2. Linear Regression and R squared.ipynb

{
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  {
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   "source": [
    "#Loading the dataset and libraries\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "housing = pd.read_csv(\"/cxldata/datasets/project/housing/housing.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "      <th>ocean_proximity</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-122.23</td>\n",
       "      <td>37.88</td>\n",
       "      <td>41.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>8.3252</td>\n",
       "      <td>452600.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-122.22</td>\n",
       "      <td>37.86</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7099.0</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>8.3014</td>\n",
       "      <td>358500.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-122.24</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1467.0</td>\n",
       "      <td>190.0</td>\n",
       "      <td>496.0</td>\n",
       "      <td>177.0</td>\n",
       "      <td>7.2574</td>\n",
       "      <td>352100.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1274.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>558.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>5.6431</td>\n",
       "      <td>341300.0</td>\n",
       "      <td>NEAR BAY</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1627.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>565.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>3.8462</td>\n",
       "      <td>342200.0</td>\n",
       "      <td>NEAR BAY</td>\n",
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       "      <th>...</th>\n",
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       "    <tr>\n",
       "      <th>20635</th>\n",
       "      <td>-121.09</td>\n",
       "      <td>39.48</td>\n",
       "      <td>25.0</td>\n",
       "      <td>1665.0</td>\n",
       "      <td>374.0</td>\n",
       "      <td>845.0</td>\n",
       "      <td>330.0</td>\n",
       "      <td>1.5603</td>\n",
       "      <td>78100.0</td>\n",
       "      <td>INLAND</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20636</th>\n",
       "      <td>-121.21</td>\n",
       "      <td>39.49</td>\n",
       "      <td>18.0</td>\n",
       "      <td>697.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>356.0</td>\n",
       "      <td>114.0</td>\n",
       "      <td>2.5568</td>\n",
       "      <td>77100.0</td>\n",
       "      <td>INLAND</td>\n",
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       "    <tr>\n",
       "      <th>20637</th>\n",
       "      <td>-121.22</td>\n",
       "      <td>39.43</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2254.0</td>\n",
       "      <td>485.0</td>\n",
       "      <td>1007.0</td>\n",
       "      <td>433.0</td>\n",
       "      <td>1.7000</td>\n",
       "      <td>92300.0</td>\n",
       "      <td>INLAND</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20638</th>\n",
       "      <td>-121.32</td>\n",
       "      <td>39.43</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>409.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>349.0</td>\n",
       "      <td>1.8672</td>\n",
       "      <td>84700.0</td>\n",
       "      <td>INLAND</td>\n",
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       "    <tr>\n",
       "      <th>20639</th>\n",
       "      <td>-121.24</td>\n",
       "      <td>39.37</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2785.0</td>\n",
       "      <td>616.0</td>\n",
       "      <td>1387.0</td>\n",
       "      <td>530.0</td>\n",
       "      <td>2.3886</td>\n",
       "      <td>89400.0</td>\n",
       "      <td>INLAND</td>\n",
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       "  </tbody>\n",
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       "<p>20640 rows × 10 columns</p>\n",
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      "text/plain": [
       "       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0        -122.23     37.88                41.0        880.0           129.0   \n",
       "1        -122.22     37.86                21.0       7099.0          1106.0   \n",
       "2        -122.24     37.85                52.0       1467.0           190.0   \n",
       "3        -122.25     37.85                52.0       1274.0           235.0   \n",
       "4        -122.25     37.85                52.0       1627.0           280.0   \n",
