Boston_housing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Houses Prices in the Boston Area\n",
    "\n",
    "In this notebook we will use the popular Boston Housing Dataset and apply a linear regression as well as some validation tests on our regression results.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "from sklearn.datasets import load_boston # dataset\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "from statsmodels.compat import lzip\n",
    "import statsmodels.stats.api as sm\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "from sklearn.model_selection import train_test_split\n",
    "import statsmodels as sm\n",
    "import statsmodels.formula.api as sm\n",
    "from sklearn import linear_model\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# instantiate dataset and create DataFrame \n",
    "boston = load_boston()\n",
    "df = pd.DataFrame(boston.data, columns=boston.feature_names)\n",
    "target = pd.DataFrame(boston.target, columns=[\"MEDV\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'DESCR': \"Boston House Prices dataset\\n===========================\\n\\nNotes\\n------\\nData Set Characteristics:  \\n\\n    :Number of Instances: 506 \\n\\n    :Number of Attributes: 13 numeric/categorical predictive\\n    \\n    :Median Value (attribute 14) is usually the target\\n\\n    :Attribute Information (in order):\\n        - CRIM     per capita crime rate by town\\n        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\\n        - INDUS    proportion of non-retail business acres per town\\n        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\\n        - NOX      nitric oxides concentration (parts per 10 million)\\n        - RM       average number of rooms per dwelling\\n        - AGE      proportion of owner-occupied units built prior to 1940\\n        - DIS      weighted distances to five Boston employment centres\\n        - RAD      index of accessibility to radial highways\\n        - TAX      full-value property-tax rate per $10,000\\n        - PTRATIO  pupil-teacher ratio by town\\n        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\\n        - LSTAT    % lower status of the population\\n        - MEDV     Median value of owner-occupied homes in $1000's\\n\\n    :Missing Attribute Values: None\\n\\n    :Creator: Harrison, D. and Rubinfeld, D.L.\\n\\nThis is a copy of UCI ML housing dataset.\\nhttp://archive.ics.uci.edu/ml/datasets/Housing\\n\\n\\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\\n\\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\\nprices and the demand for clean air', J. Environ. Economics & Management,\\nvol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\\n...', Wiley, 1980.   N.B. Various transformations are used in the table on\\npages 244-261 of the latter.\\n\\nThe Boston house-price data has been used in many machine learning papers that address regression\\nproblems.   \\n     \\n**References**\\n\\n   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\\n   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\\n   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\\n\",\n",
       " 'data': array([[  6.32000000e-03,   1.80000000e+01,   2.31000000e+00, ...,\n",
       "           1.53000000e+01,   3.96900000e+02,   4.98000000e+00],\n",
       "        [  2.73100000e-02,   0.00000000e+00,   7.07000000e+00, ...,\n",
       "           1.78000000e+01,   3.96900000e+02,   9.14000000e+00],\n",
       "        [  2.72900000e-02,   0.00000000e+00,   7.07000000e+00, ...,\n",
       "           1.78000000e+01,   3.92830000e+02,   4.03000000e+00],\n",
       "        ..., \n",
       "        [  6.07600000e-02,   0.00000000e+00,   1.19300000e+01, ...,\n",
       "           2.10000000e+01,   3.96900000e+02,   5.64000000e+00],\n",
       "        [  1.09590000e-01,   0.00000000e+00,   1.19300000e+01, ...,\n",
       "           2.10000000e+01,   3.93450000e+02,   6.48000000e+00],\n",
       "        [  4.74100000e-02,   0.00000000e+00,   1.19300000e+01, ...,\n",
       "           2.10000000e+01,   3.96900000e+02,   7.88000000e+00]]),\n",
       " 'feature_names': array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "        'TAX', 'PTRATIO', 'B', 'LSTAT'],\n",
       "       dtype='<U7'),\n",
       " 'target': array([ 24. ,  21.6,  34.7,  33.4,  36.2,  28.7,  22.9,  27.1,  16.5,\n",
       "         18.9,  15. ,  18.9,  21.7,  20.4,  18.2,  19.9,  23.1,  17.5,\n",
       "         20.2,  18.2,  13.6,  19.6,  15.2,  14.5,  15.6,  13.9,  16.6,\n",
       "         14.8,  18.4,  21. ,  12.7,  14.5,  13.2,  13.1,  13.5,  18.9,\n",
       "         20. ,  21. ,  24.7,  30.8,  34.9,  26.6,  25.3,  24.7,  21.2,\n",
       "         19.3,  20. ,  16.6,  14.4,  19.4,  19.7,  20.5,  25. ,  23.4,\n",
       "         18.9,  35.4,  24.7,  31.6,  23.3,  19.6,  18.7,  16. ,  22.2,\n",
       "         25. ,  33. ,  23.5,  19.4,  22. ,  17.4,  20.9,  24.2,  21.7,\n",
       "         22.8,  23.4,  24.1,  21.4,  20. ,  20.8,  21.2,  20.3,  28. ,\n",
       "         23.9,  24.8,  22.9,  23.9,  26.6,  22.5,  22.2,  23.6,  28.7,\n",
       "         22.6,  22. ,  22.9,  25. ,  20.6,  28.4,  21.4,  38.7,  43.8,\n",
       "         33.2,  27.5,  26.5,  18.6,  19.3,  20.1,  19.5,  19.5,  20.4,\n",
       "         19.8,  19.4,  21.7,  22.8,  18.8,  18.7,  18.5,  18.3,  21.2,\n",
       "         19.2,  20.4,  19.3,  22. ,  20.3,  20.5,  17.3,  18.8,  21.4,\n",
       "         15.7,  16.2,  18. ,  14.3,  19.2,  19.6,  23. ,  18.4,  15.6,\n",
       "         18.1,  17.4,  17.1,  13.3,  17.8,  14. ,  14.4,  13.4,  15.6,\n",
       "         11.8,  13.8,  15.6,  14.6,  17.8,  15.4,  21.5,  19.6,  15.3,\n",
       "         19.4,  17. ,  15.6,  13.1,  41.3,  24.3,  23.3,  27. ,  50. ,\n",
       "         50. ,  50. ,  22.7,  25. ,  50. ,  23.8,  23.8,  22.3,  17.4,\n",
       "         19.1,  23.1,  23.6,  22.6,  29.4,  23.2,  24.6,  29.9,  37.2,\n",
       "         39.8,  36.2,  37.9,  32.5,  26.4,  29.6,  50. ,  32. ,  29.8,\n",
       "         34.9,  37. ,  30.5,  36.4,  31.1,  29.1,  50. ,  33.3,  30.3,\n",
       "         34.6,  34.9,  32.9,  24.1,  42.3,  48.5,  50. ,  22.6,  24.4,\n",
       "         22.5,  24.4,  20. ,  21.7,  19.3,  22.4,  28.1,  23.7,  25. ,\n",
