <td>1001.666875</td>\n",
       "      <td>747.045659</td>\n",
       "      <td>453.903166</td>\n",
       "      <td>482.100374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Coeff of Variance Error</td>\n",
       "      <td>0.217860</td>\n",
       "      <td>0.062738</td>\n",
       "      <td>0.091566</td>\n",
       "      <td>0.217130</td>\n",
       "      <td>0.140968</td>\n",
       "      <td>0.047883</td>\n",
       "      <td>0.090976</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              Linear  Ridge alpha = 1  Ridge alpha = 0.5  \\\n",
       "Model Bias Error         4434.862921      5682.751452        5294.786650   \n",
       "Variance Error            966.178618       356.526277         484.820291   \n",
       "Coeff of Variance Error     0.217860         0.062738           0.091566   \n",
       "\n",
       "                         Lasso alpha = 1  Lasso alpha = 126.8  \\\n",
       "Model Bias Error             4613.220849          5299.416270   \n",
       "Variance Error               1001.666875           747.045659   \n",
       "Coeff of Variance Error         0.217130             0.140968   \n",
       "\n",
       "                         Elastic Net alpha = 1  Elastic Net alpha = 0.00632  \n",
       "Model Bias Error                   9479.429619                  5299.192809  \n",
       "Variance Error                      453.903166                   482.100374  \n",
       "Coeff of Variance Error               0.047883                     0.090976  "
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_card"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Elastic Net 0.000632 and Ridge 0.5 are better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.11665712e-07, -5.35879567e-05,  3.69014119e-02, -1.64941500e+01,\n",
       "        2.16185526e+02,  1.85510489e+01,  3.73400049e+01, -4.50522552e+01,\n",
       "       -1.09696254e+01, -2.07021630e+02, -1.72718284e+01,  3.49655158e+01,\n",
       "       -5.18383386e+03,  1.19208981e+03])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_lr = LinearRegression()\n",
    "model_lr.fit(xtrain,ytrain)\n",
    "model_lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.01188641e-06,  4.57114981e-05,  1.59738806e-01, -4.95469768e+00,\n",
       "        2.07495868e+02,  3.67503757e+01,  1.76443774e+01, -1.05945471e+01,\n",
       "       -4.11609272e+01,  7.96432119e+02, -1.24380830e+02,  4.40003488e+00,\n",
       "       -9.96094811e+03, -2.02984752e+03])"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ridge = Ridge(alpha=0.5,normalize=True)\n",
    "model_ridge.fit(xtrain,ytrain)\n",
    "model_ridge.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.        ,  0.        , -0.        , 32.28743775,\n",
       "        0.        , 32.39132481, -0.        , -0.        ,  0.        ,\n",
       "       -0.        ,  0.        , -0.        ,  0.        ])"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_lasso = Lasso(alpha=126.8,normalize=True)\n",
    "model_lasso.fit(xtrain,ytrain)\n",
    "model_lasso.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.01154724e-06,  4.57040213e-05,  1.59673807e-01, -4.96107264e+00,\n",
       "        2.07549316e+02,  3.67364360e+01,  1.76544763e+01, -1.06092056e+01,\n",
       "       -4.11523579e+01,  7.96027152e+02, -1.24366000e+02,  4.42396328e+00,\n",
       "       -9.96109061e+03, -2.02956616e+03])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_en = ElasticNet(alpha=0.00632,normalize=True)\n",
    "model_en.fit(xtrain,ytrain)\n",
    "model_en.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear</th>\n",
       "      <th>Ridge</th>\n",
       "      <th>Lasso</th>\n",
       "      <th>Elastic Net</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Population</td>\n",
       "      <td>9.116657e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Area_sqm</td>\n",
       "      <td>-5.358796e-05</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Pop_Density_per sqm</td>\n",
       "      <td>3.690141e-02</td>\n",
       "      <td>0.159739</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.159674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Coastline (coast/area ratio)</td>\n",
       "      <td>-1.649415e+01</td>\n",
       "      <td>-4.954698</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-4.961073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Net migration</td>\n",
       "      <td>2.161855e+02</td>\n",
       "      <td>207.495868</td>\n",
       "      <td>32.287438</td>\n",
       "      <td>207.549316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Literacy (%)</td>\n",
       "      <td>1.855105e+01</td>\n",
       "      <td>36.750376</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>36.736436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Phones (per 1000)</td>\n",
       "      <td>3.734000e+01</td>\n",
       "      <td>17.644377</td>\n",
       "      <td>32.391325</td>\n",
       "      <td>17.654476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Arable (%)</td>\n",
       "      <td>-4.505226e+01</td>\n",
       "      <td>-10.594547</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-10.609206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Crops (%)</td>\n",
       "      <td>-1.096963e+01</td>\n",
       "      <td>-41.160927</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-41.152358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Climate</td>\n",
       "      <td>-2.070216e+02</td>\n",
       "      <td>796.432119</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>796.027152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Birthrate</td>\n",
       "      <td>-1.727183e+01</td>\n",
       "      <td>-124.380830</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-124.366000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Deathrate</td>\n",
       "      <td>3.496552e+01</td>\n",
       "      <td>4.400035</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.423963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Agriculture</td>\n",
       "      <td>-5.183834e+03</td>\n",
       "      <td>-9960.948112</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>-9961.090613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Industry</td>\n",
       "      <td>1.192090e+03</td>\n",
       "      <td>-2029.847516</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2029.566162</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                    Linear        Ridge      Lasso  \\\n",
       "Population                    9.116657e-07     0.000001   0.000000   \n",
       "Area_sqm                     -5.358796e-05     0.000046   0.000000   \n",
       "Pop_Density_per sqm           3.690141e-02     0.159739   0.000000   \n",
       "Coastline (coast/area ratio) -1.649415e+01    -4.954698  -0.000000   \n",
       "Net migration                 2.161855e+02   207.495868  32.287438   \n",
       "Literacy (%)                  1.855105e+01    36.750376   0.000000   \n",
       "Phones (per 1000)             3.734000e+01    17.644377  32.391325   \n",
       "Arable (%)                   -4.505226e+01   -10.594547  -0.000000   \n",
       "Crops (%)                    -1.096963e+01   -41.160927  -0.000000   \n",
       "Climate                      -2.070216e+02   796.432119   0.000000   \n",
       "Birthrate                    -1.727183e+01  -124.380830  -0.000000   \n",
       "Deathrate                     3.496552e+01     4.400035   0.000000   \n",
       "Agriculture                  -5.183834e+03 -9960.948112  -0.000000   \n",
       "Industry                      1.192090e+03 -2029.847516   0.000000   \n",
       "\n",
       "                              Elastic Net  \n",
       "Population                       0.000001  \n",
       "Area_sqm                         0.000046  \n",
       "Pop_Density_per sqm              0.159674  \n",
       "Coastline (coast/area ratio)    -4.961073  \n",
       "Net migration                  207.549316  \n",
       "Literacy (%)                    36.736436  \n",
       "Phones (per 1000)               17.654476  \n",
       "Arable (%)                     -10.609206  \n",
       "Crops (%)                      -41.152358  \n",
       "Climate                        796.027152  \n",
       "Birthrate                     -124.366000  \n",
       "Deathrate                        4.423963  \n",
       "Agriculture                  -9961.090613  \n",
       "Industry                     -2029.566162  "
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_table = pd.DataFrame({'Linear':model_lr.coef_,\n",
    "                          'Ridge':model_ridge.coef_,\n",
    "                          'Lasso':model_lasso.coef_,\n",
    "                          'Elastic Net':model_en.coef_})\n",
    "\n",
    "coef_table.index= xtrain.columns\n",
    "coef_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### HYPER PARAMETER TUNING"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RIDGE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:814: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "param = {'alpha':[0.0001,0.001,0.01,0.02,0.03,0.05,0.06,0.07,0.1,0.5,1,5,10,100,125,150,200]}\n",
    "\n",
    "rid = Ridge(normalize=True)\n",
    "grid_mod = GridSearchCV(rid, param_grid=param, cv = 5, scoring = 'r2')\n",
    "\n",
    "tun_mod = grid_mod.fit(xtrain,ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': 0.03}"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tun_mod.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7488321727032482"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tun_mod.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_fit_time</th>\n",
       "      <th>std_fit_time</th>\n",
       "      <th>mean_score_time</th>\n",
       "      <th>std_score_time</th>\n",
       "      <th>param_alpha</th>\n",
       "      <th>params</th>\n",
       "      <th>split0_test_score</th>\n",
       "      <th>split1_test_score</th>\n",
       "      <th>split2_test_score</th>\n",
       "      <th>split3_test_score</th>\n",