       "...          ...       ...                 ...          ...             ...   \n",
       "20635    -121.09     39.48                25.0       1665.0           374.0   \n",
       "20636    -121.21     39.49                18.0        697.0           150.0   \n",
       "20637    -121.22     39.43                17.0       2254.0           485.0   \n",
       "20638    -121.32     39.43                18.0       1860.0           409.0   \n",
       "20639    -121.24     39.37                16.0       2785.0           616.0   \n",
       "\n",
       "       population  households  median_income  median_house_value  \\\n",
       "0           322.0       126.0         8.3252            452600.0   \n",
       "1          2401.0      1138.0         8.3014            358500.0   \n",
       "2           496.0       177.0         7.2574            352100.0   \n",
       "3           558.0       219.0         5.6431            341300.0   \n",
       "4           565.0       259.0         3.8462            342200.0   \n",
       "...           ...         ...            ...                 ...   \n",
       "20635       845.0       330.0         1.5603             78100.0   \n",
       "20636       356.0       114.0         2.5568             77100.0   \n",
       "20637      1007.0       433.0         1.7000             92300.0   \n",
       "20638       741.0       349.0         1.8672             84700.0   \n",
       "20639      1387.0       530.0         2.3886             89400.0   \n",
       "\n",
       "      ocean_proximity  \n",
       "0            NEAR BAY  \n",
       "1            NEAR BAY  \n",
       "2            NEAR BAY  \n",
       "3            NEAR BAY  \n",
       "4            NEAR BAY  \n",
       "...               ...  \n",
       "20635          INLAND  \n",
       "20636          INLAND  \n",
       "20637          INLAND  \n",
       "20638          INLAND  \n",
       "20639          INLAND  \n",
       "\n",
       "[20640 rows x 10 columns]"
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    "housing"
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     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 20640 entries, 0 to 20639\n",
      "Data columns (total 10 columns):\n",
      " #   Column              Non-Null Count  Dtype  \n",
      "---  ------              --------------  -----  \n",
      " 0   longitude           20640 non-null  float64\n",
      " 1   latitude            20640 non-null  float64\n",
      " 2   housing_median_age  20640 non-null  float64\n",
      " 3   total_rooms         20640 non-null  float64\n",
      " 4   total_bedrooms      20433 non-null  float64\n",
      " 5   population          20640 non-null  float64\n",
      " 6   households          20640 non-null  float64\n",
      " 7   median_income       20640 non-null  float64\n",
      " 8   median_house_value  20640 non-null  float64\n",
      " 9   ocean_proximity     20640 non-null  object \n",
      "dtypes: float64(9), object(1)\n",
      "memory usage: 1.6+ MB\n"
     ]
    }
   ],
   "source": [
    "housing.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
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       "      <th>median_house_value</th>\n",
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       "      <th>count</th>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20433.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-119.569704</td>\n",
       "      <td>35.631861</td>\n",
       "      <td>28.639486</td>\n",
       "      <td>2635.763081</td>\n",
       "      <td>537.870553</td>\n",
       "      <td>1425.476744</td>\n",
       "      <td>499.539680</td>\n",
       "      <td>3.870671</td>\n",
       "      <td>206855.816909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.003532</td>\n",
       "      <td>2.135952</td>\n",
       "      <td>12.585558</td>\n",
       "      <td>2181.615252</td>\n",
       "      <td>421.385070</td>\n",
       "      <td>1132.462122</td>\n",
       "      <td>382.329753</td>\n",
       "      <td>1.899822</td>\n",
       "      <td>115395.615874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-124.350000</td>\n",
       "      <td>32.540000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.499900</td>\n",
       "      <td>14999.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-121.800000</td>\n",
       "      <td>33.930000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>1447.750000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>787.000000</td>\n",
