class_1_LinReg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing All packages and Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets #contains all the datasets to work within sklearn package\n",
    "\n",
    "import pandas as pd #scientific libraries to perform operation on dataset\n",
    "import numpy as np #scientific libraries to perform operation on dataset\n",
    "\n",
    "from sklearn.linear_model import LinearRegression,Ridge,Lasso# Importing algorithms to work for prediction\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "from sklearn.model_selection import train_test_split # library to divide the data into training set\n",
    "# and testing set\n",
    "\n",
    "from sklearn.metrics import mean_squared_error,r2_score #libraries to measure the accuracy and error in prediction\n",
    "\n",
    "import matplotlib.pyplot as plt # libraries to plot graph and visualize the data distribution \n",
    "\n",
    "from sklearn.utils import shuffle #librries to shuffle the data to provide randomization\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# loading the particular dataset from given set of datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston=datasets.load_boston() #press tab after datasets. to see number of datsets present"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.keys() #to get key items that has certain values(assume like title and description)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. 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",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: 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",
      "\n"
     ]
    }
   ],
   "source": [
    "print(boston['DESCR']) # way to determine the value of particular key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "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",
       "    </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",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.02985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.430</td>\n",
       "      <td>58.7</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.12</td>\n",
       "      <td>5.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.08829</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.012</td>\n",
       "      <td>66.6</td>\n",
       "      <td>5.5605</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>395.60</td>\n",
       "      <td>12.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.14455</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.172</td>\n",
       "      <td>96.1</td>\n",
       "      <td>5.9505</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>19.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.21124</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.631</td>\n",
       "      <td>100.0</td>\n",
       "      <td>6.0821</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.63</td>\n",
       "      <td>29.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.17004</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.004</td>\n",
       "      <td>85.9</td>\n",
       "      <td>6.5921</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.71</td>\n",
       "      <td>17.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.22489</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.377</td>\n",
       "      <td>94.3</td>\n",
       "      <td>6.3467</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>392.52</td>\n",
       "      <td>20.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.11747</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.009</td>\n",
       "      <td>82.9</td>\n",
       "      <td>6.2267</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>13.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.09378</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.889</td>\n",
       "      <td>39.0</td>\n",
       "      <td>5.4509</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>390.50</td>\n",
       "      <td>15.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.62976</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.949</td>\n",
       "      <td>61.8</td>\n",
       "      <td>4.7075</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>8.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.63796</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.096</td>\n",
       "      <td>84.5</td>\n",
       "      <td>4.4619</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>380.02</td>\n",
       "      <td>10.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.62739</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.834</td>\n",
       "      <td>56.5</td>\n",
       "      <td>4.4986</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>395.62</td>\n",
       "      <td>8.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.05393</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.935</td>\n",
       "      <td>29.3</td>\n",
       "      <td>4.4986</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>386.85</td>\n",
       "      <td>6.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.78420</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.990</td>\n",
       "      <td>81.7</td>\n",
       "      <td>4.2579</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>386.75</td>\n",
       "      <td>14.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.80271</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.456</td>\n",
       "      <td>36.6</td>\n",
       "      <td>3.7965</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>288.99</td>\n",
       "      <td>11.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.72580</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.727</td>\n",