       "      <th>split4_test_score</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>rank_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.002791</td>\n",
       "      <td>7.457547e-04</td>\n",
       "      <td>0.001597</td>\n",
       "      <td>4.877018e-04</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>{'alpha': 0.0001}</td>\n",
       "      <td>0.841076</td>\n",
       "      <td>0.790135</td>\n",
       "      <td>0.646391</td>\n",
       "      <td>0.765976</td>\n",
       "      <td>0.688140</td>\n",
       "      <td>0.746588</td>\n",
       "      <td>0.070495</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.002991</td>\n",
       "      <td>6.311288e-04</td>\n",
       "      <td>0.001596</td>\n",
       "      <td>4.890647e-04</td>\n",
       "      <td>0.001</td>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>0.841088</td>\n",
       "      <td>0.790356</td>\n",
       "      <td>0.646983</td>\n",
       "      <td>0.765841</td>\n",
       "      <td>0.688189</td>\n",
       "      <td>0.746738</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.003192</td>\n",
       "      <td>3.990890e-04</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>4.855901e-04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>0.840933</td>\n",
       "      <td>0.792175</td>\n",
       "      <td>0.652262</td>\n",
       "      <td>0.764411</td>\n",
       "      <td>0.688413</td>\n",
       "      <td>0.747908</td>\n",
       "      <td>0.068922</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>5.352484e-07</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>6.143617e-07</td>\n",
       "      <td>0.02</td>\n",
       "      <td>{'alpha': 0.02}</td>\n",
       "      <td>0.840267</td>\n",
       "      <td>0.793487</td>\n",
       "      <td>0.656969</td>\n",
       "      <td>0.762691</td>\n",
       "      <td>0.688202</td>\n",
       "      <td>0.748613</td>\n",
       "      <td>0.067566</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.003390</td>\n",
       "      <td>4.879162e-04</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.890265e-04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>{'alpha': 0.03}</td>\n",
       "      <td>0.839199</td>\n",
       "      <td>0.794213</td>\n",
       "      <td>0.660702</td>\n",
       "      <td>0.760873</td>\n",
       "      <td>0.687639</td>\n",
       "      <td>0.748832</td>\n",
       "      <td>0.066387</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>3.371748e-07</td>\n",
       "      <td>0.001595</td>\n",
       "      <td>4.885202e-04</td>\n",
       "      <td>0.05</td>\n",
       "      <td>{'alpha': 0.05}</td>\n",
       "      <td>0.836207</td>\n",
       "      <td>0.794378</td>\n",
       "      <td>0.665984</td>\n",
       "      <td>0.757059</td>\n",
       "      <td>0.685815</td>\n",
       "      <td>0.748223</td>\n",
       "      <td>0.064409</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.003191</td>\n",
       "      <td>3.978016e-04</td>\n",
       "      <td>0.002195</td>\n",
       "      <td>1.164307e-03</td>\n",
       "      <td>0.06</td>\n",
       "      <td>{'alpha': 0.06}</td>\n",
       "      <td>0.834409</td>\n",
       "      <td>0.793988</td>\n",
       "      <td>0.667803</td>\n",
       "      <td>0.755104</td>\n",
       "      <td>0.684682</td>\n",
       "      <td>0.747543</td>\n",
       "      <td>0.063557</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.003790</td>\n",
       "      <td>9.779148e-04</td>\n",
       "      <td>0.001595</td>\n",
       "      <td>4.885584e-04</td>\n",
       "      <td>0.07</td>\n",
       "      <td>{'alpha': 0.07}</td>\n",
       "      <td>0.832472</td>\n",
       "      <td>0.793367</td>\n",
       "      <td>0.669205</td>\n",
       "      <td>0.753136</td>\n",
       "      <td>0.683457</td>\n",
       "      <td>0.746682</td>\n",
       "      <td>0.062771</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.003192</td>\n",
       "      <td>7.468754e-04</td>\n",
       "      <td>0.001396</td>\n",
       "      <td>4.889280e-04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>{'alpha': 0.1}</td>\n",
       "      <td>0.826123</td>\n",
       "      <td>0.790528</td>\n",
       "      <td>0.671584</td>\n",
       "      <td>0.747244</td>\n",
       "      <td>0.679505</td>\n",
       "      <td>0.743372</td>\n",
       "      <td>0.060698</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.002792</td>\n",
       "      <td>3.986602e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.989939e-04</td>\n",
       "      <td>0.5</td>\n",
       "      <td>{'alpha': 0.5}</td>\n",
       "      <td>0.746601</td>\n",
       "      <td>0.734664</td>\n",
       "      <td>0.650606</td>\n",
       "      <td>0.684375</td>\n",
       "      <td>0.639615</td>\n",
       "      <td>0.691542</td>\n",
       "      <td>0.043233</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>4.884026e-04</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.989460e-04</td>\n",
       "      <td>1</td>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>0.679329</td>\n",
       "      <td>0.678187</td>\n",
       "      <td>0.618161</td>\n",
       "      <td>0.627897</td>\n",
       "      <td>0.608594</td>\n",
       "      <td>0.642740</td>\n",
       "      <td>0.030331</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.987313e-04</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.885388e-04</td>\n",
       "      <td>5</td>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>0.414204</td>\n",
       "      <td>0.414568</td>\n",
       "      <td>0.398487</td>\n",
       "      <td>0.379604</td>\n",
       "      <td>0.414294</td>\n",
       "      <td>0.404324</td>\n",
       "      <td>0.013686</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.988982e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.983262e-04</td>\n",
       "      <td>10</td>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>0.276490</td>\n",
       "      <td>0.270005</td>\n",
       "      <td>0.249132</td>\n",
       "      <td>0.250447</td>\n",
       "      <td>0.280762</td>\n",
       "      <td>0.265364</td>\n",
       "      <td>0.013152</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>0.002194</td>\n",
       "      <td>3.993512e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.988985e-04</td>\n",
       "      <td>100</td>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>0.033131</td>\n",
       "      <td>0.015877</td>\n",
       "      <td>-0.040180</td>\n",
       "      <td>0.028025</td>\n",
       "      <td>0.019960</td>\n",
       "      <td>0.011203</td>\n",
       "      <td>0.026592</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>0.001994</td>\n",
       "      <td>6.743496e-07</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>7.466206e-04</td>\n",
       "      <td>125</td>\n",
       "      <td>{'alpha': 125}</td>\n",
       "      <td>0.025258</td>\n",
       "      <td>0.007728</td>\n",
       "      <td>-0.049892</td>\n",
       "      <td>0.020944</td>\n",
       "      <td>0.011177</td>\n",
       "      <td>0.002878</td>\n",
       "      <td>0.027345</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.988984e-04</td>\n",
       "      <td>0.000997</td>\n",
       "      <td>1.784161e-07</td>\n",
       "      <td>150</td>\n",
       "      <td>{'alpha': 150}</td>\n",
       "      <td>0.019924</td>\n",
       "      <td>0.002210</td>\n",
       "      <td>-0.056482</td>\n",
       "      <td>0.016150</td>\n",
       "      <td>0.005217</td>\n",
       "      <td>-0.002765</td>\n",
       "      <td>0.027864</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.991844e-04</td>\n",
       "      <td>0.000598</td>\n",
       "      <td>4.884220e-04</td>\n",
       "      <td>200</td>\n",
       "      <td>{'alpha': 200}</td>\n",
       "      <td>0.013158</td>\n",
       "      <td>-0.004786</td>\n",
       "      <td>-0.064853</td>\n",
       "      <td>0.010074</td>\n",
       "      <td>-0.002354</td>\n",
       "      <td>-0.009925</td>\n",
       "      <td>0.028531</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_fit_time  std_fit_time  mean_score_time  std_score_time param_alpha  \\\n",
       "0        0.002791  7.457547e-04         0.001597    4.877018e-04      0.0001   \n",
       "1        0.002991  6.311288e-04         0.001596    4.890647e-04       0.001   \n",
       "2        0.003192  3.990890e-04         0.001598    4.855901e-04        0.01   \n",
       "3        0.002992  5.352484e-07         0.001995    6.143617e-07        0.02   \n",
       "4        0.003390  4.879162e-04         0.001397    4.890265e-04        0.03   \n",
       "5        0.002992  3.371748e-07         0.001595    4.885202e-04        0.05   \n",
       "6        0.003191  3.978016e-04         0.002195    1.164307e-03        0.06   \n",
       "7        0.003790  9.779148e-04         0.001595    4.885584e-04        0.07   \n",
       "8        0.003192  7.468754e-04         0.001396    4.889280e-04         0.1   \n",
       "9        0.002792  3.986602e-04         0.001197    3.989939e-04         0.5   \n",
       "10       0.002593  4.884026e-04         0.000798    3.989460e-04           1   \n",
       "11       0.001795  3.987313e-04         0.001397    4.885388e-04           5   \n",
       "12       0.001795  3.988982e-04         0.001197    3.983262e-04          10   \n",
       "13       0.002194  3.993512e-04         0.001197    3.988985e-04         100   \n",
       "14       0.001994  6.743496e-07         0.000798    7.466206e-04         125   \n",
       "15       0.001795  3.988984e-04         0.000997    1.784161e-07         150   \n",
       "16       0.001795  3.991844e-04         0.000598    4.884220e-04         200   \n",
       "\n",
       "               params  split0_test_score  split1_test_score  \\\n",
       "0   {'alpha': 0.0001}           0.841076           0.790135   \n",
       "1    {'alpha': 0.001}           0.841088           0.790356   \n",
       "2     {'alpha': 0.01}           0.840933           0.792175   \n",