       "         23.3,  28.7,  21.5,  23. ,  26.7,  21.7,  27.5,  30.1,  44.8,\n",
       "         50. ,  37.6,  31.6,  46.7,  31.5,  24.3,  31.7,  41.7,  48.3,\n",
       "         29. ,  24. ,  25.1,  31.5,  23.7,  23.3,  22. ,  20.1,  22.2,\n",
       "         23.7,  17.6,  18.5,  24.3,  20.5,  24.5,  26.2,  24.4,  24.8,\n",
       "         29.6,  42.8,  21.9,  20.9,  44. ,  50. ,  36. ,  30.1,  33.8,\n",
       "         43.1,  48.8,  31. ,  36.5,  22.8,  30.7,  50. ,  43.5,  20.7,\n",
       "         21.1,  25.2,  24.4,  35.2,  32.4,  32. ,  33.2,  33.1,  29.1,\n",
       "         35.1,  45.4,  35.4,  46. ,  50. ,  32.2,  22. ,  20.1,  23.2,\n",
       "         22.3,  24.8,  28.5,  37.3,  27.9,  23.9,  21.7,  28.6,  27.1,\n",
       "         20.3,  22.5,  29. ,  24.8,  22. ,  26.4,  33.1,  36.1,  28.4,\n",
       "         33.4,  28.2,  22.8,  20.3,  16.1,  22.1,  19.4,  21.6,  23.8,\n",
       "         16.2,  17.8,  19.8,  23.1,  21. ,  23.8,  23.1,  20.4,  18.5,\n",
       "         25. ,  24.6,  23. ,  22.2,  19.3,  22.6,  19.8,  17.1,  19.4,\n",
       "         22.2,  20.7,  21.1,  19.5,  18.5,  20.6,  19. ,  18.7,  32.7,\n",
       "         16.5,  23.9,  31.2,  17.5,  17.2,  23.1,  24.5,  26.6,  22.9,\n",
       "         24.1,  18.6,  30.1,  18.2,  20.6,  17.8,  21.7,  22.7,  22.6,\n",
       "         25. ,  19.9,  20.8,  16.8,  21.9,  27.5,  21.9,  23.1,  50. ,\n",
       "         50. ,  50. ,  50. ,  50. ,  13.8,  13.8,  15. ,  13.9,  13.3,\n",
       "         13.1,  10.2,  10.4,  10.9,  11.3,  12.3,   8.8,   7.2,  10.5,\n",
       "          7.4,  10.2,  11.5,  15.1,  23.2,   9.7,  13.8,  12.7,  13.1,\n",
       "         12.5,   8.5,   5. ,   6.3,   5.6,   7.2,  12.1,   8.3,   8.5,\n",
       "          5. ,  11.9,  27.9,  17.2,  27.5,  15. ,  17.2,  17.9,  16.3,\n",
       "          7. ,   7.2,   7.5,  10.4,   8.8,   8.4,  16.7,  14.2,  20.8,\n",
       "         13.4,  11.7,   8.3,  10.2,  10.9,  11. ,   9.5,  14.5,  14.1,\n",
       "         16.1,  14.3,  11.7,  13.4,   9.6,   8.7,   8.4,  12.8,  10.5,\n",
       "         17.1,  18.4,  15.4,  10.8,  11.8,  14.9,  12.6,  14.1,  13. ,\n",
       "         13.4,  15.2,  16.1,  17.8,  14.9,  14.1,  12.7,  13.5,  14.9,\n",
       "         20. ,  16.4,  17.7,  19.5,  20.2,  21.4,  19.9,  19. ,  19.1,\n",
       "         19.1,  20.1,  19.9,  19.6,  23.2,  29.8,  13.8,  13.3,  16.7,\n",
       "         12. ,  14.6,  21.4,  23. ,  23.7,  25. ,  21.8,  20.6,  21.2,\n",
       "         19.1,  20.6,  15.2,   7. ,   8.1,  13.6,  20.1,  21.8,  24.5,\n",
       "         23.1,  19.7,  18.3,  21.2,  17.5,  16.8,  22.4,  20.6,  23.9,\n",
       "         22. ,  11.9])}"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rows,Columns: (506, 13)\n"
     ]
    },
    {
     "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>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>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",
       "    </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",
       "    </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",
       "    </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",
       "    </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",
       "    </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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.647423</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",
       "    </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",
       "    </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%      3.647423   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  \n",
       "count  506.000000  \n",
       "mean    12.653063  \n",
       "std      7.141062  \n",
       "min      1.730000  \n",
       "25%      6.950000  \n",
       "50%     11.360000  \n",
       "75%     16.955000  \n",
       "max     37.970000  "
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Basic exploratory analyses \n",
    "print(\"Rows,Columns:\",df.shape)\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CRIM       0\n",
      "ZN         0\n",
      "INDUS      0\n",
      "CHAS       0\n",
      "NOX        0\n",
      "RM         0\n",
      "AGE        0\n",
      "DIS        0\n",
      "RAD        0\n",
      "TAX        0\n",
      "PTRATIO    0\n",
      "B          0\n",
      "LSTAT      0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# count missing values\n",
    "print(df.isnull().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# split dataset into training and testing set\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(df, target, test_size=0.30)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fitting using stats model\n",
    "model_1 = smf.OLS(Y_train,X_train).fit()\n",
    "prediction_1 = model_1.predict(X_train) # predict y_train values\n",
    "prediction_2 = model_1.predict(X_test)# predict y_test values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.966</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.964</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   734.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 05 Oct 2017</td> <th>  Prob (F-statistic):</th> <td>2.74e-240</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:28:26</td>     <th>  Log-Likelihood:    </th> <td> -1031.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   354</td>      <th>  AIC:               </th> <td>   2089.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   341</td>      <th>  BIC:               </th> <td>   2139.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>    <td>   -0.1208</td> <td>    0.039</td> <td>   -3.122</td> <td> 0.002</td> <td>   -0.197</td> <td>   -0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>      <td>    0.0495</td> <td>    0.016</td> <td>    3.142</td> <td> 0.002</td> <td>    0.019</td> <td>    0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>INDUS</th>   <td>    0.0313</td> <td>    0.069</td> <td>    0.455</td> <td> 0.650</td> <td>   -0.104</td> <td>    0.167</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>    <td>    2.6447</td> <td>    0.999</td> <td>    2.646</td> <td> 0.009</td> <td>    0.679</td> <td>    4.611</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NOX</th>     <td>   -8.7498</td> <td>    3.795</td> <td>   -2.305</td> <td> 0.022</td> <td>  -16.215</td> <td>   -1.