       "      <td>69.5</td>\n",
       "      <td>3.7965</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>390.95</td>\n",
       "      <td>11.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.25179</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.570</td>\n",
       "      <td>98.1</td>\n",
       "      <td>3.7979</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>376.57</td>\n",
       "      <td>21.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.85204</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.965</td>\n",
       "      <td>89.2</td>\n",
       "      <td>4.0123</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>392.53</td>\n",
       "      <td>13.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.23247</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.142</td>\n",
       "      <td>91.7</td>\n",
       "      <td>3.9769</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>18.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.98843</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.813</td>\n",
       "      <td>100.0</td>\n",
       "      <td>4.0952</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>394.54</td>\n",
       "      <td>19.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.75026</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.924</td>\n",
       "      <td>94.1</td>\n",
       "      <td>4.3996</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>394.33</td>\n",
       "      <td>16.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.84054</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.599</td>\n",
       "      <td>85.7</td>\n",
       "      <td>4.4546</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>303.42</td>\n",
       "      <td>16.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.67191</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>5.813</td>\n",
       "      <td>90.3</td>\n",
       "      <td>4.6820</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>376.88</td>\n",
       "      <td>14.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.95577</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.047</td>\n",
       "      <td>88.8</td>\n",
       "      <td>4.4534</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>306.38</td>\n",
       "      <td>17.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.77299</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.495</td>\n",
       "      <td>94.4</td>\n",
       "      <td>4.4547</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>387.94</td>\n",
       "      <td>12.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1.00245</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.674</td>\n",
       "      <td>87.3</td>\n",
       "      <td>4.2390</td>\n",
       "      <td>4.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>380.23</td>\n",
       "      <td>11.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>4.87141</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.614</td>\n",
       "      <td>6.484</td>\n",
       "      <td>93.6</td>\n",
       "      <td>2.3053</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>396.21</td>\n",
       "      <td>18.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>15.02340</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.614</td>\n",
       "      <td>5.304</td>\n",
       "      <td>97.3</td>\n",
       "      <td>2.1007</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>349.48</td>\n",
       "      <td>24.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>10.23300</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.614</td>\n",
       "      <td>6.185</td>\n",
       "      <td>96.7</td>\n",
       "      <td>2.1705</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>379.70</td>\n",
       "      <td>18.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>14.33370</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.614</td>\n",
       "      <td>6.229</td>\n",
       "      <td>88.0</td>\n",
       "      <td>1.9512</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>383.32</td>\n",
       "      <td>13.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>5.82401</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.532</td>\n",
       "      <td>6.242</td>\n",
       "      <td>64.7</td>\n",
       "      <td>3.4242</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>10.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>5.70818</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.532</td>\n",
       "      <td>6.750</td>\n",
       "      <td>74.9</td>\n",
       "      <td>3.3317</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>393.07</td>\n",
       "      <td>7.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>5.73116</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.532</td>\n",
       "      <td>7.061</td>\n",
       "      <td>77.0</td>\n",
       "      <td>3.4106</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>395.28</td>\n",
       "      <td>7.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>483</th>\n",
       "      <td>2.81838</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.532</td>\n",
       "      <td>5.762</td>\n",
       "      <td>40.3</td>\n",
       "      <td>4.0983</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>392.92</td>\n",
       "      <td>10.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>2.37857</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.583</td>\n",
       "      <td>5.871</td>\n",
       "      <td>41.9</td>\n",
       "      <td>3.7240</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>370.73</td>\n",
       "      <td>13.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>3.67367</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.583</td>\n",