       "3     {'alpha': 0.02}           0.840267           0.793487   \n",
       "4     {'alpha': 0.03}           0.839199           0.794213   \n",
       "5     {'alpha': 0.05}           0.836207           0.794378   \n",
       "6     {'alpha': 0.06}           0.834409           0.793988   \n",
       "7     {'alpha': 0.07}           0.832472           0.793367   \n",
       "8      {'alpha': 0.1}           0.826123           0.790528   \n",
       "9      {'alpha': 0.5}           0.746601           0.734664   \n",
       "10       {'alpha': 1}           0.679329           0.678187   \n",
       "11       {'alpha': 5}           0.414204           0.414568   \n",
       "12      {'alpha': 10}           0.276490           0.270005   \n",
       "13     {'alpha': 100}           0.033131           0.015877   \n",
       "14     {'alpha': 125}           0.025258           0.007728   \n",
       "15     {'alpha': 150}           0.019924           0.002210   \n",
       "16     {'alpha': 200}           0.013158          -0.004786   \n",
       "\n",
       "    split2_test_score  split3_test_score  split4_test_score  mean_test_score  \\\n",
       "0            0.646391           0.765976           0.688140         0.746588   \n",
       "1            0.646983           0.765841           0.688189         0.746738   \n",
       "2            0.652262           0.764411           0.688413         0.747908   \n",
       "3            0.656969           0.762691           0.688202         0.748613   \n",
       "4            0.660702           0.760873           0.687639         0.748832   \n",
       "5            0.665984           0.757059           0.685815         0.748223   \n",
       "6            0.667803           0.755104           0.684682         0.747543   \n",
       "7            0.669205           0.753136           0.683457         0.746682   \n",
       "8            0.671584           0.747244           0.679505         0.743372   \n",
       "9            0.650606           0.684375           0.639615         0.691542   \n",
       "10           0.618161           0.627897           0.608594         0.642740   \n",
       "11           0.398487           0.379604           0.414294         0.404324   \n",
       "12           0.249132           0.250447           0.280762         0.265364   \n",
       "13          -0.040180           0.028025           0.019960         0.011203   \n",
       "14          -0.049892           0.020944           0.011177         0.002878   \n",
       "15          -0.056482           0.016150           0.005217        -0.002765   \n",
       "16          -0.064853           0.010074          -0.002354        -0.009925   \n",
       "\n",
       "    std_test_score  rank_test_score  \n",
       "0         0.070495                8  \n",
       "1         0.070341                6  \n",
       "2         0.068922                4  \n",
       "3         0.067566                2  \n",
       "4         0.066387                1  \n",
       "5         0.064409                3  \n",
       "6         0.063557                5  \n",
       "7         0.062771                7  \n",
       "8         0.060698                9  \n",
       "9         0.043233               10  \n",
       "10        0.030331               11  \n",
       "11        0.013686               12  \n",
       "12        0.013152               13  \n",
       "13        0.026592               14  \n",
       "14        0.027345               15  \n",
       "15        0.027864               16  \n",
       "16        0.028531               17  "
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(tun_mod.cv_results_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_fit_time</th>\n",
       "      <th>std_fit_time</th>\n",
       "      <th>mean_score_time</th>\n",
       "      <th>std_score_time</th>\n",
       "      <th>param_alpha</th>\n",
       "      <th>params</th>\n",
       "      <th>split0_test_score</th>\n",
       "      <th>split1_test_score</th>\n",
       "      <th>split2_test_score</th>\n",
       "      <th>split3_test_score</th>\n",
       "      <th>split4_test_score</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>rank_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.002791</td>\n",
       "      <td>7.457547e-04</td>\n",
       "      <td>0.001597</td>\n",
       "      <td>4.877018e-04</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>{'alpha': 0.0001}</td>\n",
       "      <td>0.841076</td>\n",
       "      <td>0.790135</td>\n",
       "      <td>0.646391</td>\n",
       "      <td>0.765976</td>\n",
       "      <td>0.688140</td>\n",
       "      <td>0.746588</td>\n",
       "      <td>0.070495</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.002991</td>\n",
       "      <td>6.311288e-04</td>\n",
       "      <td>0.001596</td>\n",
       "      <td>4.890647e-04</td>\n",
       "      <td>0.001</td>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>0.841088</td>\n",
       "      <td>0.790356</td>\n",
       "      <td>0.646983</td>\n",
       "      <td>0.765841</td>\n",
       "      <td>0.688189</td>\n",
       "      <td>0.746738</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.003192</td>\n",
       "      <td>3.990890e-04</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>4.855901e-04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>0.840933</td>\n",
       "      <td>0.792175</td>\n",
       "      <td>0.652262</td>\n",
       "      <td>0.764411</td>\n",
       "      <td>0.688413</td>\n",
       "      <td>0.747908</td>\n",
       "      <td>0.068922</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>5.352484e-07</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>6.143617e-07</td>\n",
       "      <td>0.02</td>\n",
       "      <td>{'alpha': 0.02}</td>\n",
       "      <td>0.840267</td>\n",
       "      <td>0.793487</td>\n",
       "      <td>0.656969</td>\n",
       "      <td>0.762691</td>\n",
       "      <td>0.688202</td>\n",
       "      <td>0.748613</td>\n",
       "      <td>0.067566</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.003390</td>\n",
       "      <td>4.879162e-04</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.890265e-04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>{'alpha': 0.03}</td>\n",
       "      <td>0.839199</td>\n",
       "      <td>0.794213</td>\n",
       "      <td>0.660702</td>\n",
       "      <td>0.760873</td>\n",
       "      <td>0.687639</td>\n",
       "      <td>0.748832</td>\n",
       "      <td>0.066387</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean_fit_time  std_fit_time  mean_score_time  std_score_time param_alpha  \\\n",
       "0       0.002791  7.457547e-04         0.001597    4.877018e-04      0.0001   \n",
       "1       0.002991  6.311288e-04         0.001596    4.890647e-04       0.001   \n",
       "2       0.003192  3.990890e-04         0.001598    4.855901e-04        0.01   \n",
       "3       0.002992  5.352484e-07         0.001995    6.143617e-07        0.02   \n",
       "4       0.003390  4.879162e-04         0.001397    4.890265e-04        0.03   \n",
       "\n",
       "              params  split0_test_score  split1_test_score  split2_test_score  \\\n",
       "0  {'alpha': 0.0001}           0.841076           0.790135           0.646391   \n",
       "1   {'alpha': 0.001}           0.841088           0.790356           0.646983   \n",
       "2    {'alpha': 0.01}           0.840933           0.792175           0.652262   \n",
       "3    {'alpha': 0.02}           0.840267           0.793487           0.656969   \n",
       "4    {'alpha': 0.03}           0.839199           0.794213           0.660702   \n",
       "\n",
       "   split3_test_score  split4_test_score  mean_test_score  std_test_score  \\\n",
       "0           0.765976           0.688140         0.746588        0.070495   \n",
       "1           0.765841           0.688189         0.746738        0.070341   \n",
       "2           0.764411           0.688413         0.747908        0.068922   \n",
       "3           0.762691           0.688202         0.748613        0.067566   \n",
       "4           0.760873           0.687639         0.748832        0.066387   \n",
       "\n",
       "   rank_test_score  \n",
       "0                8  \n",
       "1                6  \n",
       "2                4  \n",
       "3                2  \n",
       "4                1  "
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(tun_mod.cv_results_).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_fit_time</th>\n",
       "      <th>std_fit_time</th>\n",
       "      <th>mean_score_time</th>\n",
       "      <th>std_score_time</th>\n",
       "      <th>param_alpha</th>\n",
       "      <th>params</th>\n",
       "      <th>split0_test_score</th>\n",
       "      <th>split1_test_score</th>\n",
       "      <th>split2_test_score</th>\n",
       "      <th>split3_test_score</th>\n",
       "      <th>split4_test_score</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>rank_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.003390</td>\n",
       "      <td>4.879162e-04</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.890265e-04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>{'alpha': 0.03}</td>\n",
       "      <td>0.839199</td>\n",
       "      <td>0.794213</td>\n",
       "      <td>0.660702</td>\n",
       "      <td>0.760873</td>\n",
       "      <td>0.687639</td>\n",
       "      <td>0.748832</td>\n",
       "      <td>0.066387</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>5.352484e-07</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>6.143617e-07</td>\n",
       "      <td>0.02</td>\n",
       "      <td>{'alpha': 0.02}</td>\n",
       "      <td>0.840267</td>\n",
       "      <td>0.793487</td>\n",
       "      <td>0.656969</td>\n",
       "      <td>0.762691</td>\n",
       "      <td>0.688202</td>\n",
       "      <td>0.748613</td>\n",
       "      <td>0.067566</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>3.371748e-07</td>\n",