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>      <td>    6.7493</td> <td>    0.349</td> <td>   19.313</td> <td> 0.000</td> <td>    6.062</td> <td>    7.437</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>     <td>   -0.0092</td> <td>    0.015</td> <td>   -0.603</td> <td> 0.547</td> <td>   -0.039</td> <td>    0.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>     <td>   -1.0861</td> <td>    0.215</td> <td>   -5.046</td> <td> 0.000</td> <td>   -1.509</td> <td>   -0.663</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>     <td>    0.1297</td> <td>    0.071</td> <td>    1.815</td> <td> 0.070</td> <td>   -0.011</td> <td>    0.270</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>     <td>   -0.0081</td> <td>    0.004</td> <td>   -1.962</td> <td> 0.051</td> <td>   -0.016</td> <td> 2.04e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th> <td>   -0.5884</td> <td>    0.124</td> <td>   -4.734</td> <td> 0.000</td> <td>   -0.833</td> <td>   -0.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>B</th>       <td>    0.0162</td> <td>    0.003</td> <td>    5.490</td> <td> 0.000</td> <td>    0.010</td> <td>    0.022</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>   <td>   -0.3189</td> <td>    0.061</td> <td>   -5.268</td> <td> 0.000</td> <td>   -0.438</td> <td>   -0.200</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>124.358</td> <th>  Durbin-Watson:     </th> <td>   1.944</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 924.657</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.262</td>  <th>  Prob(JB):          </th> <td>1.63e-201</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>10.505</td>  <th>  Cond. No.          </th> <td>8.86e+03</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.966\n",
       "Model:                            OLS   Adj. R-squared:                  0.964\n",
       "Method:                 Least Squares   F-statistic:                     734.5\n",
       "Date:                Thu, 05 Oct 2017   Prob (F-statistic):          2.74e-240\n",
       "Time:                        18:28:26   Log-Likelihood:                -1031.6\n",
       "No. Observations:                 354   AIC:                             2089.\n",
       "Df Residuals:                     341   BIC:                             2139.\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "CRIM          -0.1208      0.039     -3.122      0.002      -0.197      -0.045\n",
       "ZN             0.0495      0.016      3.142      0.002       0.019       0.081\n",
       "INDUS          0.0313      0.069      0.455      0.650      -0.104       0.167\n",
       "CHAS           2.6447      0.999      2.646      0.009       0.679       4.611\n",
       "NOX           -8.7498      3.795     -2.305      0.022     -16.215      -1.285\n",
       "RM             6.7493      0.349     19.313      0.000       6.062       7.437\n",
       "AGE           -0.0092      0.015     -0.603      0.547      -0.039       0.021\n",
       "DIS           -1.0861      0.215     -5.046      0.000      -1.509      -0.663\n",
       "RAD            0.1297      0.071      1.815      0.070      -0.011       0.270\n",
       "TAX           -0.0081      0.004     -1.962      0.051      -0.016    2.04e-05\n",
       "PTRATIO       -0.5884      0.124     -4.734      0.000      -0.833      -0.344\n",
       "B              0.0162      0.003      5.490      0.000       0.010       0.022\n",
       "LSTAT         -0.3189      0.061     -5.268      0.000      -0.438      -0.200\n",
       "==============================================================================\n",
       "Omnibus:                      124.358   Durbin-Watson:                   1.944\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              924.657\n",
       "Skew:                           1.262   Prob(JB):                    1.63e-201\n",
       "Kurtosis:                      10.505   Cond. No.                     8.86e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 8.86e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 274,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Looking at the Summary\n",
    "\n",
    "In the summary we see some interesting results. The INDUS coefficient (proportion of non-retail business acres per town) is not nearly statistically significant at the 5% or 10% level. The same goes for the AGE and NOX variables. \n",
    "\n",
    "There seems to be no autocorrelation (as expected as this is not a time-series problem). \n",
    "\n",
    "Overall, the Adjusted R^2 score is great, but how about RMSE (root mean square error), lets have a look. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for training data: 4.459982700887825\n",
      "RMSE for test data: 6.059020669053433\n"
     ]
    }
   ],
   "source": [
    "rmse_training = sqrt(mean_squared_error(Y_train, prediction_1))\n",
    "print(\"RMSE for training data:\", rmse_training)\n",
    "rmse_test = sqrt(mean_squared_error(Y_test,prediction_2))\n",
    "print(\"RMSE for test data:\", rmse_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hmm...  The RMSE for the test data is quite low and very close to that of the training data.  But can we do better?! Lets try by doing a correlation test to identify spurious variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "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>VIF Factor</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.231618</td>\n",
       "      <td>CRIM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.511866</td>\n",
       "      <td>ZN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.406197</td>\n",
       "      <td>INDUS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.166184</td>\n",
       "      <td>CHAS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>72.391370</td>\n",
       "      <td>NOX</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>80.414370</td>\n",
       "      <td>RM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>25.537058</td>\n",
       "      <td>AGE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>15.226339</td>\n",