       "      <td>6.312</td>\n",
       "      <td>51.9</td>\n",
       "      <td>3.9917</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>388.62</td>\n",
       "      <td>10.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>5.69175</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.583</td>\n",
       "      <td>6.114</td>\n",
       "      <td>79.8</td>\n",
       "      <td>3.5459</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>392.68</td>\n",
       "      <td>14.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>4.83567</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.583</td>\n",
       "      <td>5.905</td>\n",
       "      <td>53.2</td>\n",
       "      <td>3.1523</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>388.22</td>\n",
       "      <td>11.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>0.15086</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.454</td>\n",
       "      <td>92.7</td>\n",
       "      <td>1.8209</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>395.09</td>\n",
       "      <td>18.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>0.18337</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.414</td>\n",
       "      <td>98.3</td>\n",
       "      <td>1.7554</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>344.05</td>\n",
       "      <td>23.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>0.20746</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.093</td>\n",
       "      <td>98.0</td>\n",
       "      <td>1.8226</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>318.43</td>\n",
       "      <td>29.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>0.10574</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.983</td>\n",
       "      <td>98.8</td>\n",
       "      <td>1.8681</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>390.11</td>\n",
       "      <td>18.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>0.11132</td>\n",
       "      <td>0.0</td>\n",
       "      <td>27.74</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.609</td>\n",
       "      <td>5.983</td>\n",
       "      <td>83.5</td>\n",
       "      <td>2.1099</td>\n",
       "      <td>4.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>20.1</td>\n",
       "      <td>396.90</td>\n",
       "      <td>13.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>0.17331</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.707</td>\n",
       "      <td>54.0</td>\n",
       "      <td>2.3817</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>12.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>0.27957</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.926</td>\n",
       "      <td>42.6</td>\n",
       "      <td>2.3817</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>13.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>0.17899</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.670</td>\n",
       "      <td>28.8</td>\n",
       "      <td>2.7986</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>393.29</td>\n",
       "      <td>17.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>0.28960</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.390</td>\n",
       "      <td>72.9</td>\n",
       "      <td>2.7986</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>21.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>0.26838</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.794</td>\n",
       "      <td>70.6</td>\n",
       "      <td>2.8927</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>14.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>0.23912</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>6.019</td>\n",
       "      <td>65.3</td>\n",
       "      <td>2.4091</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>12.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>0.17783</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>5.569</td>\n",
       "      <td>73.5</td>\n",
       "      <td>2.3999</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>395.77</td>\n",
       "      <td>15.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>0.22438</td>\n",
       "      <td>0.0</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.585</td>\n",
       "      <td>6.027</td>\n",
       "      <td>79.7</td>\n",
       "      <td>2.4982</td>\n",
       "      <td>6.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>14.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>9.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 13 columns</p>\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",
       "5     0.02985   0.0   2.18   0.0  0.458  6.430   58.7  6.0622   3.0  222.0   \n",
       "6     0.08829  12.5   7.87   0.0  0.524  6.012   66.6  5.5605   5.0  311.0   \n",
       "7     0.14455  12.5   7.87   0.0  0.524  6.172   96.1  5.9505   5.0  311.0   \n",
       "8     0.21124  12.5   7.87   0.0  0.524  5.631  100.0  6.0821   5.0  311.0   \n",
       "9     0.17004  12.5   7.87   0.0  0.524  6.004   85.9  6.5921   5.0  311.0   \n",
       "10    0.22489  12.5   7.87   0.0  0.524  6.377   94.3  6.3467   5.0  311.0   \n",
       "11    0.11747  12.5   7.87   0.0  0.524  6.009   82.9  6.2267   5.0  311.0   \n",
       "12    0.09378  12.5   7.87   0.0  0.524  5.889   39.0  5.4509   5.0  311.0   \n",
       "13    0.62976   0.0   8.14   0.0  0.538  5.949   61.8  4.7075   4.0  307.0   \n",
       "14    0.63796   0.0   8.14   0.0  0.538  6.096   84.5  4.4619   4.0  307.0   \n",
       "15    0.62739   0.0   8.14   0.0  0.538  5.834   56.5  4.4986   4.0  307.0   \n",
       "16    1.05393   0.0   8.14   0.0  0.538  5.935   29.3  4.4986   4.0  307.0   \n",