       "      <td>0.001595</td>\n",
       "      <td>4.885202e-04</td>\n",
       "      <td>0.05</td>\n",
       "      <td>{'alpha': 0.05}</td>\n",
       "      <td>0.836207</td>\n",
       "      <td>0.794378</td>\n",
       "      <td>0.665984</td>\n",
       "      <td>0.757059</td>\n",
       "      <td>0.685815</td>\n",
       "      <td>0.748223</td>\n",
       "      <td>0.064409</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.003192</td>\n",
       "      <td>3.990890e-04</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>4.855901e-04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>0.840933</td>\n",
       "      <td>0.792175</td>\n",
       "      <td>0.652262</td>\n",
       "      <td>0.764411</td>\n",
       "      <td>0.688413</td>\n",
       "      <td>0.747908</td>\n",
       "      <td>0.068922</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.003191</td>\n",
       "      <td>3.978016e-04</td>\n",
       "      <td>0.002195</td>\n",
       "      <td>1.164307e-03</td>\n",
       "      <td>0.06</td>\n",
       "      <td>{'alpha': 0.06}</td>\n",
       "      <td>0.834409</td>\n",
       "      <td>0.793988</td>\n",
       "      <td>0.667803</td>\n",
       "      <td>0.755104</td>\n",
       "      <td>0.684682</td>\n",
       "      <td>0.747543</td>\n",
       "      <td>0.063557</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.002991</td>\n",
       "      <td>6.311288e-04</td>\n",
       "      <td>0.001596</td>\n",
       "      <td>4.890647e-04</td>\n",
       "      <td>0.001</td>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>0.841088</td>\n",
       "      <td>0.790356</td>\n",
       "      <td>0.646983</td>\n",
       "      <td>0.765841</td>\n",
       "      <td>0.688189</td>\n",
       "      <td>0.746738</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.003790</td>\n",
       "      <td>9.779148e-04</td>\n",
       "      <td>0.001595</td>\n",
       "      <td>4.885584e-04</td>\n",
       "      <td>0.07</td>\n",
       "      <td>{'alpha': 0.07}</td>\n",
       "      <td>0.832472</td>\n",
       "      <td>0.793367</td>\n",
       "      <td>0.669205</td>\n",
       "      <td>0.753136</td>\n",
       "      <td>0.683457</td>\n",
       "      <td>0.746682</td>\n",
       "      <td>0.062771</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.002791</td>\n",
       "      <td>7.457547e-04</td>\n",
       "      <td>0.001597</td>\n",
       "      <td>4.877018e-04</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>{'alpha': 0.0001}</td>\n",
       "      <td>0.841076</td>\n",
       "      <td>0.790135</td>\n",
       "      <td>0.646391</td>\n",
       "      <td>0.765976</td>\n",
       "      <td>0.688140</td>\n",
       "      <td>0.746588</td>\n",
       "      <td>0.070495</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.003192</td>\n",
       "      <td>7.468754e-04</td>\n",
       "      <td>0.001396</td>\n",
       "      <td>4.889280e-04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>{'alpha': 0.1}</td>\n",
       "      <td>0.826123</td>\n",
       "      <td>0.790528</td>\n",
       "      <td>0.671584</td>\n",
       "      <td>0.747244</td>\n",
       "      <td>0.679505</td>\n",
       "      <td>0.743372</td>\n",
       "      <td>0.060698</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.002792</td>\n",
       "      <td>3.986602e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.989939e-04</td>\n",
       "      <td>0.5</td>\n",
       "      <td>{'alpha': 0.5}</td>\n",
       "      <td>0.746601</td>\n",
       "      <td>0.734664</td>\n",
       "      <td>0.650606</td>\n",
       "      <td>0.684375</td>\n",
       "      <td>0.639615</td>\n",
       "      <td>0.691542</td>\n",
       "      <td>0.043233</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>4.884026e-04</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.989460e-04</td>\n",
       "      <td>1</td>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>0.679329</td>\n",
       "      <td>0.678187</td>\n",
       "      <td>0.618161</td>\n",
       "      <td>0.627897</td>\n",
       "      <td>0.608594</td>\n",
       "      <td>0.642740</td>\n",
       "      <td>0.030331</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.987313e-04</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.885388e-04</td>\n",
       "      <td>5</td>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>0.414204</td>\n",
       "      <td>0.414568</td>\n",
       "      <td>0.398487</td>\n",
       "      <td>0.379604</td>\n",
       "      <td>0.414294</td>\n",
       "      <td>0.404324</td>\n",
       "      <td>0.013686</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.988982e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.983262e-04</td>\n",
       "      <td>10</td>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>0.276490</td>\n",
       "      <td>0.270005</td>\n",
       "      <td>0.249132</td>\n",
       "      <td>0.250447</td>\n",
       "      <td>0.280762</td>\n",
       "      <td>0.265364</td>\n",
       "      <td>0.013152</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>0.002194</td>\n",
       "      <td>3.993512e-04</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.988985e-04</td>\n",
       "      <td>100</td>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>0.033131</td>\n",
       "      <td>0.015877</td>\n",
       "      <td>-0.040180</td>\n",
       "      <td>0.028025</td>\n",
       "      <td>0.019960</td>\n",
       "      <td>0.011203</td>\n",
       "      <td>0.026592</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>0.001994</td>\n",
       "      <td>6.743496e-07</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>7.466206e-04</td>\n",
       "      <td>125</td>\n",
       "      <td>{'alpha': 125}</td>\n",
       "      <td>0.025258</td>\n",
       "      <td>0.007728</td>\n",
       "      <td>-0.049892</td>\n",
       "      <td>0.020944</td>\n",
       "      <td>0.011177</td>\n",
       "      <td>0.002878</td>\n",
       "      <td>0.027345</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.988984e-04</td>\n",
       "      <td>0.000997</td>\n",
       "      <td>1.784161e-07</td>\n",
       "      <td>150</td>\n",
       "      <td>{'alpha': 150}</td>\n",
       "      <td>0.019924</td>\n",
       "      <td>0.002210</td>\n",
       "      <td>-0.056482</td>\n",
       "      <td>0.016150</td>\n",
       "      <td>0.005217</td>\n",
       "      <td>-0.002765</td>\n",
       "      <td>0.027864</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>3.991844e-04</td>\n",
       "      <td>0.000598</td>\n",
       "      <td>4.884220e-04</td>\n",
       "      <td>200</td>\n",
       "      <td>{'alpha': 200}</td>\n",
       "      <td>0.013158</td>\n",
       "      <td>-0.004786</td>\n",
       "      <td>-0.064853</td>\n",
       "      <td>0.010074</td>\n",
       "      <td>-0.002354</td>\n",
       "      <td>-0.009925</td>\n",
       "      <td>0.028531</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_fit_time  std_fit_time  mean_score_time  std_score_time param_alpha  \\\n",
       "4        0.003390  4.879162e-04         0.001397    4.890265e-04        0.03   \n",
       "3        0.002992  5.352484e-07         0.001995    6.143617e-07        0.02   \n",
       "5        0.002992  3.371748e-07         0.001595    4.885202e-04        0.05   \n",
       "2        0.003192  3.990890e-04         0.001598    4.855901e-04        0.01   \n",
       "6        0.003191  3.978016e-04         0.002195    1.164307e-03        0.06   \n",
       "1        0.002991  6.311288e-04         0.001596    4.890647e-04       0.001   \n",
       "7        0.003790  9.779148e-04         0.001595    4.885584e-04        0.07   \n",
       "0        0.002791  7.457547e-04         0.001597    4.877018e-04      0.0001   \n",
       "8        0.003192  7.468754e-04         0.001396    4.889280e-04         0.1   \n",
       "9        0.002792  3.986602e-04         0.001197    3.989939e-04         0.5   \n",
       "10       0.002593  4.884026e-04         0.000798    3.989460e-04           1   \n",
       "11       0.001795  3.987313e-04         0.001397    4.885388e-04           5   \n",
       "12       0.001795  3.988982e-04         0.001197    3.983262e-04          10   \n",
       "13       0.002194  3.993512e-04         0.001197    3.988985e-04         100   \n",
       "14       0.001994  6.743496e-07         0.000798    7.466206e-04         125   \n",
       "15       0.001795  3.988984e-04         0.000997    1.784161e-07         150   \n",
       "16       0.001795  3.991844e-04         0.000598    4.884220e-04         200   \n",
       "\n",
       "               params  split0_test_score  split1_test_score  \\\n",
       "4     {'alpha': 0.03}           0.839199           0.794213   \n",
       "3     {'alpha': 0.02}           0.840267           0.793487   \n",
       "5     {'alpha': 0.05}           0.836207           0.794378   \n",
       "2     {'alpha': 0.01}           0.840933           0.792175   \n",
       "6     {'alpha': 0.06}           0.834409           0.793988   \n",
       "1    {'alpha': 0.001}           0.841088           0.790356   \n",
       "7     {'alpha': 0.07}           0.832472           0.793367   \n",
       "0   {'alpha': 0.0001}           0.841076           0.790135   \n",
       "8      {'alpha': 0.1}           0.826123           0.790528   \n",
       "9      {'alpha': 0.5}           0.746601           0.734664   \n",
       "10       {'alpha': 1}           0.679329           0.678187   \n",
       "11       {'alpha': 5}           0.414204           0.414568   \n",
       "12      {'alpha': 10}           0.276490           0.270005   \n",
       "13     {'alpha': 100}           0.033131           0.015877   \n",
       "14     {'alpha': 125}           0.025258           0.007728   \n",
       "15     {'alpha': 150}           0.019924           0.002210   \n",
       "16     {'alpha': 200}           0.013158          -0.004786   \n",
       "\n",