       "      <td>DIS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>16.615485</td>\n",
       "      <td>RAD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>74.680713</td>\n",
       "      <td>TAX</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>79.288185</td>\n",
       "      <td>PTRATIO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>22.429977</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>8.240870</td>\n",
       "      <td>LSTAT</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    VIF Factor features\n",
       "0     2.231618     CRIM\n",
       "1     2.511866       ZN\n",
       "2    17.406197    INDUS\n",
       "3     1.166184     CHAS\n",
       "4    72.391370      NOX\n",
       "5    80.414370       RM\n",
       "6    25.537058      AGE\n",
       "7    15.226339      DIS\n",
       "8    16.615485      RAD\n",
       "9    74.680713      TAX\n",
       "10   79.288185  PTRATIO\n",
       "11   22.429977        B\n",
       "12    8.240870    LSTAT"
      ]
     },
     "execution_count": 276,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif = pd.DataFrame()\n",
    "vif[\"VIF Factor\"] = [variance_inflation_factor(X_test.values, i) for i in range(X_test.shape[1])]\n",
    "vif[\"features\"] = X_test.columns\n",
    "vif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no hard and fast rules on VIF factors, while a score above 10 is undesirable as it suggests very correlation that artificially inflates our R score, a subjective call must be taken depending on the problem. For example, while the TAX variable (full-value property-tax rate per 10,000 dollars) is highly correlated with the rest of the variables, it is too important of a variable to ignore, plus it is very significant at the 5% level. \n",
    "\n",
    "NOX and INDUS on the other hand, we can try and remove and see if we get a better model.\n",
    "Let's re-create our training sets.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 11)\n",
      "(152, 11)\n"
     ]
    }
   ],
   "source": [
    "#create second training set\n",
    "#df = df.drop([\"NOX\",\"INDUS\"], axis = 1)\n",
    "X_train1, X_test1, Y_train1, Y_test1 = train_test_split(df, target, test_size=0.30)\n",
    "print(df.shape)\n",
    "print(X_test1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit second model\n",
    "model_2 = smf.OLS(Y_train1,X_train1).fit()\n",
    "prediction_3 = model_2.predict(X_train1)# predict y_test values\n",
    "prediction_4 = model_2.predict(X_test1)# predict y_test values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.961</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.960</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   765.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 05 Oct 2017</td> <th>  Prob (F-statistic):</th> <td>9.06e-234</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:32:47</td>     <th>  Log-Likelihood:    </th> <td> -1053.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   354</td>      <th>  AIC:               </th> <td>   2128.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   343</td>      <th>  BIC:               </th> <td>   2171.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    11</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>    <td>   -0.1273</td> <td>    0.038</td> <td>   -3.318</td> <td> 0.001</td> <td>   -0.203</td> <td>   -0.052</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>      <td>    0.0601</td> <td>    0.017</td> <td>    3.614</td> <td> 0.000</td> <td>    0.027</td> <td>    0.093</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>    <td>    2.4752</td> <td>    0.996</td> <td>    2.485</td> <td> 0.013</td> <td>    0.516</td> <td>    4.435</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>      <td>    5.5777</td> <td>    0.311</td> <td>   17.956</td> <td> 0.000</td> <td>    4.967</td> <td>    6.189</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>     <td>    0.0003</td> <td>    0.016</td> <td>    0.021</td> <td> 0.983</td> <td>   -0.030</td> <td>    0.031</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>     <td>   -0.8542</td> <td>    0.212</td> <td>   -4.030</td> <td> 0.000</td> <td>   -1.271</td> <td>   -0.437</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>     <td>    0.1758</td> <td>    0.072</td> <td>    2.446</td> <td> 0.015</td> <td>    0.034</td> <td>    0.317</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>     <td>   -0.0112</td> <td>    0.004</td> <td>   -2.980</td> <td> 0.003</td> <td>   -0.019</td> <td>   -0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th> <td>   -0.4047</td> <td>    0.125</td> <td>   -3.247</td> <td> 0.001</td> <td>   -0.650</td> <td>   -0.160</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>B</th>       <td>    0.0163</td> <td>    0.003</td> <td>    5.118</td> <td> 0.000</td> <td>    0.010</td> <td>    0.023</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>   <td>   -0.4200</td> <td>    0.056</td> <td>   -7.555</td> <td> 0.000</td> <td>   -0.529</td> <td>   -0.311</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>138.371</td> <th>  Durbin-Watson:     </th> <td>   2.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 870.746</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.501</td>  <th>  Prob(JB):          </th> <td>8.31e-190</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>10.072</td>  <th>  Cond. No.          </th> <td>2.18e+03</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.961\n",
       "Model:                            OLS   Adj. R-squared:                  0.960\n",
       "Method:                 Least Squares   F-statistic:                     765.1\n",
       "Date:                Thu, 05 Oct 2017   Prob (F-statistic):          9.06e-234\n",
       "Time:                        18:32:47   Log-Likelihood:                -1053.1\n",
       "No. Observations:                 354   AIC:                             2128.\n",
       "Df Residuals:                     343   BIC:                             2171.\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "CRIM          -0.1273      0.038     -3.318      0.001      -0.203      -0.052\n",
       "ZN             0.0601      0.017      3.614      0.000       0.027       0.093\n",