       "17    0.78420   0.0   8.14   0.0  0.538  5.990   81.7  4.2579   4.0  307.0   \n",
       "18    0.80271   0.0   8.14   0.0  0.538  5.456   36.6  3.7965   4.0  307.0   \n",
       "19    0.72580   0.0   8.14   0.0  0.538  5.727   69.5  3.7965   4.0  307.0   \n",
       "20    1.25179   0.0   8.14   0.0  0.538  5.570   98.1  3.7979   4.0  307.0   \n",
       "21    0.85204   0.0   8.14   0.0  0.538  5.965   89.2  4.0123   4.0  307.0   \n",
       "22    1.23247   0.0   8.14   0.0  0.538  6.142   91.7  3.9769   4.0  307.0   \n",
       "23    0.98843   0.0   8.14   0.0  0.538  5.813  100.0  4.0952   4.0  307.0   \n",
       "24    0.75026   0.0   8.14   0.0  0.538  5.924   94.1  4.3996   4.0  307.0   \n",
       "25    0.84054   0.0   8.14   0.0  0.538  5.599   85.7  4.4546   4.0  307.0   \n",
       "26    0.67191   0.0   8.14   0.0  0.538  5.813   90.3  4.6820   4.0  307.0   \n",
       "27    0.95577   0.0   8.14   0.0  0.538  6.047   88.8  4.4534   4.0  307.0   \n",
       "28    0.77299   0.0   8.14   0.0  0.538  6.495   94.4  4.4547   4.0  307.0   \n",
       "29    1.00245   0.0   8.14   0.0  0.538  6.674   87.3  4.2390   4.0  307.0   \n",
       "..        ...   ...    ...   ...    ...    ...    ...     ...   ...    ...   \n",
       "476   4.87141   0.0  18.10   0.0  0.614  6.484   93.6  2.3053  24.0  666.0   \n",
       "477  15.02340   0.0  18.10   0.0  0.614  5.304   97.3  2.1007  24.0  666.0   \n",
       "478  10.23300   0.0  18.10   0.0  0.614  6.185   96.7  2.1705  24.0  666.0   \n",
       "479  14.33370   0.0  18.10   0.0  0.614  6.229   88.0  1.9512  24.0  666.0   \n",
       "480   5.82401   0.0  18.10   0.0  0.532  6.242   64.7  3.4242  24.0  666.0   \n",
       "481   5.70818   0.0  18.10   0.0  0.532  6.750   74.9  3.3317  24.0  666.0   \n",
       "482   5.73116   0.0  18.10   0.0  0.532  7.061   77.0  3.4106  24.0  666.0   \n",
       "483   2.81838   0.0  18.10   0.0  0.532  5.762   40.3  4.0983  24.0  666.0   \n",
       "484   2.37857   0.0  18.10   0.0  0.583  5.871   41.9  3.7240  24.0  666.0   \n",
       "485   3.67367   0.0  18.10   0.0  0.583  6.312   51.9  3.9917  24.0  666.0   \n",
       "486   5.69175   0.0  18.10   0.0  0.583  6.114   79.8  3.5459  24.0  666.0   \n",
       "487   4.83567   0.0  18.10   0.0  0.583  5.905   53.2  3.1523  24.0  666.0   \n",
       "488   0.15086   0.0  27.74   0.0  0.609  5.454   92.7  1.8209   4.0  711.0   \n",
       "489   0.18337   0.0  27.74   0.0  0.609  5.414   98.3  1.7554   4.0  711.0   \n",
       "490   0.20746   0.0  27.74   0.0  0.609  5.093   98.0  1.8226   4.0  711.0   \n",
       "491   0.10574   0.0  27.74   0.0  0.609  5.983   98.8  1.8681   4.0  711.0   \n",
       "492   0.11132   0.0  27.74   0.0  0.609  5.983   83.5  2.1099   4.0  711.0   \n",
       "493   0.17331   0.0   9.69   0.0  0.585  5.707   54.0  2.3817   6.0  391.0   \n",
       "494   0.27957   0.0   9.69   0.0  0.585  5.926   42.6  2.3817   6.0  391.0   \n",
       "495   0.17899   0.0   9.69   0.0  0.585  5.670   28.8  2.7986   6.0  391.0   \n",
       "496   0.28960   0.0   9.69   0.0  0.585  5.390   72.9  2.7986   6.0  391.0   \n",
       "497   0.26838   0.0   9.69   0.0  0.585  5.794   70.6  2.8927   6.0  391.0   \n",
       "498   0.23912   0.0   9.69   0.0  0.585  6.019   65.3  2.4091   6.0  391.0   \n",
       "499   0.17783   0.0   9.69   0.0  0.585  5.569   73.5  2.3999   6.0  391.0   \n",
       "500   0.22438   0.0   9.69   0.0  0.585  6.027   79.7  2.4982   6.0  391.0   \n",
       "501   0.06263   0.0  11.93   0.0  0.573  6.593   69.1  2.4786   1.0  273.0   \n",
       "502   0.04527   0.0  11.93   0.0  0.573  6.120   76.7  2.2875   1.0  273.0   \n",
       "503   0.06076   0.0  11.93   0.0  0.573  6.976   91.0  2.1675   1.0  273.0   \n",
       "504   0.10959   0.0  11.93   0.0  0.573  6.794   89.3  2.3889   1.0  273.0   \n",
       "505   0.04741   0.0  11.93   0.0  0.573  6.030   80.8  2.5050   1.0  273.0   \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  \n",
       "5       18.7  394.12   5.21  \n",
       "6       15.2  395.60  12.43  \n",
       "7       15.2  396.90  19.15  \n",
       "8       15.2  386.63  29.93  \n",
       "9       15.2  386.71  17.10  \n",
       "10      15.2  392.52  20.45  \n",
       "11      15.2  396.90  13.27  \n",
       "12      15.2  390.50  15.71  \n",
       "13      21.0  396.90   8.26  \n",
       "14      21.0  380.02  10.26  \n",
       "15      21.0  395.62   8.47  \n",
       "16      21.0  386.85   6.58  \n",
       "17      21.0  386.75  14.67  \n",
       "18      21.0  288.99  11.69  \n",
       "19      21.0  390.95  11.28  \n",
       "20      21.0  376.57  21.02  \n",
       "21      21.0  392.53  13.83  \n",
       "22      21.0  396.90  18.72  \n",
       "23      21.0  394.54  19.88  \n",
       "24      21.0  394.33  16.30  \n",
       "25      21.0  303.42  16.51  \n",
       "26      21.0  376.88  14.81  \n",
       "27      21.0  306.38  17.28  \n",
       "28      21.0  387.94  12.80  \n",
       "29      21.0  380.23  11.98  \n",
       "..       ...     ...    ...  \n",
       "476     20.2  396.21  18.68  \n",
       "477     20.2  349.48  24.91  \n",
       "478     20.2  379.70  18.03  \n",
       "479     20.2  383.32  13.11  \n",
       "480     20.2  396.90  10.74  \n",
       "481     20.2  393.07   7.74  \n",
       "482     20.2  395.28   7.01  \n",
       "483     20.2  392.92  10.42  \n",
       "484     20.2  370.73  13.34  \n",
       "485     20.2  388.62  10.58  \n",
       "486     20.2  392.68  14.98  \n",
       "487     20.2  388.22  11.45  \n",
       "488     20.1  395.09  18.06  \n",
       "489     20.1  344.05  23.97  \n",
       "490     20.1  318.43  29.68  \n",
       "491     20.1  390.11  18.07  \n",