       "      <td>280.000000</td>\n",
       "      <td>2.563400</td>\n",
       "      <td>119600.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-118.490000</td>\n",
       "      <td>34.260000</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>2127.000000</td>\n",
       "      <td>435.000000</td>\n",
       "      <td>1166.000000</td>\n",
       "      <td>409.000000</td>\n",
       "      <td>3.534800</td>\n",
       "      <td>179700.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-118.010000</td>\n",
       "      <td>37.710000</td>\n",
       "      <td>37.000000</td>\n",
       "      <td>3148.000000</td>\n",
       "      <td>647.000000</td>\n",
       "      <td>1725.000000</td>\n",
       "      <td>605.000000</td>\n",
       "      <td>4.743250</td>\n",
       "      <td>264725.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-114.310000</td>\n",
       "      <td>41.950000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>39320.000000</td>\n",
       "      <td>6445.000000</td>\n",
       "      <td>35682.000000</td>\n",
       "      <td>6082.000000</td>\n",
       "      <td>15.000100</td>\n",
       "      <td>500001.000000</td>\n",
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      "text/plain": [
       "          longitude      latitude  housing_median_age   total_rooms  \\\n",
       "count  20640.000000  20640.000000        20640.000000  20640.000000   \n",
       "mean    -119.569704     35.631861           28.639486   2635.763081   \n",
       "std        2.003532      2.135952           12.585558   2181.615252   \n",
       "min     -124.350000     32.540000            1.000000      2.000000   \n",
       "25%     -121.800000     33.930000           18.000000   1447.750000   \n",
       "50%     -118.490000     34.260000           29.000000   2127.000000   \n",
       "75%     -118.010000     37.710000           37.000000   3148.000000   \n",
       "max     -114.310000     41.950000           52.000000  39320.000000   \n",
       "\n",
       "       total_bedrooms    population    households  median_income  \\\n",
       "count    20433.000000  20640.000000  20640.000000   20640.000000   \n",
       "mean       537.870553   1425.476744    499.539680       3.870671   \n",
       "std        421.385070   1132.462122    382.329753       1.899822   \n",
       "min          1.000000      3.000000      1.000000       0.499900   \n",
       "25%        296.000000    787.000000    280.000000       2.563400   \n",
       "50%        435.000000   1166.000000    409.000000       3.534800   \n",
       "75%        647.000000   1725.000000    605.000000       4.743250   \n",
       "max       6445.000000  35682.000000   6082.000000      15.000100   \n",
       "\n",
       "       median_house_value  \n",
       "count        20640.000000  \n",
       "mean        206855.816909  \n",
       "std         115395.615874  \n",
       "min          14999.000000  \n",
       "25%         119600.000000  \n",
       "50%         179700.000000  \n",
       "75%         264725.000000  \n",
       "max         500001.000000  "
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two type of Linear Regression-\n",
    "\n",
    "## Simple Linear Regression:\n",
    "which you can also interpret as correlation as it tells upto what extent there is a linear relationship between two variables. In case of simple linear Regression, there will be only one feature(independent variable x) in the dataset.\n",
    "\n",
    "Equation: y= m*x+c\n",
    "\n",
    "For each instance it will be like:\n",
    "\n",
    "y1 = m*x1+c\n",
    "\n",
    "y2 = m*x2+c\n",
    "\n",
    "#suppose after training the model, we get m value as 0.5, c as 2, and we have to predict the median_house_value for the first instance that has median_income as 8.3252.\n",
    "\n",
    "y = m*x+c\n",
    "\n",
    "y = 0.5*8.3252 + 2\n",
    "\n",
    "\"y\" represents the predicted value of the house price.\n",
    "\n",
    "\"x\" represents the income of the homeowner.\n",
    "\n",
    "\"m\" represents the slope of the line, which determines how much the house price changes for every change in income.\n",
    "\n",
    "\"c\" represents the y-intercept, which is the starting point of the line on the y-axis.\n",
    "\n",
    "Essentially, we're using the equation to find a line that best fits the relationship between income and house price. By knowing the slope (m) and y-intercept (c), we can make predictions for new instances based on their income.\n",
    "\n",
    "Why did we take median_income for our example?"