       "    split2_test_score  split3_test_score  split4_test_score  mean_test_score  \\\n",
       "4            0.660702           0.760873           0.687639         0.748832   \n",
       "3            0.656969           0.762691           0.688202         0.748613   \n",
       "5            0.665984           0.757059           0.685815         0.748223   \n",
       "2            0.652262           0.764411           0.688413         0.747908   \n",
       "6            0.667803           0.755104           0.684682         0.747543   \n",
       "1            0.646983           0.765841           0.688189         0.746738   \n",
       "7            0.669205           0.753136           0.683457         0.746682   \n",
       "0            0.646391           0.765976           0.688140         0.746588   \n",
       "8            0.671584           0.747244           0.679505         0.743372   \n",
       "9            0.650606           0.684375           0.639615         0.691542   \n",
       "10           0.618161           0.627897           0.608594         0.642740   \n",
       "11           0.398487           0.379604           0.414294         0.404324   \n",
       "12           0.249132           0.250447           0.280762         0.265364   \n",
       "13          -0.040180           0.028025           0.019960         0.011203   \n",
       "14          -0.049892           0.020944           0.011177         0.002878   \n",
       "15          -0.056482           0.016150           0.005217        -0.002765   \n",
       "16          -0.064853           0.010074          -0.002354        -0.009925   \n",
       "\n",
       "    std_test_score  rank_test_score  \n",
       "4         0.066387                1  \n",
       "3         0.067566                2  \n",
       "5         0.064409                3  \n",
       "2         0.068922                4  \n",
       "6         0.063557                5  \n",
       "1         0.070341                6  \n",
       "7         0.062771                7  \n",
       "0         0.070495                8  \n",
       "8         0.060698                9  \n",
       "9         0.043233               10  \n",
       "10        0.030331               11  \n",
       "11        0.013686               12  \n",
       "12        0.013152               13  \n",
       "13        0.026592               14  \n",
       "14        0.027345               15  \n",
       "15        0.027864               16  \n",
       "16        0.028531               17  "
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(tun_mod.cv_results_).sort_values('mean_test_score', ascending = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LASSO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\dell\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:814: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "param = {'alpha':[0.0001,0.001,0.01,0.02,0.03,0.05,0.06,0.07,0.1,0.5,1,5,10,100,125,150,200]}\n",
    "\n",
    "las = Lasso(normalize=True)\n",
    "grid_mod = GridSearchCV(las, param_grid=param, cv = 5, scoring = 'r2')\n",
    "\n",
    "tun_mod = grid_mod.fit(xtrain,ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': 10}"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tun_mod.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7591627666428141"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tun_mod.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_fit_time</th>\n",
       "      <th>std_fit_time</th>\n",
       "      <th>mean_score_time</th>\n",
       "      <th>std_score_time</th>\n",
       "      <th>param_alpha</th>\n",
       "      <th>params</th>\n",
       "      <th>split0_test_score</th>\n",
       "      <th>split1_test_score</th>\n",
       "      <th>split2_test_score</th>\n",
       "      <th>split3_test_score</th>\n",
       "      <th>split4_test_score</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>rank_test_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>0.000630</td>\n",
       "      <td>0.000997</td>\n",
       "      <td>9.122432e-07</td>\n",
       "      <td>10</td>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>0.850201</td>\n",
       "      <td>0.790899</td>\n",
       "      <td>0.673052</td>\n",
       "      <td>0.777646</td>\n",
       "      <td>0.702833</td>\n",
       "      <td>0.759163</td>\n",
       "      <td>0.063827</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>0.002992</td>\n",
       "      <td>0.000630</td>\n",
       "      <td>0.001001</td>\n",
       "      <td>6.778136e-06</td>\n",
       "      <td>5</td>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>0.846243</td>\n",
       "      <td>0.791033</td>\n",
       "      <td>0.663675</td>\n",
       "      <td>0.773676</td>\n",
       "      <td>0.697891</td>\n",
       "      <td>0.754741</td>\n",
       "      <td>0.065928</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>0.002195</td>\n",
       "      <td>0.000746</td>\n",
       "      <td>0.000996</td>\n",
       "      <td>9.887906e-07</td>\n",
       "      <td>1</td>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>0.842066</td>\n",
       "      <td>0.790414</td>\n",
       "      <td>0.650082</td>\n",
       "      <td>0.768153</td>\n",
       "      <td>0.690359</td>\n",
       "      <td>0.748455</td>\n",
       "      <td>0.069496</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.000797</td>\n",
       "      <td>0.001196</td>\n",
       "      <td>3.993532e-04</td>\n",
       "      <td>0.5</td>\n",
       "      <td>{'alpha': 0.5}</td>\n",
       "      <td>0.841517</td>\n",
       "      <td>0.790271</td>\n",
       "      <td>0.648216</td>\n",
       "      <td>0.767159</td>\n",
       "      <td>0.689286</td>\n",
       "      <td>0.747531</td>\n",
       "      <td>0.069985</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>0.000746</td>\n",
       "      <td>0.000998</td>\n",
       "      <td>1.016010e-06</td>\n",
       "      <td>0.1</td>\n",
       "      <td>{'alpha': 0.1}</td>\n",
       "      <td>0.841159</td>\n",
       "      <td>0.790144</td>\n",
       "      <td>0.646704</td>\n",
       "      <td>0.766229</td>\n",
       "      <td>0.688389</td>\n",
       "      <td>0.746768</td>\n",
       "      <td>0.070402</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>0.000631</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.885779e-04</td>\n",
       "      <td>0.07</td>\n",
       "      <td>{'alpha': 0.07}</td>\n",
       "      <td>0.841133</td>\n",
       "      <td>0.790134</td>\n",
       "      <td>0.646590</td>\n",
       "      <td>0.766158</td>\n",
       "      <td>0.688312</td>\n",
       "      <td>0.746709</td>\n",
       "      <td>0.070435</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.002194</td>\n",
       "      <td>0.000399</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>4.882875e-04</td>\n",
       "      <td>0.06</td>\n",
       "      <td>{'alpha': 0.06}</td>\n",
       "      <td>0.841125</td>\n",
       "      <td>0.790130</td>\n",
       "      <td>0.646552</td>\n",
       "      <td>0.766134</td>\n",
       "      <td>0.688287</td>\n",
       "      <td>0.746689</td>\n",
       "      <td>0.070447</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.002193</td>\n",
       "      <td>0.000399</td>\n",
       "      <td>0.000998</td>\n",
       "      <td>1.072619e-06</td>\n",
       "      <td>0.05</td>\n",
       "      <td>{'alpha': 0.05}</td>\n",
       "      <td>0.841117</td>\n",
       "      <td>0.790127</td>\n",
       "      <td>0.646514</td>\n",
       "      <td>0.766110</td>\n",
       "      <td>0.688261</td>\n",
       "      <td>0.746669</td>\n",
       "      <td>0.070458</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.002393</td>\n",
       "      <td>0.000488</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.990433e-04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>{'alpha': 0.03}</td>\n",
       "      <td>0.841100</td>\n",
       "      <td>0.790120</td>\n",
       "      <td>0.646437</td>\n",
       "      <td>0.766063</td>\n",
       "      <td>0.688210</td>\n",
       "      <td>0.746630</td>\n",
       "      <td>0.070480</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.002392</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.982074e-04</td>\n",
       "      <td>0.02</td>\n",
       "      <td>{'alpha': 0.02}</td>\n",
       "      <td>0.841092</td>\n",
       "      <td>0.790117</td>\n",
       "      <td>0.646400</td>\n",
       "      <td>0.766039</td>\n",
       "      <td>0.688185</td>\n",
       "      <td>0.746610</td>\n",
       "      <td>0.070491</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>0.000998</td>\n",
       "      <td>6.143617e-07</td>\n",
       "      <td>0.01</td>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>0.841083</td>\n",
       "      <td>0.790113</td>\n",
       "      <td>0.646362</td>\n",
       "      <td>0.766015</td>\n",
       "      <td>0.688159</td>\n",
       "      <td>0.746590</td>\n",
       "      <td>0.070502</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.002393</td>\n",
       "      <td>0.000488</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>3.987322e-04</td>\n",
       "      <td>0.001</td>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>0.841076</td>\n",
       "      <td>0.790110</td>\n",
       "      <td>0.646328</td>\n",
       "      <td>0.765993</td>\n",
       "      <td>0.688137</td>\n",
       "      <td>0.746573</td>\n",
       "      <td>0.070511</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.002195</td>\n",
       "      <td>0.000977</td>\n",
       "      <td>0.001197</td>\n",
       "      <td>7.464805e-04</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>{'alpha': 0.0001}</td>\n",
       "      <td>0.841075</td>\n",
       "      <td>0.790110</td>\n",
       "      <td>0.646325</td>\n",
       "      <td>0.765991</td>\n",
       "      <td>0.688135</td>\n",
       "      <td>0.746571</td>\n",
       "      <td>0.070512</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>0.001795</td>\n",