       "492     20.1  396.90  13.35  \n",
       "493     19.2  396.90  12.01  \n",
       "494     19.2  396.90  13.59  \n",
       "495     19.2  393.29  17.60  \n",
       "496     19.2  396.90  21.14  \n",
       "497     19.2  396.90  14.10  \n",
       "498     19.2  396.90  12.92  \n",
       "499     19.2  395.77  15.10  \n",
       "500     19.2  396.90  14.33  \n",
       "501     21.0  391.99   9.67  \n",
       "502     21.0  396.90   9.08  \n",
       "503     21.0  396.90   5.64  \n",
       "504     21.0  393.45   6.48  \n",
       "505     21.0  396.90   7.88  \n",
       "\n",
       "[506 rows x 13 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=pd.DataFrame(boston.data,columns=boston.feature_names) # Creating a dataframe to perform operations on data \n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>3.613524</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>8.601545</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>3.677083</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     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   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%      3.677083   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": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.describe() #getting overall info of data distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y=boston.target # assigning the target value or end feature to be predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n",
       "       18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n",
       "       15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n",
       "       13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n",
       "       21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n",
       "       35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n",
       "       19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n",
       "       20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n",
       "       23.6, 28.7, 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, 19.8, 19.4,\n",
       "       21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n",
       "       20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n",
       "       23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n",
       "       15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n",
       "       17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n",
       "       25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n",
       "       23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n",
       "       32. , 29.8, 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, 22.5, 24.4,\n",
       "       20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n",
       "       26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n",
       "       31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n",
       "       22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n",
       "       42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n",
       "       36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n",
       "       32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n",
       "       20.1, 23.2, 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, 33.4, 28.2,\n",
       "       22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n",
       "       21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n",
       "       19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n",
       "       32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n",
       "       18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n",
       "       16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n",
       "       13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n",
       "        7.2, 10.5,  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,  5. , 11.9,\n",
       "       27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n",
       "        8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n",
       "        9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n",
       "       10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n",
       "       15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n",
       "       19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n",
       "       29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n",
       "       20.6, 21.2, 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, 22. , 11.9])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# creating new dataframe for single regression i.e how one feature affects target value Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>12.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>19.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>29.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>13.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>15.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>10.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>14.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>11.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>11.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>13.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>18.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>19.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>16.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>16.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>14.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>17.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>12.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>11.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>18.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>24.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>18.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>13.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>10.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>7.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>7.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>483</th>\n",