   ]
  },
  {
   "cell_type": "code",
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       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>housing_median_age</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>longitude</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.924664</td>\n",
       "      <td>-0.108197</td>\n",
       "      <td>0.044568</td>\n",
       "      <td>0.069608</td>\n",
       "      <td>0.099773</td>\n",
       "      <td>0.055310</td>\n",
       "      <td>-0.015176</td>\n",
       "      <td>-0.045967</td>\n",
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       "    <tr>\n",
       "      <th>latitude</th>\n",
       "      <td>-0.924664</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.011173</td>\n",
       "      <td>-0.036100</td>\n",
       "      <td>-0.066983</td>\n",
       "      <td>-0.108785</td>\n",
       "      <td>-0.071035</td>\n",
       "      <td>-0.079809</td>\n",
       "      <td>-0.144160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>housing_median_age</th>\n",
       "      <td>-0.108197</td>\n",
       "      <td>0.011173</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.361262</td>\n",
       "      <td>-0.320451</td>\n",
       "      <td>-0.296244</td>\n",
       "      <td>-0.302916</td>\n",
       "      <td>-0.119034</td>\n",
       "      <td>0.105623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_rooms</th>\n",
       "      <td>0.044568</td>\n",
       "      <td>-0.036100</td>\n",
       "      <td>-0.361262</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.930380</td>\n",
       "      <td>0.857126</td>\n",
       "      <td>0.918484</td>\n",
       "      <td>0.198050</td>\n",
       "      <td>0.134153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_bedrooms</th>\n",
       "      <td>0.069608</td>\n",
       "      <td>-0.066983</td>\n",
       "      <td>-0.320451</td>\n",
       "      <td>0.930380</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.877747</td>\n",
       "      <td>0.979728</td>\n",
       "      <td>-0.007723</td>\n",
       "      <td>0.049686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>population</th>\n",
       "      <td>0.099773</td>\n",
       "      <td>-0.108785</td>\n",
       "      <td>-0.296244</td>\n",
       "      <td>0.857126</td>\n",
       "      <td>0.877747</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.907222</td>\n",
       "      <td>0.004834</td>\n",
       "      <td>-0.024650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>households</th>\n",
       "      <td>0.055310</td>\n",
       "      <td>-0.071035</td>\n",
       "      <td>-0.302916</td>\n",
       "      <td>0.918484</td>\n",
       "      <td>0.979728</td>\n",
       "      <td>0.907222</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.013033</td>\n",
       "      <td>0.065843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>median_income</th>\n",
       "      <td>-0.015176</td>\n",
       "      <td>-0.079809</td>\n",
       "      <td>-0.119034</td>\n",
       "      <td>0.198050</td>\n",
       "      <td>-0.007723</td>\n",
       "      <td>0.004834</td>\n",
       "      <td>0.013033</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.688075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>median_house_value</th>\n",
       "      <td>-0.045967</td>\n",
       "      <td>-0.144160</td>\n",
       "      <td>0.105623</td>\n",
       "      <td>0.134153</td>\n",
       "      <td>0.049686</td>\n",
       "      <td>-0.024650</td>\n",
       "      <td>0.065843</td>\n",
       "      <td>0.688075</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    longitude  latitude  housing_median_age  total_rooms  \\\n",
       "longitude            1.000000 -0.924664           -0.108197     0.044568   \n",
       "latitude            -0.924664  1.000000            0.011173    -0.036100   \n",
       "housing_median_age  -0.108197  0.011173            1.000000    -0.361262   \n",
       "total_rooms          0.044568 -0.036100           -0.361262     1.000000   \n",
       "total_bedrooms       0.069608 -0.066983           -0.320451     0.930380   \n",
       "population           0.099773 -0.108785           -0.296244     0.857126   \n",
       "households           0.055310 -0.071035           -0.302916     0.918484   \n",
       "median_income       -0.015176 -0.079809           -0.119034     0.198050   \n",
       "median_house_value  -0.045967 -0.144160            0.105623     0.134153   \n",
       "\n",
       "                    total_bedrooms  population  households  median_income  \\\n",
       "longitude                 0.069608    0.099773    0.055310      -0.015176   \n",
       "latitude                 -0.066983   -0.108785   -0.071035      -0.079809   \n",
       "housing_median_age       -0.320451   -0.296244   -0.302916      -0.119034   \n",
       "total_rooms               0.930380    0.857126    0.918484       0.198050   \n",
       "total_bedrooms            1.000000    0.877747    0.979728      -0.007723   \n",