       "      <td>0.000399</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.990892e-04</td>\n",
       "      <td>100</td>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>0.808579</td>\n",
       "      <td>0.720150</td>\n",
       "      <td>0.664896</td>\n",
       "      <td>0.734620</td>\n",
       "      <td>0.706864</td>\n",
       "      <td>0.727101</td>\n",
       "      <td>0.047217</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>0.001596</td>\n",
       "      <td>0.000489</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.989938e-04</td>\n",
       "      <td>125</td>\n",
       "      <td>{'alpha': 125}</td>\n",
       "      <td>0.795979</td>\n",
       "      <td>0.715278</td>\n",
       "      <td>0.649972</td>\n",
       "      <td>0.720797</td>\n",
       "      <td>0.711160</td>\n",
       "      <td>0.718671</td>\n",
       "      <td>0.046697</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>0.001597</td>\n",
       "      <td>0.000490</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>3.988267e-04</td>\n",
       "      <td>150</td>\n",
       "      <td>{'alpha': 150}</td>\n",
       "      <td>0.780357</td>\n",
       "      <td>0.710590</td>\n",
       "      <td>0.636526</td>\n",
       "      <td>0.705933</td>\n",
       "      <td>0.710726</td>\n",
       "      <td>0.708833</td>\n",
       "      <td>0.045804</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>0.001596</td>\n",
       "      <td>0.000489</td>\n",
       "      <td>0.000997</td>\n",
       "      <td>2.132481e-07</td>\n",
       "      <td>200</td>\n",
       "      <td>{'alpha': 200}</td>\n",
       "      <td>0.747473</td>\n",
       "      <td>0.695275</td>\n",
       "      <td>0.607182</td>\n",
       "      <td>0.671380</td>\n",
       "      <td>0.699882</td>\n",
       "      <td>0.684221</td>\n",
       "      <td>0.046017</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_fit_time  std_fit_time  mean_score_time  std_score_time param_alpha  \\\n",
       "12       0.001995      0.000630         0.000997    9.122432e-07          10   \n",
       "11       0.002992      0.000630         0.001001    6.778136e-06           5   \n",
       "10       0.002195      0.000746         0.000996    9.887906e-07           1   \n",
       "9        0.002593      0.000797         0.001196    3.993532e-04         0.5   \n",
       "8        0.001795      0.000746         0.000998    1.016010e-06         0.1   \n",
       "7        0.001995      0.000631         0.001397    4.885779e-04        0.07   \n",
       "6        0.002194      0.000399         0.001397    4.882875e-04        0.06   \n",
       "5        0.002193      0.000399         0.000998    1.072619e-06        0.05   \n",
       "4        0.002393      0.000488         0.000798    3.990433e-04        0.03   \n",
       "3        0.002392      0.000487         0.001197    3.982074e-04        0.02   \n",
       "2        0.001995      0.000001         0.000998    6.143617e-07        0.01   \n",
       "1        0.002393      0.000488         0.001197    3.987322e-04       0.001   \n",
       "0        0.002195      0.000977         0.001197    7.464805e-04      0.0001   \n",
       "13       0.001795      0.000399         0.000798    3.990892e-04         100   \n",
       "14       0.001596      0.000489         0.000798    3.989938e-04         125   \n",
       "15       0.001597      0.000490         0.000798    3.988267e-04         150   \n",
       "16       0.001596      0.000489         0.000997    2.132481e-07         200   \n",
       "\n",
       "               params  split0_test_score  split1_test_score  \\\n",
       "12      {'alpha': 10}           0.850201           0.790899   \n",
       "11       {'alpha': 5}           0.846243           0.791033   \n",
       "10       {'alpha': 1}           0.842066           0.790414   \n",
       "9      {'alpha': 0.5}           0.841517           0.790271   \n",
       "8      {'alpha': 0.1}           0.841159           0.790144   \n",
       "7     {'alpha': 0.07}           0.841133           0.790134   \n",
       "6     {'alpha': 0.06}           0.841125           0.790130   \n",
       "5     {'alpha': 0.05}           0.841117           0.790127   \n",
       "4     {'alpha': 0.03}           0.841100           0.790120   \n",
       "3     {'alpha': 0.02}           0.841092           0.790117   \n",
       "2     {'alpha': 0.01}           0.841083           0.790113   \n",
       "1    {'alpha': 0.001}           0.841076           0.790110   \n",
       "0   {'alpha': 0.0001}           0.841075           0.790110   \n",
       "13     {'alpha': 100}           0.808579           0.720150   \n",
       "14     {'alpha': 125}           0.795979           0.715278   \n",
       "15     {'alpha': 150}           0.780357           0.710590   \n",
       "16     {'alpha': 200}           0.747473           0.695275   \n",
       "\n",
       "    split2_test_score  split3_test_score  split4_test_score  mean_test_score  \\\n",
       "12           0.673052           0.777646           0.702833         0.759163   \n",
       "11           0.663675           0.773676           0.697891         0.754741   \n",
       "10           0.650082           0.768153           0.690359         0.748455   \n",
       "9            0.648216           0.767159           0.689286         0.747531   \n",
       "8            0.646704           0.766229           0.688389         0.746768   \n",
       "7            0.646590           0.766158           0.688312         0.746709   \n",
       "6            0.646552           0.766134           0.688287         0.746689   \n",
       "5            0.646514           0.766110           0.688261         0.746669   \n",
       "4            0.646437           0.766063           0.688210         0.746630   \n",
       "3            0.646400           0.766039           0.688185         0.746610   \n",
       "2            0.646362           0.766015           0.688159         0.746590   \n",
       "1            0.646328           0.765993           0.688137         0.746573   \n",
       "0            0.646325           0.765991           0.688135         0.746571   \n",
       "13           0.664896           0.734620           0.706864         0.727101   \n",
       "14           0.649972           0.720797           0.711160         0.718671   \n",
       "15           0.636526           0.705933           0.710726         0.708833   \n",
       "16           0.607182           0.671380           0.699882         0.684221   \n",
       "\n",
       "    std_test_score  rank_test_score  \n",
       "12        0.063827                1  \n",
       "11        0.065928                2  \n",
       "10        0.069496                3  \n",
       "9         0.069985                4  \n",
       "8         0.070402                5  \n",
       "7         0.070435                6  \n",
       "6         0.070447                7  \n",
       "5         0.070458                8  \n",
       "4         0.070480                9  \n",
       "3         0.070491               10  \n",
       "2         0.070502               11  \n",
       "1         0.070511               12  \n",
       "0         0.070512               13  \n",
       "13        0.047217               14  \n",
       "14        0.046697               15  \n",
       "15        0.045804               16  \n",
       "16        0.046017               17  "
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(tun_mod.cv_results_).sort_values('mean_test_score', ascending = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GRADIENT DESCENT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()\n",
    "A = X.drop(['Infant mortality (per 1000 births)','Other (%)','Service'],axis = 1)\n",
    "X_scaled = sc.fit_transform(A)\n",
    "X_scaled = pd.DataFrame(X_scaled, columns = A.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population</th>\n",
       "      <th>Area_sqm</th>\n",
       "      <th>Pop_Density_per sqm</th>\n",
       "      <th>Coastline (coast/area ratio)</th>\n",
       "      <th>Net migration</th>\n",
       "      <th>Literacy (%)</th>\n",
       "      <th>Phones (per 1000)</th>\n",
       "      <th>Arable (%)</th>\n",
       "      <th>Crops (%)</th>\n",
       "      <th>Climate</th>\n",
       "      <th>Birthrate</th>\n",
       "      <th>Deathrate</th>\n",
       "      <th>Agriculture</th>\n",
       "      <th>Industry</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>-0.115094</td>\n",
       "      <td>-0.220266</td>\n",
       "      <td>-0.347864</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>2.143829</td>\n",
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       "      <td>3.055247</td>\n",
       "      <td>1.612835</td>\n",
       "      <td>-0.263552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.414949</td>\n",
       "      <td>-0.418770</td>\n",
       "      <td>-0.306272</td>\n",
       "      <td>-0.458127</td>\n",
       "      <td>-1.993115</td>\n",
       "      <td>0.181254</td>\n",
       "      <td>-0.736564</td>\n",
       "      <td>0.539398</td>\n",
       "      <td>-0.218337</td>\n",
       "      <td>1.260999</td>\n",
       "      <td>-0.631504</td>\n",
       "      <td>-0.738826</td>\n",
       "      <td>0.583345</td>\n",
       "      <td>-0.645495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-0.094652</td>\n",
       "      <td>2.659029</td>\n",
       "      <td>-0.366433</td>\n",
       "      <td>-0.469797</td>\n",
       "      <td>-0.107041</td>\n",
       "      <td>-0.650571</td>\n",
       "      <td>-0.705662</td>\n",
       "      <td>-0.799921</td>\n",
       "      <td>-0.500325</td>\n",
       "      <td>-1.694570</td>\n",
       "      <td>-0.448316</td>\n",
       "      <td>-0.842529</td>\n",
       "      <td>-0.327892</td>\n",
       "      <td>2.850162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-0.453407</td>\n",
       "      <td>-0.427929</td>\n",
       "      <td>-0.216248</td>\n",
       "      <td>2.263057</td>\n",
