linearregression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = os.getcwd() + '/data/ex1data1.txt'  \n",
    "data = pd.read_csv(path, header=None, names=['Population', 'Profit'])  \n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population     Profit\n",
       "count   97.000000  97.000000\n",
       "mean     8.159800   5.839135\n",
       "std      3.869884   5.510262\n",
       "min      5.026900  -2.680700\n",
       "25%      5.707700   1.986900\n",
       "50%      6.589400   4.562300\n",
       "75%      8.578100   7.046700\n",
       "max     22.203000  24.147000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1cf40288d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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NdHL75MEcmujk/JnjwgH0eKMJjBoj0ezYqH/cutVI1yD+gJ8+cSSnjh0e2VF86Ke1N5pn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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1cf42d0b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.insert(0, 'Ones', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population   Profit\n",
       "0     1      6.1101  17.5920\n",
       "1     1      5.5277   9.1302\n",
       "2     1      8.5186  13.6620\n",
       "3     1      7.0032  11.8540\n",
       "4     1      5.8598   6.8233"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = data.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>8.3829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>7.4764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>6.4862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>14.1640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>8.4084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>5.6407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>5.3794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>6.4296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>20.2700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>18.9450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>12.8280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>10.9570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>13.1760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>22.2030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>1</td>\n",
       "      <td>10.2360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>1</td>\n",
       "      <td>20.3410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>1</td>\n",
       "      <td>10.1360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>1</td>\n",
       "      <td>7.3345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>1</td>\n",
       "      <td>6.0062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>1</td>\n",
       "      <td>7.2259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>1</td>\n",
       "      <td>6.5479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>1</td>\n",
       "      <td>7.5386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>1</td>\n",
       "      <td>10.2740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>1</td>\n",
       "      <td>9.7687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>1</td>\n",
       "      <td>6.5159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>1</td>\n",
       "      <td>9.1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>1</td>\n",
       "      <td>6.0020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>1</td>\n",
       "      <td>7.6366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>1</td>\n",
       "      <td>5.3054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>1</td>\n",
       "      <td>8.2934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1</td>\n",
       "      <td>13.3940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4369</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>97 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Ones  Population\n",
       "0      1      6.1101\n",
       "1      1      5.5277\n",
       "2      1      8.5186\n",
       "3      1      7.0032\n",
       "4      1      5.8598\n",
       "5      1      8.3829\n",
       "6      1      7.4764\n",
       "7      1      8.5781\n",
       "8      1      6.4862\n",
       "9      1      5.0546\n",
       "10     1      5.7107\n",
       "11     1     14.1640\n",
       "12     1      5.7340\n",
       "13     1      8.4084\n",
       "14     1      5.6407\n",
       "15     1      5.3794\n",
       "16     1      6.3654\n",
       "17     1      5.1301\n",
       "18     1      6.4296\n",
       "19     1      7.0708\n",
       "20     1      6.1891\n",
       "21     1     20.2700\n",
       "22     1      5.4901\n",
       "23     1      6.3261\n",
       "24     1      5.5649\n",
       "25     1     18.9450\n",
       "26     1     12.8280\n",
       "27     1     10.9570\n",
       "28     1     13.1760\n",
       "29     1     22.2030\n",
       "..   ...         ...\n",
       "67     1     10.2360\n",
       "68     1      5.4994\n",
       "69     1     20.3410\n",
       "70     1     10.1360\n",
       "71     1      7.3345\n",
       "72     1      6.0062\n",
       "73     1      7.2259\n",
       "74     1      5.0269\n",
       "75     1      6.5479\n",