       "population                0.877747    1.000000    0.907222       0.004834   \n",
       "households                0.979728    0.907222    1.000000       0.013033   \n",
       "median_income            -0.007723    0.004834    0.013033       1.000000   \n",
       "median_house_value        0.049686   -0.024650    0.065843       0.688075   \n",
       "\n",
       "                    median_house_value  \n",
       "longitude                    -0.045967  \n",
       "latitude                     -0.144160  \n",
       "housing_median_age            0.105623  \n",
       "total_rooms                   0.134153  \n",
       "total_bedrooms                0.049686  \n",
       "population                   -0.024650  \n",
       "households                    0.065843  \n",
       "median_income                 0.688075  \n",
       "median_house_value            1.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As Simple Linear Regression tells us about the linear relationship between two variables, we see that median_income is most correlated with median_house_value. That means it can be most useful in predicting the median_house_value. That's why we choose median_income for the explanation of simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression\n",
    "\n",
    "In multiple linear regression, we consider more than one feature in the dataset to predict the value of a target variable. Let's say we want to predict the median house value based on various factors such as longitude, latitude, housing median age, total rooms, total bedrooms, and ocean proximity.\n",
    "\n",
    "The equation for multiple linear regression can be written as:\n",
    "\n",
    "y = m1 * longitude + m2 * latitude + m3 * housing_median_age + ... + m9 * ocean_proximity + c\n",
    "\n",
    "To make it more concise, we can represent the weights associated with each feature (m1, m2, m3, ..., m9) as a vector called m_vec and the features (longitude, latitude, ..., ocean_proximity) as a vector called x_vector. The equation becomes:\n",
    "\n",
    "y = m_vec * x_vector + c\n",
    "\n",
    "In this equation:\n",
    "\n",
    "m_vec represents a vector of weights associated with each feature.\n",
    "\n",
    "x_vector represents a vector of the respective feature values (longitude, latitude, ..., ocean_proximity).\n",
    "\n",
    "y represents the predicted median house value.\n",
    "\n",
    "c represents the intercept.\n",
    "\n",
    "To calculate the median house value for the first instance in the dataset, we can plug in the corresponding feature values into the equation. For example, let's assume the values are:\n",
    "  \n",
    "y = m1*-122.23 + m2*37.88 + m3*41.0 +.....+m9*1 + c #NEAR_BAY is denoted as 1\n",
    "#Numpy works good on computations of vectors and that's why we vectrorize it\n",
    "\n",
    "y = m_vec.x_vec\n",
    "\n",
    "m_vec = [m1,m2,m3,..m9]\n",
    "\n",
    "x_vec = [-122.23\t37.88\t..... 1]\n",
    "\n",
    "By performing this vectorized computation, we can calculate the predicted median house value (y) based on the given feature values and their corresponding weights.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now from here for a better explanation, i will explain on the basis of one variable, i.e. median_income"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = housing['median_income']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = housing['median_house_value']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "x = housing['median_income']\n",
    "y = housing['median_house_value']\n",
    "plt.scatter(x,y)\n",
    "plt.xlabel(\"Median Income\")\n",
    "plt.ylabel(\"Median House Value\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot here, we can easily see that median_house_value is positively correlated with median_income, i.e., it increases with the increase in median_income\n",
    "\n",
    "Here median_house_value is capped at 50000. That means there were initially data points which had values more than 50000 but we reduced all of them to 50000\n",
    "median_house_value = 60000 ->50000\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# R_Squared:\n",
    "\n",
    "R-Squared is a number that explains the amount of variation that is explained/captured by the developed model. In easy words, it tells us how much our model is better than the baseline model. R-Squared uses mean of the actual values as the baseline model. So it is telling us how much our line is better in prediction in comparison to if we used the mean value of the dataset as prediction.\n",
    "\n",
    "We use it when we want to know how well your model is doing compared to a very simple model that just uses the average median house value for every instance, regardless of their weight. \n",
    "\n",
    "R-squared helps you measure that. It's a number between 0 and 1 that tells you how much better your model is at making predictions compared to just using the average value. \n",
    "\n",
