simple _linear_regression_house_dataset.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\program files\\python36\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "housing_df = pd.read_csv(\"data/housing.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  PRICE  \n",
       "0     15.3  396.90   4.98   24.0  \n",
       "1     17.8  396.90   9.14   21.6  \n",
       "2     17.8  392.83   4.03   34.7  \n",
       "3     18.7  394.63   2.94   33.4  \n",
       "4     18.7  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 14)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.593761</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.596783</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.647422</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.593761   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.596783   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.647422   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT       PRICE  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = housing_df.drop('PRICE', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y = housing_df['PRICE']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    24.0\n",
       "1    21.6\n",
       "2    34.7\n",
       "3    33.4\n",
       "4    36.2\n",
       "Name: PRICE, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.33, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(339, 13)\n",
      "(167, 13)\n",
      "(339,)\n",
      "(167,)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X_train, Y_train)\n",
    "\n",
    "Y_pred = lm.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1f7c1243cc0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7mV3B/HmjzJu7X2ZlnNbZPDk1zQXrtnLD7TsKV+Z5Zp1tdg6ptGDkdFiz/lIo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f7bf1ada20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Y_test, Y_pred)\n",
    "plt.xlabel(\"Prices: $Y_i$\")\n",
    "plt.ylabel(\"Predicted prices: $\\hat{Y}_i$\")\n",
    "plt.title(\"Prices vs Predicted prices: $Y_i$ vs $\\hat{Y}_i$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28.5413672756\n"
     ]
    }
   ],
   "source": [
    "mse = sklearn.metrics.mean_squared_error(Y_test, Y_pred)\n",
    "print(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}