       "76     1      7.5386\n",
       "77     1      5.0365\n",
       "78     1     10.2740\n",
       "79     1      5.1077\n",
       "80     1      5.7292\n",
       "81     1      5.1884\n",
       "82     1      6.3557\n",
       "83     1      9.7687\n",
       "84     1      6.5159\n",
       "85     1      8.5172\n",
       "86     1      9.1802\n",
       "87     1      6.0020\n",
       "88     1      5.5204\n",
       "89     1      5.0594\n",
       "90     1      5.7077\n",
       "91     1      7.6366\n",
       "92     1      5.8707\n",
       "93     1      5.3054\n",
       "94     1      8.2934\n",
       "95     1     13.3940\n",
       "96     1      5.4369\n",
       "\n",
       "[97 rows x 2 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data.iloc[:,0:cols-1]  \n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.59200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.13020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.66200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.85400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.82330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>11.88600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.34830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.59870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.81660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.25220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>15.50500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.15510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.22580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.71618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>3.51290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5.30480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.56077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3.65180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.38930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3.13860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>21.76700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>4.26300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.18750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>3.08250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>22.63800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>13.50100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>7.04670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>14.69200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>24.14700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>7.77540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>1.01730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>20.99200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>6.67990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>4.02590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>1.27840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>3.34110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>-2.68070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.29678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>3.88450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>5.70140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>6.75260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>2.05760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.47953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.20421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.67861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>7.54350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>5.34360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>4.24150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>6.79810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.92695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.15200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>2.82140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1.84510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>4.29590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>7.20290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>1.98690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.14454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>9.05510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>97 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Profit\n",
       "0   17.59200\n",
       "1    9.13020\n",
       "2   13.66200\n",
       "3   11.85400\n",
       "4    6.82330\n",
       "5   11.88600\n",
       "6    4.34830\n",
       "7   12.00000\n",
       "8    6.59870\n",
       "9    3.81660\n",
       "10   3.25220\n",
       "11  15.50500\n",
       "12   3.15510\n",
       "13   7.22580\n",
       "14   0.71618\n",
       "15   3.51290\n",
       "16   5.30480\n",
       "17   0.56077\n",
       "18   3.65180\n",
       "19   5.38930\n",
       "20   3.13860\n",
       "21  21.76700\n",
       "22   4.26300\n",
       "23   5.18750\n",
       "24   3.08250\n",
       "25  22.63800\n",
       "26  13.50100\n",
       "27   7.04670\n",
       "28  14.69200\n",
       "29  24.14700\n",
       "..       ...\n",