       "CHAS           2.4752      0.996      2.485      0.013       0.516       4.435\n",
       "RM             5.5777      0.311     17.956      0.000       4.967       6.189\n",
       "AGE            0.0003      0.016      0.021      0.983      -0.030       0.031\n",
       "DIS           -0.8542      0.212     -4.030      0.000      -1.271      -0.437\n",
       "RAD            0.1758      0.072      2.446      0.015       0.034       0.317\n",
       "TAX           -0.0112      0.004     -2.980      0.003      -0.019      -0.004\n",
       "PTRATIO       -0.4047      0.125     -3.247      0.001      -0.650      -0.160\n",
       "B              0.0163      0.003      5.118      0.000       0.010       0.023\n",
       "LSTAT         -0.4200      0.056     -7.555      0.000      -0.529      -0.311\n",
       "==============================================================================\n",
       "Omnibus:                      138.371   Durbin-Watson:                   2.001\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              870.746\n",
       "Skew:                           1.501   Prob(JB):                    8.31e-190\n",
       "Kurtosis:                      10.072   Cond. No.                     2.18e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.18e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for training data: 4.459982700887825\n",
      "RMSE for test data: 6.059020669053433\n"
     ]
    }
   ],
   "source": [
    "rmse_training_2 = sqrt(mean_squared_error(Y_train1, prediction_3))\n",
    "print(\"RMSE for training data:\", rmse_training)\n",
    "rmse_test_2 = sqrt(mean_squared_error(Y_test1,prediction_4))\n",
    "print(\"RMSE for test data:\", rmse_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm = linear_model.LinearRegression()\n",
    "model_2 = lm.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "167\n"
     ]
    }
   ],
   "source": [
    "prediction_2 = lm.predict(X_test)\n",
    "print(len(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 24.93101064]\n",
      " [ 29.52566742]\n",
      " [ 23.28927759]\n",
      " [ 24.86474122]\n",
      " [ 17.18109593]\n",
      " [ 23.93953384]\n",
      " [ 15.73549876]\n",
      " [ 21.88206282]\n",
      " [ 15.77205129]\n",
      " [ 29.06148497]\n",
      " [ 32.52231388]\n",
      " [ 22.56740932]\n",
      " [  1.60320867]\n",
      " [ 39.00231523]\n",
      " [ 26.12719255]\n",
      " [ 18.22103353]\n",
      " [ 13.06823989]\n",
      " [ 30.70157051]\n",
      " [ 26.7870631 ]\n",
      " [ 37.80196742]\n",
      " [ 33.18831139]\n",
      " [ 27.10456909]\n",
      " [ 32.7730165 ]\n",
      " [ 24.71090862]\n",
      " [ 28.01924685]\n",
      " [ 35.77140321]\n",
      " [ 27.06213037]\n",
      " [ 21.33265029]\n",
      " [ 32.83470147]\n",
      " [ 20.77433682]\n",
      " [  9.28279042]\n",
      " [  0.80637391]\n",
      " [ 13.89853271]\n",
      " [ 20.39609319]\n",
      " [ 30.7861978 ]\n",
      " [ 32.87643599]\n",
      " [ 19.38656497]\n",
      " [ 20.27290692]\n",
      " [ 37.03600825]\n",
      " [ 16.33424276]\n",
      " [ 34.46325352]\n",
      " [ 26.80945427]\n",
      " [ 19.21311236]\n",
      " [  5.74423457]\n",
      " [ 19.54542228]\n",
      " [ 34.13714117]\n",
      " [ 42.57848429]\n",
      " [ 12.31451876]\n",
      " [ 39.99039672]\n",
      " [ 21.92648157]\n",
      " [ 21.6803994 ]\n",
      " [ 16.10590152]\n",
      " [ 14.72540036]\n",
      " [ 24.49987889]\n",
      " [  8.90829631]\n",
      " [ 19.670386  ]\n",
      " [  5.29485335]\n",
      " [ 22.69172355]\n",
      " [ 20.26629712]\n",
      " [ 11.25330515]\n",
      " [ 24.44917333]\n",
      " [ 14.07438618]\n",
      " [ 25.89326311]\n",
      " [ 42.32009141]\n",
      " [ 19.97738248]\n",
      " [ 24.679276  ]\n",
      " [ 36.22343484]\n",
      " [ 33.77617492]\n",
      " [ 16.93055361]\n",
      " [ 31.69305078]\n",
      " [ 25.90058344]\n",
      " [ 18.88896144]\n",
      " [ 19.76401204]\n",
      " [ 20.51077724]\n",
      " [ 35.29832432]\n",
      " [ 14.33752579]\n",
      " [ 20.487249  ]\n",
      " [ 27.75240509]\n",
      " [ 18.08956748]\n",
      " [ 23.99952233]\n",
      " [ 20.78461053]\n",
      " [ 21.04596959]\n",
      " [ 24.83455476]\n",
      " [ 19.48082315]\n",
      " [ 16.97153853]\n",
      " [ 25.15920786]\n",
      " [ 17.77294926]\n",
      " [ 27.76654458]\n",
      " [ 20.73182141]\n",
      " [ 22.05359214]\n",
      " [ 23.22032908]\n",
      " [ 31.81712199]\n",
      " [ 19.19906027]\n",
      " [ 27.99875954]\n",
      " [ 22.76497144]\n",
      " [ 10.58300553]\n",
      " [ 22.3307416 ]\n",
      " [ 34.21015498]\n",
      " [ 30.03671438]\n",
      " [ 13.42408249]\n",
      " [ 11.72937251]\n",
      " [ 28.54705596]\n",
      " [ 23.92401959]\n",
      " [ 27.79776855]\n",
      " [ 28.7543958 ]\n",
      " [ 15.26518724]\n",
      " [ 10.57621342]\n",
      " [ 27.26139278]\n",
      " [ 35.19010821]\n",
      " [ 23.94061764]\n",
      " [ 19.70573529]\n",
      " [ 36.39665131]\n",
      " [ 25.55552767]\n",
      " [ 25.24250946]\n",
      " [ 34.42927631]\n",
      " [ 17.56285134]\n",
      " [ 15.78632888]\n",
      " [ 20.77149723]\n",
      " [ 14.38462242]\n",
      " [ 39.72853719]\n",
      " [ 26.85757923]\n",
      " [ 25.95671605]\n",
      " [ 34.28405531]\n",
      " [ 39.6531421 ]\n",
      " [ -6.50470286]\n",
      " [ 22.18243009]\n",
      " [ 22.23182503]\n",
      " [ 21.03731947]\n",
      " [ 32.38015575]\n",
      " [ 13.92090886]\n",
      " [ 19.19625191]\n",
      " [ 28.72295229]\n",
      " [ 13.74747309]\n",
      " [ 23.91017715]\n",
      " [ 18.78236026]\n",
      " [ 14.73015519]\n",
      " [  4.13311799]\n",
      " [ 17.55908206]\n",
      " [ 24.81437447]\n",
      " [ 18.10702807]\n",
      " [ 23.50570589]\n",
      " [ 20.57335786]\n",
      " [ 18.52762801]\n",
      " [ 26.23028791]\n",
      " [ 29.08341291]\n",
      " [ 16.51877622]\n",
      " [ 22.09893402]\n",
      " [ 35.39893646]\n",
      " [ 20.17136396]\n",
      " [ 16.86716148]\n",
      " [ 11.92091362]\n",
      " [ 16.96319363]\n",
      " [  5.88256679]\n",
      " [ 15.66257803]\n",
      " [ 23.8526761 ]\n",
      " [ 21.8681319 ]\n",