       "      <td>-1.993115</td>\n",
       "      <td>0.710596</td>\n",
       "      <td>0.106750</td>\n",
       "      <td>-0.291774</td>\n",
       "      <td>2.527233</td>\n",
       "      <td>-0.216785</td>\n",
       "      <td>0.031762</td>\n",
       "      <td>-1.070336</td>\n",
       "      <td>-0.199902</td>\n",
       "      <td>-0.476559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-0.453260</td>\n",
       "      <td>-0.427843</td>\n",
       "      <td>-0.291340</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>2.143829</td>\n",
       "      <td>0.861837</td>\n",
       "      <td>1.171305</td>\n",
       "      <td>-0.874869</td>\n",
       "      <td>-0.517231</td>\n",
       "      <td>1.260999</td>\n",
       "      <td>-1.209041</td>\n",
       "      <td>-0.563721</td>\n",
       "      <td>-0.670128</td>\n",
       "      <td>-0.394294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <td>222</td>\n",
       "      <td>-0.427185</td>\n",
       "      <td>-0.426113</td>\n",
       "      <td>-0.145933</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>0.363187</td>\n",
       "      <td>-0.234154</td>\n",
       "      <td>-0.405151</td>\n",
       "      <td>0.225366</td>\n",
       "      <td>2.527233</td>\n",
       "      <td>1.260999</td>\n",
       "      <td>0.862875</td>\n",
       "      <td>-0.959833</td>\n",
       "      <td>-0.404408</td>\n",
       "      <td>0.030250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>223</td>\n",
       "      <td>-0.451058</td>\n",
       "      <td>-0.342656</td>\n",
       "      <td>-0.373383</td>\n",
       "      <td>-0.466162</td>\n",
       "      <td>-0.057088</td>\n",
       "      <td>0.468611</td>\n",
       "      <td>0.248631</td>\n",
       "      <td>-1.039754</td>\n",
       "      <td>-0.517231</td>\n",
       "      <td>-1.694570</td>\n",
       "      <td>-0.207014</td>\n",
       "      <td>-0.596702</td>\n",
       "      <td>-0.231899</td>\n",
       "      <td>-0.901103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>224</td>\n",
       "      <td>-0.219874</td>\n",
       "      <td>-0.258613</td>\n",
       "      <td>-0.351882</td>\n",
       "      <td>-0.466736</td>\n",
       "      <td>-0.052623</td>\n",
       "      <td>-1.648760</td>\n",
       "      <td>-0.888836</td>\n",
       "      <td>-0.832898</td>\n",
       "      <td>-0.501002</td>\n",
       "      <td>-1.694570</td>\n",
       "      <td>1.875371</td>\n",
       "      <td>-0.215210</td>\n",
       "      <td>-0.091388</td>\n",
       "      <td>1.440500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>225</td>\n",
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       "      <td>-0.186544</td>\n",
       "      <td>-0.365619</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>-0.052623</td>\n",
       "      <td>-0.116187</td>\n",
       "      <td>-1.018714</td>\n",
       "      <td>-0.510622</td>\n",
       "      <td>-0.515202</td>\n",
       "      <td>-0.216785</td>\n",
       "      <td>1.704816</td>\n",
       "      <td>3.055247</td>\n",
       "      <td>0.499873</td>\n",
       "      <td>0.103700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>226</td>\n",
       "      <td>-0.320490</td>\n",
       "      <td>-0.302689</td>\n",
       "      <td>-0.356931</td>\n",
       "      <td>-0.470180</td>\n",
       "      <td>-0.052623</td>\n",
       "      <td>0.392991</td>\n",
       "      <td>-0.935413</td>\n",
       "      <td>-0.417687</td>\n",
       "      <td>-0.494239</td>\n",
       "      <td>-0.216785</td>\n",
       "      <td>0.532596</td>\n",
       "      <td>3.055247</td>\n",
       "      <td>0.214677</td>\n",
       "      <td>-0.241517</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>227 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Population  Area_sqm  Pop_Density_per sqm  Coastline (coast/area ratio)  \\\n",
       "0     -0.115094 -0.220266            -0.347864                     -0.470180   \n",
       "1     -0.414949 -0.418770            -0.306272                     -0.458127   \n",
       "2     -0.094652  2.659029            -0.366433                     -0.469797   \n",
       "3     -0.453407 -0.427929            -0.216248                      2.263057   \n",
       "4     -0.453260 -0.427843            -0.291340                     -0.470180   \n",
       "..          ...       ...                  ...                           ...   \n",
       "222   -0.427185 -0.426113            -0.145933                     -0.470180   \n",
       "223   -0.451058 -0.342656            -0.373383                     -0.466162   \n",
       "224   -0.219874 -0.258613            -0.351882                     -0.466736   \n",
       "225   -0.328509 -0.186544            -0.365619                     -0.470180   \n",
       "226   -0.320490 -0.302689            -0.356931                     -0.470180   \n",
       "\n",
       "     Net migration  Literacy (%)  Phones (per 1000)  Arable (%)  Crops (%)  \\\n",
       "0         2.143829     -2.537552          -1.041107   -0.132135  -0.502354   \n",
       "1        -1.993115      0.181254          -0.736564    0.539398  -0.218337   \n",
       "2        -0.107041     -0.650571          -0.705662   -0.799921  -0.500325   \n",
       "3        -1.993115      0.710596           0.106750   -0.291774   2.527233   \n",
       "4         2.143829      0.861837           1.171305   -0.874869  -0.517231   \n",
       "..             ...           ...                ...         ...        ...   \n",
       "222       0.363187     -0.234154          -0.405151    0.225366   2.527233   \n",
       "223      -0.057088      0.468611           0.248631   -1.039754  -0.517231   \n",
       "224      -0.052623     -1.648760          -0.888836   -0.832898  -0.501002   \n",
       "225      -0.052623     -0.116187          -1.018714   -0.510622  -0.515202   \n",
       "226      -0.052623      0.392991          -0.935413   -0.417687  -0.494239   \n",
       "\n",
       "      Climate  Birthrate  Deathrate  Agriculture  Industry  \n",
       "0   -1.694570   2.210162   3.055247     1.612835 -0.263552  \n",
       "1    1.260999  -0.631504  -0.738826     0.583345 -0.645495  \n",
       "2   -1.694570  -0.448316  -0.842529    -0.327892  2.850162  \n",
       "3   -0.216785   0.031762  -1.070336    -0.199902 -0.476559  \n",
       "4    1.260999  -1.209041  -0.563721    -0.670128 -0.394294  \n",
       "..        ...        ...        ...          ...       ...  \n",
       "222  1.260999   0.862875  -0.959833    -0.404408  0.030250  \n",
       "223 -1.694570  -0.207014  -0.596702    -0.231899 -0.901103  \n",
       "224 -1.694570   1.875371  -0.215210    -0.091388  1.440500  \n",
       "225 -0.216785   1.704816   3.055247     0.499873  0.103700  \n",
       "226 -0.216785   0.532596   3.055247     0.214677 -0.241517  \n",
       "\n",
       "[227 rows x 14 columns]"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [],
   "source": [
    "xtrain_sc , xtest_sc, ytrain_sc, ytest_sc  = train_test_split(X_scaled, y, test_size = 0.3, random_state = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import SGDRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7662432193147222"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd = SGDRegressor()\n",
    "sgd.fit(xtrain_sc,ytrain_sc)\n",
    "ypred = sgd.predict(xtest_sc)\n",
    "\n",
    "r2_score(ytest_sc,ypred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf  = PolynomialFeatures(degree = 2, include_bias= False, interaction_only=True)\n",
    "x_pf = pf.fit_transform(A)\n",
    "x_pf = pd.DataFrame(x_pf, index = A.index)\n",
    "x_pf.columns = pf.get_feature_names()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>Country</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>31056997.0</td>\n",
       "      <td>647500.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>15.7414</td>\n",
       "      <td>32.57</td>\n",
       "      <td>3.20</td>\n",
       "      <td>12.13</td>\n",
       "      <td>0.220</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>46.600</td>\n",
       "      <td>27.5374</td>\n",
       "      <td>0.3800</td>\n",
       "      <td>0.24000</td>\n",
       "      <td>1283.242840</td>\n",
       "      <td>17.708000</td>\n",
       "      <td>11.184000</td>\n",
       "      <td>10.464212</td>\n",
       "      <td>6.608976</td>\n",
       "      <td>0.091200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Albania</td>\n",
       "      <td>3581655.0</td>\n",
       "      <td>28748.0</td>\n",
       "      <td>124.6</td>\n",
       "      <td>1.2600</td>\n",
       "      <td>-13.9070</td>\n",
       "      <td>86.50</td>\n",
       "      <td>71.20</td>\n",
       "      <td>21.09</td>\n",
       "      <td>4.420</td>\n",
       "      <td>3.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>15.6600</td>\n",
       "      <td>0.6960</td>\n",
       "      <td>0.56400</td>\n",
       "      <td>78.874200</td>\n",
       "      <td>3.505520</td>\n",
       "      <td>2.840680</td>\n",
       "      <td>1.211040</td>\n",
       "      <td>0.981360</td>\n",
       "      <td>0.043616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Algeria</td>\n",
       "      <td>32930091.0</td>\n",
       "      <td>9622460.4</td>\n",
       "      <td>13.8</td>\n",
       "      <td>0.0400</td>\n",
       "      <td>-0.3900</td>\n",
       "      <td>70.00</td>\n",
       "      <td>78.10</td>\n",
       "      <td>3.22</td>\n",
       "      <td>0.250</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>17.140</td>\n",
       "      <td>4.6100</td>\n",
       "      <td>0.1010</td>\n",
       "      <td>0.66392</td>\n",
       "      <td>79.015400</td>\n",
       "      <td>1.731140</td>\n",
       "      <td>11.379589</td>\n",
       "      <td>0.465610</td>\n",
       "      <td>3.060671</td>\n",
       "      <td>0.067056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>American Samoa</td>\n",
       "      <td>57794.0</td>\n",
       "      <td>199.0</td>\n",
       "      <td>290.4</td>\n",