       "67   7.77540\n",
       "68   1.01730\n",
       "69  20.99200\n",
       "70   6.67990\n",
       "71   4.02590\n",
       "72   1.27840\n",
       "73   3.34110\n",
       "74  -2.68070\n",
       "75   0.29678\n",
       "76   3.88450\n",
       "77   5.70140\n",
       "78   6.75260\n",
       "79   2.05760\n",
       "80   0.47953\n",
       "81   0.20421\n",
       "82   0.67861\n",
       "83   7.54350\n",
       "84   5.34360\n",
       "85   4.24150\n",
       "86   6.79810\n",
       "87   0.92695\n",
       "88   0.15200\n",
       "89   2.82140\n",
       "90   1.84510\n",
       "91   4.29590\n",
       "92   7.20290\n",
       "93   1.98690\n",
       "94   0.14454\n",
       "95   9.05510\n",
       "96   0.61705\n",
       "\n",
       "[97 rows x 1 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data.iloc[:,cols-1:cols]\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.matrix(X.values)  \n",
    "y = np.matrix(y.values) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  1.    ,   6.1101],\n",
       "        [  1.    ,   5.5277],\n",
       "        [  1.    ,   8.5186],\n",
       "        [  1.    ,   7.0032],\n",
       "        [  1.    ,   5.8598],\n",
       "        [  1.    ,   8.3829],\n",
       "        [  1.    ,   7.4764],\n",
       "        [  1.    ,   8.5781],\n",
       "        [  1.    ,   6.4862],\n",
       "        [  1.    ,   5.0546],\n",
       "        [  1.    ,   5.7107],\n",
       "        [  1.    ,  14.164 ],\n",
       "        [  1.    ,   5.734 ],\n",
       "        [  1.    ,   8.4084],\n",
       "        [  1.    ,   5.6407],\n",
       "        [  1.    ,   5.3794],\n",
       "        [  1.    ,   6.3654],\n",
       "        [  1.    ,   5.1301],\n",
       "        [  1.    ,   6.4296],\n",
       "        [  1.    ,   7.0708],\n",
       "        [  1.    ,   6.1891],\n",
       "        [  1.    ,  20.27  ],\n",
       "        [  1.    ,   5.4901],\n",
       "        [  1.    ,   6.3261],\n",
       "        [  1.    ,   5.5649],\n",
       "        [  1.    ,  18.945 ],\n",
       "        [  1.    ,  12.828 ],\n",
       "        [  1.    ,  10.957 ],\n",
       "        [  1.    ,  13.176 ],\n",
       "        [  1.    ,  22.203 ],\n",
       "        [  1.    ,   5.2524],\n",
       "        [  1.    ,   6.5894],\n",
       "        [  1.    ,   9.2482],\n",
       "        [  1.    ,   5.8918],\n",
       "        [  1.    ,   8.2111],\n",
       "        [  1.    ,   7.9334],\n",
       "        [  1.    ,   8.0959],\n",
       "        [  1.    ,   5.6063],\n",
       "        [  1.    ,  12.836 ],\n",
       "        [  1.    ,   6.3534],\n",
       "        [  1.    ,   5.4069],\n",
       "        [  1.    ,   6.8825],\n",
       "        [  1.    ,  11.708 ],\n",
       "        [  1.    ,   5.7737],\n",
       "        [  1.    ,   7.8247],\n",
       "        [  1.    ,   7.0931],\n",
       "        [  1.    ,   5.0702],\n",
       "        [  1.    ,   5.8014],\n",
       "        [  1.    ,  11.7   ],\n",
       "        [  1.    ,   5.5416],\n",
       "        [  1.    ,   7.5402],\n",
       "        [  1.    ,   5.3077],\n",
       "        [  1.    ,   7.4239],\n",
       "        [  1.    ,   7.6031],\n",
       "        [  1.    ,   6.3328],\n",
       "        [  1.    ,   6.3589],\n",
       "        [  1.    ,   6.2742],\n",
       "        [  1.    ,   5.6397],\n",
       "        [  1.    ,   9.3102],\n",
       "        [  1.    ,   9.4536],\n",
       "        [  1.    ,   8.8254],\n",
       "        [  1.    ,   5.1793],\n",
       "        [  1.    ,  21.279 ],\n",
       "        [  1.    ,  14.908 ],\n",
       "        [  1.    ,  18.959 ],\n",
       "        [  1.    ,   7.2182],\n",
       "        [  1.    ,   8.2951],\n",
       "        [  1.    ,  10.236 ],\n",
       "        [  1.    ,   5.4994],\n",
       "        [  1.    ,  20.341 ],\n",
       "        [  1.    ,  10.136 ],\n",
       "        [  1.    ,   7.3345],\n",
       "        [  1.    ,   6.0062],\n",
       "        [  1.    ,   7.2259],\n",
       "        [  1.    ,   5.0269],\n",
       "        [  1.    ,   6.5479],\n",
       "        [  1.    ,   7.5386],\n",
       "        [  1.    ,   5.0365],\n",
       "        [  1.    ,  10.274 ],\n",
       "        [  1.    ,   5.1077],\n",
       "        [  1.    ,   5.7292],\n",
       "        [  1.    ,   5.1884],\n",
       "        [  1.    ,   6.3557],\n",
       "        [  1.    ,   9.7687],\n",
       "        [  1.    ,   6.5159],\n",
       "        [  1.    ,   8.5172],\n",
       "        [  1.    ,   9.1802],\n",
       "        [  1.    ,   6.002 ],\n",
       "        [  1.    ,   5.5204],\n",
       "        [  1.    ,   5.0594],\n",
       "        [  1.    ,   5.7077],\n",
       "        [  1.    ,   7.6366],\n",
       "        [  1.    ,   5.8707],\n",
       "        [  1.    ,   5.3054],\n",
       "        [  1.    ,   8.2934],\n",
       "        [  1.    ,  13.394 ],\n",
       "        [  1.    ,   5.4369]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((97, 2), (1, 2), (97, 1))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, theta.shape, y.shape  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def computecost(X,y,theta):\n",