    "Here's an example: Let's say your model has an R-squared value of 0.8. This means that about 80% of the variation in median house value can be explained by the weight in your model. In other words, your model is doing a pretty good job of capturing the relationship between median_income and median_house_value, and it's much better than just using the average value for everyone.\n",
    "\n",
    "So, R-squared is a way to measure how well your model is performing compared to a simple baseline model. The higher the R-squared value, the better your model is at explaining the variation in the data and making predictions.\n",
    "\n",
    "R-squared = 1 - (RSS / TSS)\n",
    "\n",
    "RSS (Residual Sum of Squares) represents the sum of the squared differences between the actual target variable values and the predicted values obtained from the regression model.\n",
    "TSS (Total Sum of Squares) represents the sum of the squared differences between the actual target variable values and the mean of the target variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's visualize it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "206855.81690891474\n"
     ]
    }
   ],
   "source": [
    "#We'll calculate the mean value of the median_house_value and will use it as predictions to see that r square\n",
    "#value will be 0 for the mean line\n",
    "\n",
    "mean = np.mean(housing['median_house_value'])\n",
    "print(mean)\n",
    "mean_pred = np.array([mean]*20640)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error,r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13315503000.818077"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(housing['median_house_value'],mean_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(housing['median_house_value'],mean_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now let's build a real LinearRegression model which we'll use to predict the median_house_value for input value\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20640, 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array(housing['median_income'])\n",
    "x = x.reshape(-1,1)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model=LinearRegression()\n",
    "model.fit(x,housing['median_house_value'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([41793.8492019]), 45085.57670326799)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#These are the model coefficients m and c\n",
    "model.coef_,model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now  lets generate prediction for our dataset using the LinearRegression model\n",
    "model_prediction = model.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47344749180719903"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see its r square value\n",
    "r2_score(housing['median_house_value'],model_prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7011311502.929527"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(housing['median_house_value'],model_prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": [
    "plt.scatter(housing['median_income'],housing['median_house_value'],label=\"Actual Values\")\n",
    "plt.plot(x,model_prediction, color='violet',label = 'Model Line')\n",
    "plt.xlabel(\"Median Income\")\n",
    "plt.ylabel(\"Median House Value\")\n",
    "plt.plot([0,14],[206855,206855],color='red',label=\"Mean Line\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A better visualization\n",
    "plt.rcParams[\"figure.figsize\"] = (8,8)\n",
    "plt.scatter(x[:10],y[:10],label=\"Actual values\")\n",
    "plt.xlabel(\"Median Income\")\n",
    "plt.ylabel(\"Median House Value\")\n",
    "plt.plot(x,model_prediction, color='violet',label = 'Model Line')\n",
    "plt.plot([0,14],[206855,206855],color='red', label=\"Mean Line\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:7: MatplotlibDeprecationWarning: Case-insensitive properties were deprecated in 3.3 and support will be removed two minor releases later\n",
      "  import sys\n",
      "/usr/local/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:10: MatplotlibDeprecationWarning: Case-insensitive properties were deprecated in 3.3 and support will be removed two minor releases later\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now let's zoom in a little to show RSS and TSS\n",
    "plt.scatter(x[:10],y[:10],label=\"Actual values\")\n",
    "plt.xlabel(\"Median Income\")\n",
    "plt.ylabel(\"Median House Value\")\n",
    "plt.plot(x,model_prediction, color='violet',label = 'Model Line')\n",
    "plt.plot([0,14],[206855,206855],color='red', label=\"Mean Line\")\n",
    "plt.plot([8.3014,8.3014],[358500,392033],color='green', Label=\"RSS\",linestyle='--', linewidth=2.0)\n",
    "plt.plot(8.3014,392033,color='green',marker='.',markersize=20)\n",
    "plt.plot(8.3014,206855,color='orange',marker='.',markersize=20)\n",
    "plt.plot([8.3014,8.3014],[206855,358500],color='orange', Label=\"TSS\",linestyle='--', linewidth=2.0)\n",
    "plt.legend()\n",
    "plt.xlim(6,10)\n",
    "plt.ylim((190000,400000))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}