      " [ 31.52950855]\n",
      " [ 23.24732514]\n",
      " [ 19.2617064 ]\n",
      " [ 33.41436411]\n",
      " [ 17.70388847]\n",
      " [ 34.92178972]\n",
      " [ 35.22899947]\n",
      " [ 25.15814726]\n",
      " [ 22.6745287 ]\n",
      " [ 19.36937806]\n",
      " [ 20.25317603]]\n",
      "167\n"
     ]
    }
   ],
   "source": [
    "print(prediction_2)\n",
    "print(len(prediction_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE_test: 5.33182748129862\n",
      "RMSE_train: 4.631271759950048\n"
     ]
    }
   ],
   "source": [
    "\n",
    "rms = sqrt(mean_squared_error(Y_test, prediction_2))\n",
    "print(\"RMSE_test:\",rms)\n",
    "rms_1 = sqrt(mean_squared_error(Y_train,prediction_1))\n",
    "print(\"RMSE_train:\",rms_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  2.90024038]\n",
      " [ -2.74778897]\n",
      " [  4.44702108]\n",
      " [ -1.01034046]\n",
      " [  1.35702304]\n",
      " [ -2.73866117]\n",
      " [ -1.91675234]\n",
      " [  2.51670708]\n",
      " [ 24.93215238]\n",
      " [  2.83268166]\n",
      " [ -5.45369573]\n",
      " [-10.46215808]\n",
      " [ -3.59466484]\n",
      " [ -1.17765221]\n",
      " [  0.55055327]\n",
      " [ -4.88614364]\n",
      " [  2.60252099]\n",
      " [  1.16675699]\n",
      " [ -0.2379838 ]\n",
      " [ -1.13691677]\n",
      " [ -1.91023729]\n",
      " [ -1.08386836]\n",
      " [ -6.81738937]\n",
      " [  5.53531495]\n",
      " [ -0.1219255 ]\n",
      " [  3.71422041]\n",
      " [ -2.62655246]\n",
      " [  2.60069759]\n",
      " [ -6.16821515]\n",
      " [ 15.77935196]\n",
      " [ -1.9339368 ]\n",
      " [  9.84628258]\n",
      " [-17.71175025]\n",
      " [ -1.42402499]\n",
      " [ -4.25392835]\n",
      " [  1.11320551]\n",
      " [ -1.82747898]\n",
      " [ 11.13423043]\n",
      " [ -7.29084672]\n",
      " [ -3.56070318]\n",
      " [  0.31564998]\n",
      " [  3.89398976]\n",
      " [  3.86004092]\n",
      " [  2.26195659]\n",
      " [ -5.71266475]\n",
      " [  1.13554286]\n",
      " [ -2.3787463 ]\n",
      " [ -0.32646067]\n",
      " [  0.88896207]\n",
      " [  0.2785366 ]\n",
      " [  0.9292323 ]\n",
      " [ -4.6715069 ]\n",
      " [ -3.5076354 ]\n",
      " [ -2.16909823]\n",
      " [ -1.87710621]\n",
      " [ -1.37610767]\n",
      " [  6.97058255]\n",
      " [  0.23036737]\n",
      " [  6.91000535]\n",
      " [  0.86460235]\n",
      " [ -2.44652064]\n",
      " [ -2.61639307]\n",
      " [  3.63734333]\n",
      " [  3.34600889]\n",
      " [  0.1484907 ]\n",
      " [ -0.86240901]\n",
      " [  7.23071945]\n",
      " [ -2.23049574]\n",
      " [ -6.02326275]\n",
      " [  8.161459  ]\n",
      " [ -3.1595989 ]\n",
      " [ -1.872473  ]\n",
      " [  2.94196381]\n",
      " [ -4.52083445]\n",
      " [  5.70216203]\n",
      " [ -4.78703426]\n",
      " [ -0.69184376]\n",
      " [ -3.03426164]\n",
      " [ 16.80094662]\n",
      " [ -3.47020159]\n",
      " [ -2.0851382 ]\n",
      " [ -1.61817031]\n",
      " [ -0.88686349]\n",
      " [  0.84661506]\n",
      " [  0.83802941]\n",
      " [  3.7251262 ]\n",
      " [ -3.19060796]\n",
      " [ -6.47804975]\n",
      " [ -1.08782207]\n",
      " [ 26.94121766]\n",
      " [ -3.06515396]\n",
      " [ -1.25935235]\n",
      " [ -2.76058481]\n",
      " [ -1.16558583]\n",
      " [ -1.17351762]\n",
      " [ -2.85001901]\n",
      " [  0.06092398]\n",
      " [  1.36109722]\n",
      " [  3.28116773]\n",
      " [  2.11557421]\n",
      " [ -2.45853485]\n",
      " [ -1.04198526]\n",
      " [ -0.20804447]\n",
      " [  3.07587687]\n",
      " [ -0.45189569]\n",
      " [  1.89189345]\n",
      " [  0.48583379]\n",
      " [ -1.24125595]\n",
      " [ -2.02459533]\n",
      " [ -3.36331688]\n",
      " [-10.81172154]\n",
      " [ -3.50041465]\n",
      " [ -1.19571794]\n",
      " [ -1.78860445]\n",
      " [ -0.925654  ]\n",
      " [ -3.40538289]\n",
      " [ -3.4327206 ]\n",
      " [  3.71943497]\n",
      " [  1.23469127]\n",
      " [  5.51503643]\n",
      " [ -1.19026942]\n",
      " [ -0.32738823]\n",
      " [  2.75279696]\n",
      " [  3.9620081 ]\n",
      " [ -7.75213276]\n",
      " [ -1.90760327]\n",
      " [ -1.58466804]\n",
      " [ -3.53134841]\n",
      " [  1.91099235]\n",
      " [ -7.62345067]\n",
      " [ -2.63205714]\n",
      " [ -3.33828708]\n",
      " [ -3.92893275]\n",
      " [ -6.31522766]\n",
      " [  3.82105169]\n",
      " [ -1.87661108]\n",
      " [ -1.10115012]\n",
      " [ -1.5115061 ]\n",
      " [ 13.48381005]\n",
      " [  3.58380425]\n",
      " [  4.57339278]\n",
      " [ -1.96241953]\n",
      " [  9.11505717]\n",
      " [ -0.57727279]\n",
      " [ -3.77964371]\n",
      " [  1.07748698]\n",
      " [  0.33431228]\n",
      " [  0.86841358]\n",
      " [  1.88589375]\n",
      " [ -3.1079144 ]\n",
      " [ -1.25810075]\n",
      " [  1.20824766]\n",
      " [ -3.72731424]\n",
      " [ -1.16600583]\n",
      " [  1.78215622]\n",
      " [  0.03776578]\n",
      " [  3.39806961]\n",
      " [  0.14513386]\n",
      " [ -1.29459602]\n",
      " [  3.23291407]\n",
      " [ 14.14639476]\n",
      " [ -4.07052425]\n",
      " [  3.27499313]\n",
      " [  7.71744164]\n",
      " [ -0.97655341]\n",
      " [ -2.95769776]\n",
      " [ -2.51832104]]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1163aac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkqRSBoUkqZRBIUkqZVBIkkoZFJKkUv8fPF8mJEyDcE4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11797c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dac1278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAG/tJREFUeJzt3X+Q3HV9x/HXO5cjbLB6sWSoOYKJloaCKHFuLJoZR0Aa\nLKIpU1usOFadMm1pK5RJTfQPdEaHTFOtTn+aqi0tDIRqGlHUgMROp7SoFy4aA16lopgL1Dh6aMkK\nl8u7f+x3c3t73+9nv7v73f1+v7vPxwyTu+/e7X6ywOe13/fnl7m7AABIsizvBgAAio2gAAAEERQA\ngCCCAgAQRFAAAIIICgBAEEEBAAgiKAAAQQQFACBoed4NyMKZZ57p69aty7sZAFAqBw4c+KG7r271\ncwMRFOvWrdPk5GTezQCAUjGz76X5OUpPAIAgggIAEERQAACCCAoAQBBBAQAIGohZTwCKZe/UjHbu\nm9bR2arWjFW0dfMGbdk4nnez0CGCAkCm9k7NaPueQ6rOzUuSZmar2r7nkCQRFiVF6QlApnbumz4V\nEnXVuXnt3DedU4vQLYICQKaOzlbbuo7iIygAZGrNWKWt6yg+ggJAprZu3qDK6Miia5XREW3dvCGn\nFqFbDGYDyFR9wJpZT4ODoACQuS0bxwmGAULpCQAQxB0FgCAWz4GgAJCIxXOQKD0BCGDxHCSCAkAA\ni+cgERQAAlg8B4mgABDA4jlIDGYDCGDxHCSCAkALLJ4DpScAQBBBAQAIIigAAEEEBQAgiKAAAAQR\nFACAIIICABBEUAAAgggKAEAQQQEACCIoAABBBAUAIIigAAAE5RYUZrbWzL5sZg+b2WEze1d0/flm\ndp+ZfTv6c1VebQQA5HtHcULSTe5+vqSLJV1vZudL2ibpfnc/V9L90fcAgJzkFhTu/oS7PxR9/VNJ\nj0gal/RGSbdGP3arpC35tBAAIBVkjMLM1knaKOkrks5y9yeih56UdFZOzQIAqABBYWbPkfRpSTe4\n+08aH3N3l+QJv3edmU2a2eSxY8f60FIAGE65BoWZjaoWEre7+57o8v+a2Quix18g6Qdxv+vuu9x9\nwt0nVq9e3Z8GA8AQynPWk0n6hKRH3P3DDQ/dLelt0ddvk/SZfrcNALBgeY6vvUnSWyUdMrOD0bX3\nSNoh6S4ze6ek70n6zZzaBwBQjkHh7v8hyRIevqyfbQEAJMt9MBsAUGwEBQAgiKAAAAQRFACAIIIC\nABBEUAAAgvJcRwEAmdk7NaOd+6Z1dLaqNWMVbd28QVs2jufdrIFAUAAovb1TM9q+55Cqc/OSpJnZ\nqrbvOSRJhEUGKD0BKL2d+6ZPhURddW5eO/dN59SiwUJQACi9o7PVtq6jPQQFgNJbM1Zp6zraQ1Bg\nKO2dmtGmHfu1fts92rRjv/ZOzeTdJHRh6+YNqoyOLLpWGR3R1s0bcmrRYGEwG0OHgc/BU//3xqyn\n3iAoMHRCA590LOW1ZeM4//56hNIThg4Dn0B7CAoMHQY+gfYQFBg6DHwC7WGMAkOHgU+gPQQFhhID\nn0jCnlFLERQAEGHqdDzGKAAgwp5R8bijAIBIFlOnB7F0xR0FAES6nTpdL13NzFblWihdlX2LGIIC\nACLdTp0e1NIVpScAiHQ7dXpQV/0TFADQoJup02vGKpqJCYWyr/qn9AQAGRnUVf/cUQBARgZ11T9B\nAQAZGsRV/5SeAABBBAUAIIjSEwDkqAwruQkKAMhJWTYhpPQEADkpy0puggIAclKWldwEBQDkpCzn\nt+caFGb2STP7gZl9s+Ha883sPjP7dvTnqjzbCAC9UpaV3HnfUfyjpCuarm2TdL+7nyvp/uh7YGjt\nnZrRph37tX7bPdq0Y3/pt6zGgi0bx3XL1RdqfKwikzQ+VtEtV19YqIFsSTJ3z7cBZuskfc7dXxJ9\nPy3pNe7+hJm9QNK/uXswXicmJnxycrLnbQX6rXlWjFT7xFnEzgTlY2YH3H2i1c/lfUcR5yx3fyL6\n+klJZ8X9kJldZ2aTZjZ57Nix/rUO6KOyzIrBYCv0Ogp3dzOLveVx912Sdkm1O4q+Ngzok7LMiima\nMixiK5Mi3lH8b1RyUvTnD3JuD5CbssyKKZJBPY40T0UMirslvS36+m2SPpNjW4BclWVWTJFQrste\nqqAws3eZ2XOt5hNm9pCZ/Wq3L25md0j6L0kbzOyImb1T0g5Jl5vZtyW9NvoeGEplmRVTJJTrspd2\njOId7v5RM9ssaZWkt0r6Z0n3dvPi7v7mhIcu6+Z5gTKLq68/sO3SvJtVGoN6HGme0paeLPrz1yT9\ns7sfbrgGICPU17tHuS57ae8oDpjZvZLWS9puZj8n6WTvmgUMp1B9nXJTOv0+jnQYZlilDYp3SrpI\n0nfc/biZ/bykt/euWcBwor6ejX4dR1qWbcK7FSw9mdnLzezlqoWEJL0o+v6FKvgaDKCMmA5bLsMy\nw6pVZ/+hwGMuiRE2IENbN2+I3bKD+nrvdVJCGpY7wGBQuPsl/WoIgMX19ZnZqkbMFn1CrT8+DHXx\nfuq0hDQsM6xSl4/M7CWSzpd0ev2au/9TLxoFDLN6x5TUcYUeIyw60+kkgmG5A0wVFGZ2s6TXqBYU\nn5f0Okn/IYmgAHqgVe2bmVHZ6rSE1O8ZVnlJe0fxG5JeJmnK3d9uZmdJuq13zQKGWycd16DVxfup\nmxJSv2ZY5Sntgruqu5+UdMLMnqvaRn1re9csYLiFZj8xMyp7LNILSxsUk2Y2JunvJR2Q9JBqezQB\n6IFQx5Vlp8bpeTXsqRXW9gl30Yl0z3X3b/SiQZ3ghDsMotDMpixmPXF6XrI07+8gzDxLe8JdqqAw\ns1fHXXf3f++gbZkjKID2bdqxP7YuPz5WGepNCNME6KCEbNqgSDuYvbXh69MlvUK1EtTw/tcElNyw\nLBZrV5qpssO2J1eqoHD3qxq/N7O1kj7SkxYB6IthWSzWrjQBOmwh2+kJd0ck/XKWDQGGQZEGj5np\nEy/NrLJhm3mWdsHdX6q2t5NUC5eLVJv5BCClou00OkiLxbIcWE6z2npYVmTXpR2jaBwpPiHpDnd/\noAftAQZWEevag7BYLOsAThOggxSyaaQdo7i11w0BBt0g1bWbP8Ffct5qfflbxzLvNNPcKfQigNME\n6CCEbFrBoDCzQ1ooOS3h7i/NvEXAgEozeNxtCaUfc/vjPsHf9uDjpx7PqqSW9k6hVQC3857kvTYi\n79dP0mow+/WSrpL0xeift0T/fEG1zQEBpNRq8Ljb87L7cd723qkZ3XTX15d8gm+WxeE9aQ8FCg0s\nx70nN+4+qHUxkwnyPq8879cPaXUexfckycwud/eNDQ+928wekrStl40DBkmruna3JZSsSzBx5aVP\nH5jRfMrdHEIltTSlq7SlutDActx7Um998x1K3mNIeb9+SNrBbDOzTfUBbDN7lTqfWgsMrVBdu9sx\njCzHQOLKPrc/+HhyHTpG0if9NKWrG3cf1PJl0tzJpb//vMroou9DAXzD7oPBNjZ2xHmPIeX9+iFp\ng+Kdkj5pZs+TZJJ+LOkdPWsVMIS6XQDX7u+H6uGhT+JphKaKxj13M1d8SEiS2eLvk/4ee6dmZCna\nXe+I816AmPfrh6S6K3D3A+7+MtXOpHipu1/k7qyjADIUN4YhSU8/cyJVnbqdBXRx9fAbdh/URe+/\nV3unZtr6FDtipmsvPqflzqv1xYZxnWE7Zo/PBf8e9br+zn3TqcKt3hHnvQAx79cPaTXr6Vp3v83M\n/qTpuiTJ3T/cw7YBQ6Xesb7/s4f144bOcLY6l2oWUTtz+5M+1ddfa2zl6KI2JDFJH/rNl7Wsocdt\notepxk/Yobp+mrBr7IjzXhuR9+uHtCo9nRH9+XO9bgiAhUHV5k467aBm2rn9oU60OjevFcuXaXTE\nNDcf/kzuSjcFNk25KY3mT9ihun5SKWfETCfdExfS5dkx5/36SVrNevpY9Of7+9McAN0Maqadh5/U\nidbNVudkiY8uGE9ZPw+1fXysonU/X9F//s+PgqWiVStHdfNVFyz6+4Tq+ls3b9DWf/m65k4uPOvo\nMtPON7W+A8JiqcYozOzPzOy5ZjZqZveb2TEzu7bXjQOGUacbzrUzDz9pPKQuzSBwO/XzpLbXz764\n/Xdfqb/4rYuCwbPytOVLOviWdf3mtEuTflgi7RTXX3X3n6i2AO+7kn5Ri8+oAJCRTgc10y5Qq1ux\nPP5//zQhMVYZbeuQnjR/py0bx/XAtksT+/K4u5LQEaY7900vKZ3Nzbve/9nDqdqMBWmnx9Z/7kpJ\n/+LuT1nzHDUAmeh0UDNtySpuYLkeDuMtSlJ1Z6xY+HQfV+6Ka/8tV1/YVVks6a4kqa6f9H78+Pic\n9k7NUH5qQ9qg+JyZfUtSVdLvm9lqST/rXbOA4dbJoGbaDjZpjcRYZVSXnLd60eK3JI37KDUvntv6\nqa9LrlNjA/US2C1XX5jqiNW4ldbSwjThtO9LaBymCKudyyTtOoptkl4lacLd5yQdl/TGXjYMQHvS\nlqySPmnPVudShYQkLTPT+m33xO77NDfviwaQpfb2fqqXk1atXLwCuz51N+3eR6FSXRFWO5dJ2sHs\nlZL+QNLfRpfWSGp5IDeA/gnV6xtlsdJ33l0e/ZlWO53zlo3jWnna0oJHu4Ez1rTdR13zNiAISzuY\n/Q+SnlXtrkKSZiR9oCctAtCx+oDwYzuu1APbLo0tr+S10rfdgEoqG7UTOO97wwWxndzTz6Zb7Y6a\ntEHxYnf/M0lzkuTux9XjiWZmdoWZTZvZo2bGLrVABuoDz/1mWgioNOeG1/dpirPMLPF34p43bsuo\nuXnP5X0oq7SD2c+aWUXRrDkze7GkZ3rVKDMbkfTXki6XdETS18zsbnd/uFevCQy6LLfRaJerNoB8\nw+6Di6bfJh1GFNqnad59ye8kHXKUNAVYYpyiHS2DwmrzYP9OtYOL1prZ7ZI2SfqdHrbrFZIedffv\nRG24U7XBc4ICaEPj1NVlZoljCs1rJ0aX1ba5aLGDR2qmhVJS81PGbU/SqhNv/p2kNSShUCzCrqxl\n0bL05O6u2uK6q1ULhztUm/30bz1s17ik7zd8fyS6doqZXWdmk2Y2eezYsR42BSin5pXaoZCor4o2\n1abJzgdCopOac9qtvuvSdOKNv9Pu3UFjKQytpR2jeEjSi9z9Hnf/nLv/sJeNSsPdd7n7hLtPrF69\nOu/mAIWTdiO+NWOVRYPgZ6xYrpOBnj2jm4wlz9k4rtBqixFpcZgkBcuqlaNLnsckveXic1hH0Ya0\nYxS/IuktZvY9SU8rulN195f2qF0zktY2fH92dA1ASu1usy3V7kK6PS+i2Uig5NUobrxi575pzcxW\nl5TGmtuddBzqzVddcOp5irZ1d5mYp/gXaGYvjLteP1M7a2a2XNJ/S7pMtYD4mqTfdvfYTVomJiZ8\ncnKyF00BSivpkKDGbbYbz6p+XmVUTz97ouXW4r1W3yiw0d6pmUXndDRuOdJ4oh2B0B4zO+DuLdfE\npbqj6FUgBF7vhJn9oaR9kkYkfTIpJADES/qUXV+E1zxTaLba+qCifpiZrcZu1fGzhrNRk2ZNEQy9\nkbb01Hfu/nlJn8+7HUBZtdpcMKvDhHohrgSV1Na0hzqhc4UNCgDdC33KLvI6gubOv1Vbi/x3GQRp\nZz0BGDBFX0fQOL7Sqq1F/7uUHUEBDKm4Kaijy0yrVo6e2lRwNMceYqThzJvQdNl2TtpDZyg9AUOq\n1RjG3qkZ3bD7YG7ta5xS2zxdtj7ldpzZTX1BUAAF1c/pni7pyad+pht2H9TOfdPaunmD3nd3vhMN\nm8/PZlZTfggKoICSNrmTlFln2fwa9U/wM7NV3bj7YE9WYKfV6RYbrKXoDcYogAJK2uQuy62xQ1NO\nswqJ5lPq0nK1H4jNe1vVw5VzJ7rHHQVQQEnTPbOcBtqPKaX1ldTtGjHTum33LPr+zb+yVh/YcmHi\nXUMoXLmr6A5BARTQmrFK7PYbWU4DTXqNImjeG2reXbc9+LgeO/Z/eujxp2JLcu2GK2Wq9Cg9AQUU\nNx0062mgaXZo7ekxlh283gP/86PEu4akEI27TpmqPQQFUEBbNo7rlqsvPHVGxPhY5dQeTVm/xlgl\nfhxhdJn1fUC709c7OlttK1z7MQY0SCg9AQXVj+mg9dp+3IaAzzl9uVaetjx1eWqsMqpnT8zr+Fzc\nKdW9VT9TQ0q3pXg/xoAGCUEBDLmkznH2+JxuvuqC1Odsn7Gi1p10ExSrVo7qZ3MnE19v04ufr69+\n98eLtkIfHbFTdw1pw7UfY0CDhNITMKD2Ts1o0479Wr/tnkWnxzVL6hyXmenG3Qd1+uiyVGMVR2er\neiphq3KT9JGm41ZHRxY/a/2goXrJrdGIma69+By9aeKcpfWpDupV/RgDGiTcUQADqJ0Fe3HnVkgL\nM4/STnGtB07SJ/XmT/uhWUdJdwWbduzXXNM5rXMnve0psO2UqUBQAAOpnTUFzZ3mspRHlzZq/DQe\nd1hS3Cf1TsZgshxbYEuQ9AgKYAC126E2dprrGxa6hcQdR1rXuHlf42yibjtmxhbyQVAAAyjUobZa\naJb0u6tWjmrlactblmrq13qxV1XS8a6MLfQWQQEMoKQO9ZLzVrfswJN+9+arLkjdybe7nUbaVdKM\nLeSDoAAGUFKHmqYDz6IzTipxzcxWtWnH/kXPK7W++2C7jXyZtzloVUQTExM+OTmZdzOAwlu/7Z7Y\n2aQm6bEdV2b2Opt27I8tX9XHNeoqoyNasXxZ7IK/8bGKHth26ZIZXPXfy3ql+jAyswPuPtHq51hH\nAQyRdvZD6sYl562Ovd4cUtW5+diQkBbuSthuI38EBTBEslholmYh35e/dazrttbDi+028scYBTBE\nuh1/SLuQr51OPG7bjsbwYkps/ggKYMh0s9As7WympM69eYzCVFv5PVYZ1emjyzR7fG5JeDElNn+U\nngCklrYMlFTiesvF55zax6kxNGarc5o9Phc70N6PLdcRxh0FUHBFmhqatgzUqsQVNyuqHhJx5Sy2\n28gXQQEUWDub+/VDO2WgUOfeagyDs66LhdITUGBFmxqaVRkozUA0s5qKgzsKoMCKODU0izJQ0tbm\njZjVVBzcUQAF1q8Fcv3WeGciacnBSMxqKhaCAiiwQT6JbcvGcT2w7VJ9d8eV+ouG0++Y1VQ8lJ6A\nAhuW3VKZ1VRsBAVQcHSiyBulJwBAUC5BYWZvMrPDZnbSzCaaHttuZo+a2bSZbc6jfQCABXmVnr4p\n6WpJH2u8aGbnS7pG0gWS1kj6kpn9krsnz6EDAPRULncU7v6Iu8etGHqjpDvd/Rl3f0zSo5Je0d/W\nAQAaFW0we1zSgw3fH4muAUBmirR/Vhn0LCjM7EuSfiHmofe6+2cyeP7rJF0nSeecc063TwegTWXt\nbIu2f1YZ9Cwo3P21HfzajKS1Dd+fHV2Le/5dknZJtTOzO3gtAB0qc2eb9kwNLCja9Ni7JV1jZivM\nbL2kcyV9Nec2AWhStM0K21HE/bOKLq/psb9uZkckvVLSPWa2T5Lc/bCkuyQ9LOmLkq5nxhNQPGXu\nbAd1/6xeymvW07+6+9nuvsLdz3L3zQ2PfdDdX+zuG9z9C3m0D0BYmTvbQd4/q1eKVnoCUAJl7mw5\nWrV9RZseC6AEyr5ZIftntYegANAROtvhQekJABBEUAAAgggKAEAQQQEACCIoAABBBAUAIIigAAAE\nERQAgCCCAgAQRFAAAIIICgBAEEEBAAgiKAAAQQQFACCIoAAABBEUAIAgggIAEERQAACCCAoAQBBB\nAQAIIigAAEEEBQAgiKAAAAQtz7sBAIDs7J2a0c590zo6W9WasYq2bt6gLRvHu3pOggIABsTeqRlt\n33NI1bl5SdLMbFXb9xySpK7CgtITAAyInfumT4VEXXVuXjv3TXf1vAQFAAyIo7PVtq6nRVAAwIBY\nM1Zp63paBAUADIitmzeoMjqy6FpldERbN2/o6nkZzAaAAVEfsGbWEwAg0ZaN410HQzNKTwCAoFyC\nwsx2mtm3zOwbZvavZjbW8Nh2M3vUzKbNbHMe7QMALMjrjuI+SS9x95dK+m9J2yXJzM6XdI2kCyRd\nIelvzGwk8VkAAD2XS1C4+73ufiL69kFJZ0dfv1HSne7+jLs/JulRSa/Io40AgJoijFG8Q9IXoq/H\nJX2/4bEj0TUAQE56NuvJzL4k6RdiHnqvu38m+pn3Sjoh6fYOnv86SddF3z5jZt/stK1D5ExJP8y7\nESXA+5Qe71U6RX2fXpjmh3oWFO7+2tDjZvY7kl4v6TJ39+jyjKS1DT92dnQt7vl3SdoVPdeku090\n2+ZBx/uUDu9TerxX6ZT9fcpr1tMVkv5U0hvc/XjDQ3dLusbMVpjZeknnSvpqHm0EANTkteDurySt\nkHSfmUnSg+7+e+5+2MzukvSwaiWp6919PvA8AIAeyyUo3P0XA499UNIH23zKXd21aGjwPqXD+5Qe\n71U6pX6fbGF4AACApYowPRYAUGClDwozuyLa7uNRM9uWd3uKyMzWmtmXzexhMztsZu/Ku01FZmYj\nZjZlZp/Luy1FZWZjZvapaCueR8zslXm3qYjM7Mbo/7lvmtkdZnZ63m3qRKmDItre468lvU7S+ZLe\nHG0DgsVOSLrJ3c+XdLGk63mfgt4l6ZG8G1FwH5X0RXc/T9LLxPu1hJmNS/pjSRPu/hJJI6ptUVQ6\npQ4K1bb3eNTdv+Puz0q6U7VtQNDA3Z9w94eir3+q2v/UrHiPYWZnS7pS0sfzbktRmdnzJL1a0ick\nyd2fdffZfFtVWMslVcxsuaSVko7m3J6OlD0o2PKjTWa2TtJGSV/JtyWF9RHV1viczLshBbZe0jFJ\n/xCV6D5uZmfk3aiicfcZSX8u6XFJT0h6yt3vzbdVnSl7UKANZvYcSZ+WdIO7/yTv9hSNmb1e0g/c\n/UDebSm45ZJeLulv3X2jpKclMT7YxMxWqVbhWC9pjaQzzOzafFvVmbIHReotP4admY2qFhK3u/ue\nvNtTUJskvcHMvqtaGfNSM7st3yYV0hFJR9y9flf6KdWCA4u9VtJj7n7M3eck7ZH0qpzb1JGyB8XX\nJJ1rZuvN7DTVBoruzrlNhWO15e+fkPSIu3847/YUlbtvd/ez3X2dav8t7Xf3Un4C7CV3f1LS981s\nQ3TpMtV2U8Bij0u62MxWRv8PXqaSDvqX+sxsdz9hZn8oaZ9qMwo+6e6Hc25WEW2S9FZJh8zsYHTt\nPe7++RzbhHL7I0m3Rx/QviPp7Tm3p3Dc/Stm9ilJD6k283BKJV2hzcpsAEBQ2UtPAIAeIygAAEEE\nBQAgiKAAAAQRFACAIIICyICZzZvZwWiX0M+a2Vh0fZ2ZuZl9oOFnzzSzOTP7q/xaDKRHUADZqLr7\nRdEuoT+SdH3DY4+pttFg3Zsksd4HpUFQANn7Ly3enPK4pEfMbCL6/rck3dX3VgEdIiiADEVnpFym\npVvJ3CnpGjNbK2leJd1uGsOJoACyUYm2R3lS0lmS7mt6/IuSLldtD6ndfW4b0BWCAshG1d0vkvRC\nSabFYxSKDtY6IOkm1XZbBUqDoAAy5O7HVTv+8qboVLNGH5L0bnf/Uf9bBnSOoAAy5u5Tkr4h6c1N\n1w+7+635tAroHLvHAgCCuKMAAAQRFACAIIICABBEUAAAgggKAEAQQQEACCIoAABBBAUAIOj/AVH2\n41XxUlUeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11797c470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSCwFChERiaVAISIisRQoREQk1v8HmMzB1oS0+bUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1177f9860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niAQpUIiISJAChYiIBClQiIhI0P8HMSBoSR2T7CcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117938c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEKCAYAAADjDHn2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1172557f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d794eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlChERCRIiUJERIKUKEREJEiJQkREgv4/oyjuiQnQ6gUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178a1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11715d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEwURERkxURARkdH/B/q2IIDteMnuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dab1e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "residual = Y_test.values-prediction_2\n",
    "print(residual)\n",
    "for i in X_test:\n",
    "    plt.scatter(X_test[i],residual)\n",
    "    plt.xlim(0,)\n",
    "    plt.xlabel(i)\n",
    "    plt.ylabel(\"residuals\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "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>VIF Factor</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.495032</td>\n",
       "      <td>CRIM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.446779</td>\n",
       "      <td>ZN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.162942</td>\n",
       "      <td>CHAS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>68.307321</td>\n",
       "      <td>RM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22.786796</td>\n",
       "      <td>AGE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12.665816</td>\n",
       "      <td>DIS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>16.738498</td>\n",
       "      <td>RAD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>51.081136</td>\n",
       "      <td>TAX</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>71.515551</td>\n",
       "      <td>PTRATIO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>25.781496</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.584347</td>\n",
       "      <td>LSTAT</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    VIF Factor features\n",
       "0     2.495032     CRIM\n",
       "1     2.446779       ZN\n",
       "2     1.162942     CHAS\n",
       "3    68.307321       RM\n",
       "4    22.786796      AGE\n",
       "5    12.665816      DIS\n",
       "6    16.738498      RAD\n",
       "7    51.081136      TAX\n",
       "8    71.515551  PTRATIO\n",
       "9    25.781496        B\n",
       "10   10.584347    LSTAT"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/ipykernel_launcher.py:4: DeprecationWarning: `het_breushpagan` is deprecated, use `het_breuschpagan` instead!\n",
      "Use het_breuschpagan, het_breushpagan will be removed in 0.9 \n",
      "(Note: misspelling missing 'c')\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[('p-value', 59.611040782255223)]"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [ 'p-value']\n",
    "test = sms.het_breushpagan(model_1.resid, model_1.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "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
}