    "    inner=np.power(((X*theta.T)-y),2)\n",
    "    suminner=np.sum(inner)\n",
    "    return suminner/(2*len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computecost(X,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradient(X,y,theta,alpha,iters):\n",
    "    temp=np.matrix(np.zeros(theta.shape))\n",
    "    parameter=int(theta.shape[1])\n",
    "    cost=np.zeros(iters)\n",
    "    for i in range(iters):\n",
    "        error=(X*theta.T)-y\n",
    "        for j in range(parameter):\n",
    "            term=np.multiply(error,X[:,j])\n",
    "            temp[0,j]=theta[0,j]-((alpha/len(X))*np.sum(term))\n",
    "        theta = temp\n",
    "        cost[i]=computecost(X,y,theta)\n",
    "    return theta,cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha=0.011\n",
    "iters=2000\n",
    "theta , cost=gradient(X,y,theta,alpha,iters)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-3.82072289,  1.18549325]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000,)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.4774842648966278"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computecost(X,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  5.0269    ,   5.20039596,   5.37389192,   5.54738788,\n",
       "         5.72088384,   5.8943798 ,   6.06787576,   6.24137172,\n",
       "         6.41486768,   6.58836364,   6.7618596 ,   6.93535556,\n",
       "         7.10885152,   7.28234747,   7.45584343,   7.62933939,\n",
       "         7.80283535,   7.97633131,   8.14982727,   8.32332323,\n",
       "         8.49681919,   8.67031515,   8.84381111,   9.01730707,\n",
       "         9.19080303,   9.36429899,   9.53779495,   9.71129091,\n",
       "         9.88478687,  10.05828283,  10.23177879,  10.40527475,\n",
       "        10.57877071,  10.75226667,  10.92576263,  11.09925859,\n",
       "        11.27275455,  11.44625051,  11.61974646,  11.79324242,\n",
       "        11.96673838,  12.14023434,  12.3137303 ,  12.48722626,\n",
       "        12.66072222,  12.83421818,  13.00771414,  13.1812101 ,\n",
       "        13.35470606,  13.52820202,  13.70169798,  13.87519394,\n",
       "        14.0486899 ,  14.22218586,  14.39568182,  14.56917778,\n",
       "        14.74267374,  14.9161697 ,  15.08966566,  15.26316162,\n",
       "        15.43665758,  15.61015354,  15.78364949,  15.95714545,\n",
       "        16.13064141,  16.30413737,  16.47763333,  16.65112929,\n",
       "        16.82462525,  16.99812121,  17.17161717,  17.34511313,\n",
       "        17.51860909,  17.69210505,  17.86560101,  18.03909697,\n",
       "        18.21259293,  18.38608889,  18.55958485,  18.73308081,\n",
       "        18.90657677,  19.08007273,  19.25356869,  19.42706465,\n",
       "        19.60056061,  19.77405657,  19.94755253,  20.12104848,\n",
       "        20.29454444,  20.4680404 ,  20.64153636,  20.81503232,\n",
       "        20.98852828,  21.16202424,  21.3355202 ,  21.50901616,\n",
       "        21.68251212,  21.85600808,  22.02950404,  22.203     ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(data.Population.min(), data.Population.max(), 100) \n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.13863315,   2.34431144,   2.54998973,   2.75566802,\n",
       "         2.96134631,   3.1670246 ,   3.37270289,   3.57838118,\n",
       "         3.78405947,   3.98973776,   4.19541605,   4.40109434,\n",
       "         4.60677263,   4.81245092,   5.01812921,   5.2238075 ,\n",
       "         5.42948579,   5.63516408,   5.84084237,   6.04652066,\n",
       "         6.25219895,   6.45787724,   6.66355553,   6.86923382,\n",
       "         7.07491211,   7.2805904 ,   7.48626869,   7.69194698,\n",
       "         7.89762527,   8.10330356,   8.30898185,   8.51466014,\n",
       "         8.72033843,   8.92601672,   9.13169501,   9.3373733 ,\n",
       "         9.54305159,   9.74872988,   9.95440817,  10.16008646,\n",
       "        10.36576475,  10.57144304,  10.77712133,  10.98279962,\n",
       "        11.18847791,  11.3941562 ,  11.59983449,  11.80551278,\n",
       "        12.01119107,  12.21686936,  12.42254765,  12.62822594,\n",
       "        12.83390423,  13.03958252,  13.24526081,  13.4509391 ,\n",
       "        13.65661739,  13.86229568,  14.06797397,  14.27365226,\n",
       "        14.47933055,  14.68500884,  14.89068713,  15.09636542,\n",
       "        15.30204371,  15.507722  ,  15.71340029,  15.91907858,\n",
       "        16.12475687,  16.33043516,  16.53611345,  16.74179174,\n",
       "        16.94747003,  17.15314832,  17.3588266 ,  17.56450489,\n",
       "        17.77018318,  17.97586147,  18.18153976,  18.38721805,\n",
       "        18.59289634,  18.79857463,  19.00425292,  19.20993121,\n",
       "        19.4156095 ,  19.62128779,  19.82696608,  20.03264437,\n",
       "        20.23832266,  20.44400095,  20.64967924,  20.85535753,\n",
       "        21.06103582,  21.26671411,  21.4723924 ,  21.67807069,\n",