       "      <td>285.7248</td>\n",
       "      <td>-13.9070</td>\n",
       "      <td>97.00</td>\n",
       "      <td>259.50</td>\n",
       "      <td>10.00</td>\n",
       "      <td>45.021</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>44.920</td>\n",
       "      <td>6.5400</td>\n",
       "      <td>0.2388</td>\n",
       "      <td>0.42200</td>\n",
       "      <td>73.444200</td>\n",
       "      <td>2.681724</td>\n",
       "      <td>4.739060</td>\n",
       "      <td>0.390438</td>\n",
       "      <td>0.689970</td>\n",
       "      <td>0.025193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Andorra</td>\n",
       "      <td>71201.0</td>\n",
       "      <td>468.0</td>\n",
       "      <td>152.1</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>15.7414</td>\n",
       "      <td>100.00</td>\n",
       "      <td>497.20</td>\n",
       "      <td>2.22</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3.0</td>\n",
       "      <td>...</td>\n",
       "      <td>26.130</td>\n",
       "      <td>18.7500</td>\n",
       "      <td>0.1554</td>\n",
       "      <td>0.66660</td>\n",
       "      <td>54.437500</td>\n",
       "      <td>0.451178</td>\n",
       "      <td>1.935362</td>\n",
       "      <td>0.323750</td>\n",
       "      <td>1.388750</td>\n",
       "      <td>0.011510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>West Bank</td>\n",
       "      <td>2460492.0</td>\n",
       "      <td>5860.0</td>\n",
       "      <td>419.9</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>2.9800</td>\n",
       "      <td>78.26</td>\n",
       "      <td>145.20</td>\n",
       "      <td>16.90</td>\n",
       "      <td>45.021</td>\n",
       "      <td>3.0</td>\n",
       "      <td>...</td>\n",
       "      <td>95.010</td>\n",
       "      <td>11.7600</td>\n",
       "      <td>0.2700</td>\n",
       "      <td>0.84000</td>\n",
       "      <td>124.146400</td>\n",
       "      <td>2.850300</td>\n",
       "      <td>8.867600</td>\n",
       "      <td>0.352800</td>\n",
       "      <td>1.097600</td>\n",
       "      <td>0.025200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Western Sahara</td>\n",
       "      <td>273008.0</td>\n",
       "      <td>266000.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.4200</td>\n",
       "      <td>-0.0320</td>\n",
       "      <td>92.20</td>\n",
       "      <td>291.18</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>19.814</td>\n",
       "      <td>6.0560</td>\n",
       "      <td>0.1148</td>\n",
       "      <td>0.15320</td>\n",
       "      <td>119.993584</td>\n",
       "      <td>2.274647</td>\n",
       "      <td>3.035505</td>\n",
       "      <td>0.695229</td>\n",
       "      <td>0.927779</td>\n",
       "      <td>0.017587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Yemen</td>\n",
       "      <td>21456188.0</td>\n",
       "      <td>527970.0</td>\n",
       "      <td>40.6</td>\n",
       "      <td>0.3600</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>50.20</td>\n",
       "      <td>37.20</td>\n",
       "      <td>2.78</td>\n",
       "      <td>0.240</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>42.890</td>\n",
       "      <td>8.3000</td>\n",
       "      <td>0.1350</td>\n",
       "      <td>0.47200</td>\n",
       "      <td>355.987000</td>\n",
       "      <td>5.790150</td>\n",
       "      <td>20.244080</td>\n",
       "      <td>1.120500</td>\n",
       "      <td>3.917600</td>\n",
       "      <td>0.063720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Zambia</td>\n",
       "      <td>11502010.0</td>\n",
       "      <td>752614.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>80.60</td>\n",
       "      <td>8.20</td>\n",
       "      <td>7.08</td>\n",
       "      <td>0.030</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>82.000</td>\n",
       "      <td>55.0748</td>\n",
       "      <td>0.4400</td>\n",
       "      <td>0.58000</td>\n",
       "      <td>1129.033400</td>\n",
       "      <td>9.020000</td>\n",
       "      <td>11.890000</td>\n",
       "      <td>6.058228</td>\n",
       "      <td>7.985846</td>\n",
       "      <td>0.063800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>12236805.0</td>\n",
       "      <td>390580.0</td>\n",
       "      <td>31.3</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>90.70</td>\n",
       "      <td>26.80</td>\n",
       "      <td>8.32</td>\n",
       "      <td>0.340</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>56.020</td>\n",
       "      <td>55.0748</td>\n",
       "      <td>0.3580</td>\n",
       "      <td>0.48600</td>\n",
       "      <td>771.322574</td>\n",
       "      <td>5.013790</td>\n",
       "      <td>6.806430</td>\n",
       "      <td>4.929195</td>\n",
       "      <td>6.691588</td>\n",
       "      <td>0.043497</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>227 rows × 105 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                        x0         x1     x2        x3       x4      x5  \\\n",
       "Country                                                                   \n",
       "Afghanistan     31056997.0   647500.0   48.0    0.0000  15.7414   32.57   \n",
       "Albania          3581655.0    28748.0  124.6    1.2600 -13.9070   86.50   \n",
       "Algeria         32930091.0  9622460.4   13.8    0.0400  -0.3900   70.00   \n",
       "American Samoa     57794.0      199.0  290.4  285.7248 -13.9070   97.00   \n",
       "Andorra            71201.0      468.0  152.1    0.0000  15.7414  100.00   \n",
       "...                    ...        ...    ...       ...      ...     ...   \n",
       "West Bank        2460492.0     5860.0  419.9    0.0000   2.9800   78.26   \n",
       "Western Sahara    273008.0   266000.0    1.0    0.4200  -0.0320   92.20   \n",
       "Yemen           21456188.0   527970.0   40.6    0.3600   0.0000   50.20   \n",
       "Zambia          11502010.0   752614.0   15.3    0.0000   0.0000   80.60   \n",
       "Zimbabwe        12236805.0   390580.0   31.3    0.0000   0.0000   90.70   \n",
       "\n",
       "                    x6     x7      x8   x9  ...  x9 x10   x9 x11  x9 x12  \\\n",
       "Country                                     ...                            \n",
       "Afghanistan       3.20  12.13   0.220  1.0  ...  46.600  27.5374  0.3800   \n",
       "Albania          71.20  21.09   4.420  3.0  ...  45.330  15.6600  0.6960   \n",
       "Algeria          78.10   3.22   0.250  1.0  ...  17.140   4.6100  0.1010   \n",
       "American Samoa  259.50  10.00  45.021  2.0  ...  44.920   6.5400  0.2388   \n",
       "Andorra         497.20   2.22   0.000  3.0  ...  26.130  18.7500  0.1554   \n",
       "...                ...    ...     ...  ...  ...     ...      ...     ...   \n",
       "West Bank       145.20  16.90  45.021  3.0  ...  95.010  11.7600  0.2700   \n",
       "Western Sahara  291.18   0.02   0.000  1.0  ...  19.814   6.0560  0.1148   \n",
       "Yemen            37.20   2.78   0.240  1.0  ...  42.890   8.3000  0.1350   \n",
       "Zambia            8.20   7.08   0.030  2.0  ...  82.000  55.0748  0.4400   \n",
       "Zimbabwe         26.80   8.32   0.340  2.0  ...  56.020  55.0748  0.3580   \n",
       "\n",
       "                 x9 x13      x10 x11    x10 x12    x10 x13    x11 x12  \\\n",
       "Country                                                                 \n",
       "Afghanistan     0.24000  1283.242840  17.708000  11.184000  10.464212   \n",
       "Albania         0.56400    78.874200   3.505520   2.840680   1.211040   \n",
       "Algeria         0.66392    79.015400   1.731140  11.379589   0.465610   \n",
       "American Samoa  0.42200    73.444200   2.681724   4.739060   0.390438   \n",
       "Andorra         0.66660    54.437500   0.451178   1.935362   0.323750   \n",
       "...                 ...          ...        ...        ...        ...   \n",
       "West Bank       0.84000   124.146400   2.850300   8.867600   0.352800   \n",
       "Western Sahara  0.15320   119.993584   2.274647   3.035505   0.695229   \n",
       "Yemen           0.47200   355.987000   5.790150  20.244080   1.120500   \n",
       "Zambia          0.58000  1129.033400   9.020000  11.890000   6.058228   \n",
       "Zimbabwe        0.48600   771.322574   5.013790   6.806430   4.929195   \n",
       "\n",
       "                 x11 x13   x12 x13  \n",
       "Country                             \n",
       "Afghanistan     6.608976  0.091200  \n",
       "Albania         0.981360  0.043616  \n",
       "Algeria         3.060671  0.067056  \n",
       "American Samoa  0.689970  0.025193  \n",
       "Andorra         1.388750  0.011510  \n",
       "...                  ...       ...  \n",
       "West Bank       1.097600  0.025200  \n",
       "Western Sahara  0.927779  0.017587  \n",
       "Yemen           3.917600  0.063720  \n",
       "Zambia          7.985846  0.063800  \n",
       "Zimbabwe        6.691588  0.043497  \n",
       "\n",
       "[227 rows x 105 columns]"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_pf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(227, 105)"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_pf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(227, 14)"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('x2',\n",
       " 'x6',\n",
       " 'x11',\n",
       " 'x0 x9',\n",
       " 'x0 x13',\n",
       " 'x2 x9',\n",
       " 'x3 x6',\n",
       " 'x3 x10',\n",
       " 'x3 x12',\n",
       " 'x4 x6',\n",
       " 'x4 x7',\n",
       " 'x5 x10',\n",
       " 'x5 x12',\n",
       " 'x6 x10',\n",
       " 'x6 x11',\n",
       " 'x7 x9',\n",
       " 'x9 x10',\n",
       " 'x10 x11',\n",
       " 'x10 x12')"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr_backward = sfs(estimator=lr, k_features='best',scoring='r2', forward = False)\n",
    "y = df_1['GDP ($ per capita)']\n",
    "sfs_backward = lr_backward.fit(x_pf, y)\n",
    "sfs_backward.k_feature_names_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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