       "        21.88374898,  22.08942727,  22.29510556,  22.50078385])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y=theta[0,0]+(theta[0,1]*x)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,u'Predicted Profit vs. Population Size')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bb7xxyjxbtmzxyYgW1tozPhceHn7ycXBwMFVVVU2+fhEREZHWQLf99rExY8awbt06XC4X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\nmlTPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1cec119410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))  \n",
    "ax.plot(x, Y, label='Prediction')  \n",
    "ax.scatter(data.Population, data.Profit, label='Traning Data')  \n",
    "ax.legend(loc=2)  \n",
    "ax.set_xlabel('Population')  \n",
    "ax.set_ylabel('Profit')  \n",
    "ax.set_title('Predicted Profit vs. Population Size')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-3.82072289,  1.18549325]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0424988829830486"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h=theta[0,0]+(theta[0,1]*7.4764)\n",
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ones</th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.59200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.13020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.66200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.85400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.82330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>8.3829</td>\n",
       "      <td>11.88600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>7.4764</td>\n",
       "      <td>4.34830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5781</td>\n",
       "      <td>12.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>6.4862</td>\n",
       "      <td>6.59870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0546</td>\n",
       "      <td>3.81660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7107</td>\n",
       "      <td>3.25220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>14.1640</td>\n",
       "      <td>15.50500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7340</td>\n",
       "      <td>3.15510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>8.4084</td>\n",
       "      <td>7.22580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>5.6407</td>\n",
       "      <td>0.71618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>5.3794</td>\n",
       "      <td>3.51290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3654</td>\n",
       "      <td>5.30480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1301</td>\n",
       "      <td>0.56077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>6.4296</td>\n",
       "      <td>3.65180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0708</td>\n",
       "      <td>5.38930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1891</td>\n",
       "      <td>3.13860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>20.2700</td>\n",
       "      <td>21.76700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4901</td>\n",
       "      <td>4.26300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3261</td>\n",
       "      <td>5.18750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5649</td>\n",
       "      <td>3.08250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>18.9450</td>\n",
       "      <td>22.63800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>12.8280</td>\n",
       "      <td>13.50100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>10.9570</td>\n",
       "      <td>7.04670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>13.1760</td>\n",
       "      <td>14.69200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>22.2030</td>\n",
       "      <td>24.14700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>1</td>\n",
       "      <td>10.2360</td>\n",
       "      <td>7.77540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4994</td>\n",
       "      <td>1.01730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>1</td>\n",
       "      <td>20.3410</td>\n",
       "      <td>20.99200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>1</td>\n",
       "      <td>10.1360</td>\n",
       "      <td>6.67990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>1</td>\n",
       "      <td>7.3345</td>\n",
       "      <td>4.02590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>1</td>\n",
       "      <td>6.0062</td>\n",
       "      <td>1.27840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>1</td>\n",
       "      <td>7.2259</td>\n",
       "      <td>3.34110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0269</td>\n",
       "      <td>-2.68070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>1</td>\n",
       "      <td>6.5479</td>\n",
       "      <td>0.29678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>1</td>\n",
       "      <td>7.5386</td>\n",
       "      <td>3.88450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0365</td>\n",
       "      <td>5.70140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>1</td>\n",
       "      <td>10.2740</td>\n",
       "      <td>6.75260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1077</td>\n",
       "      <td>2.05760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7292</td>\n",
       "      <td>0.47953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1884</td>\n",
       "      <td>0.20421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1</td>\n",
       "      <td>6.3557</td>\n",
       "      <td>0.67861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>1</td>\n",
       "      <td>9.7687</td>\n",
       "      <td>7.54350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>1</td>\n",
       "      <td>6.5159</td>\n",
       "      <td>5.34360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5172</td>\n",
       "      <td>4.24150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>1</td>\n",
       "      <td>9.1802</td>\n",
       "      <td>6.79810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>1</td>\n",
       "      <td>6.0020</td>\n",
       "      <td>0.92695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5204</td>\n",
       "      <td>0.15200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0594</td>\n",
       "      <td>2.82140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1</td>\n",
       "      <td>5.7077</td>\n",
       "      <td>1.84510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>1</td>\n",
       "      <td>7.6366</td>\n",
       "      <td>4.29590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8707</td>\n",
       "      <td>7.20290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>1</td>\n",
       "      <td>5.3054</td>\n",
       "      <td>1.98690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>1</td>\n",
       "      <td>8.2934</td>\n",
       "      <td>0.14454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1</td>\n",
       "      <td>13.3940</td>\n",
       "      <td>9.05510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>1</td>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>97 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Ones  Population    Profit\n",
       "0      1      6.1101  17.59200\n",
       "1      1      5.5277   9.13020\n",
       "2      1      8.5186  13.66200\n",
       "3      1      7.0032  11.85400\n",
       "4      1      5.8598   6.82330\n",
       "5      1      8.3829  11.88600\n",
       "6      1      7.4764   4.34830\n",
       "7      1      8.5781  12.00000\n",
       "8      1      6.4862   6.59870\n",
       "9      1      5.0546   3.81660\n",
       "10     1      5.7107   3.25220\n",
       "11     1     14.1640  15.50500\n",
       "12     1      5.7340   3.15510\n",
       "13     1      8.4084   7.22580\n",
       "14     1      5.6407   0.71618\n",
       "15     1      5.3794   3.51290\n",
       "16     1      6.3654   5.30480\n",
       "17     1      5.1301   0.56077\n",
       "18     1      6.4296   3.65180\n",
       "19     1      7.0708   5.38930\n",
       "20     1      6.1891   3.13860\n",
       "21     1     20.2700  21.76700\n",
       "22     1      5.4901   4.26300\n",
       "23     1      6.3261   5.18750\n",
       "24     1      5.5649   3.08250\n",
       "25     1     18.9450  22.63800\n",
       "26     1     12.8280  13.50100\n",
       "27     1     10.9570   7.04670\n",
       "28     1     13.1760  14.69200\n",
       "29     1     22.2030  24.14700\n",
       "..   ...         ...       ...\n",
       "67     1     10.2360   7.77540\n",
       "68     1      5.4994   1.01730\n",
       "69     1     20.3410  20.99200\n",
       "70     1     10.1360   6.67990\n",
       "71     1      7.3345   4.02590\n",
       "72     1      6.0062   1.27840\n",
       "73     1      7.2259   3.34110\n",
       "74     1      5.0269  -2.68070\n",
       "75     1      6.5479   0.29678\n",
       "76     1      7.5386   3.88450\n",
       "77     1      5.0365   5.70140\n",
       "78     1     10.2740   6.75260\n",
       "79     1      5.1077   2.05760\n",
       "80     1      5.7292   0.47953\n",
       "81     1      5.1884   0.20421\n",
       "82     1      6.3557   0.67861\n",
       "83     1      9.7687   7.54350\n",
       "84     1      6.5159   5.34360\n",
       "85     1      8.5172   4.24150\n",
       "86     1      9.1802   6.79810\n",
       "87     1      6.0020   0.92695\n",
       "88     1      5.5204   0.15200\n",
       "89     1      5.0594   2.82140\n",
       "90     1      5.7077   1.84510\n",
       "91     1      7.6366   4.29590\n",
       "92     1      5.8707   7.20290\n",
       "93     1      5.3054   1.98690\n",
       "94     1      8.2934   0.14454\n",
       "95     1     13.3940   9.05510\n",
       "96     1      5.4369   0.61705\n",
       "\n",
       "[97 rows x 3 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,u'Error vs. Training Epoch')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JklpIYfNop5SmAZtUWX9xp8c/AX7Sk+c2td13h3POgddfz4K3JEmS+rVGmt6vf9ttN5g/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1cec1bb450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))  \n",
    "ax.plot(np.arange(iters), cost, 'r')  \n",
    "ax.set_xlabel('Iterations')  \n",
    "ax.set_ylabel('Cost')  \n",
    "ax.set_title('Error vs. Training Epoch')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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