       "      <td>10.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>13.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>10.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>14.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>11.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>18.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>23.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>29.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>18.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>13.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>12.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>13.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>17.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>21.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>14.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>12.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>15.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>14.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>9.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>9.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>5.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>7.88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     LSTAT\n",
       "0     4.98\n",
       "1     9.14\n",
       "2     4.03\n",
       "3     2.94\n",
       "4     5.33\n",
       "5     5.21\n",
       "6    12.43\n",
       "7    19.15\n",
       "8    29.93\n",
       "9    17.10\n",
       "10   20.45\n",
       "11   13.27\n",
       "12   15.71\n",
       "13    8.26\n",
       "14   10.26\n",
       "15    8.47\n",
       "16    6.58\n",
       "17   14.67\n",
       "18   11.69\n",
       "19   11.28\n",
       "20   21.02\n",
       "21   13.83\n",
       "22   18.72\n",
       "23   19.88\n",
       "24   16.30\n",
       "25   16.51\n",
       "26   14.81\n",
       "27   17.28\n",
       "28   12.80\n",
       "29   11.98\n",
       "..     ...\n",
       "476  18.68\n",
       "477  24.91\n",
       "478  18.03\n",
       "479  13.11\n",
       "480  10.74\n",
       "481   7.74\n",
       "482   7.01\n",
       "483  10.42\n",
       "484  13.34\n",
       "485  10.58\n",
       "486  14.98\n",
       "487  11.45\n",
       "488  18.06\n",
       "489  23.97\n",
       "490  29.68\n",
       "491  18.07\n",
       "492  13.35\n",
       "493  12.01\n",
       "494  13.59\n",
       "495  17.60\n",
       "496  21.14\n",
       "497  14.10\n",
       "498  12.92\n",
       "499  15.10\n",
       "500  14.33\n",
       "501   9.67\n",
       "502   9.08\n",
       "503   5.64\n",
       "504   6.48\n",
       "505   7.88\n",
       "\n",
       "[506 rows x 1 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new=pd.DataFrame(X['LSTAT'])\n",
    "X_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 21.,  55.,  82., 154.,  84.,  41.,  30.,   8.,  10.,  21.]),\n",
       " array([ 5. ,  9.5, 14. , 18.5, 23. , 27.5, 32. , 36.5, 41. , 45.5, 50. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Regression\n",
    "\n",
    "creating a model of our algorithm,\n",
    "dividing the data into training and testing set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>469</th>\n",
       "      <td>14.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>34.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>454</th>\n",
       "      <td>18.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>426</th>\n",
       "      <td>15.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>362</th>\n",
       "      <td>10.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>162</th>\n",
       "      <td>1.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>216</th>\n",
       "      <td>13.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324</th>\n",
       "      <td>6.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>238</th>\n",
       "      <td>6.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>406</th>\n",
       "      <td>23.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>7.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>11.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>314</th>\n",
       "      <td>9.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>6.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>425</th>\n",
       "      <td>24.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>4.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>5.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>438</th>\n",
       "      <td>34.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>8.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>395</th>\n",
       "      <td>17.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>139</th>\n",
       "      <td>18.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>267</th>\n",
       "      <td>7.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>278</th>\n",
       "      <td>7.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>10.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>424</th>\n",
       "      <td>17.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>259</th>\n",
       "      <td>6.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>365</th>\n",
       "      <td>7.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>220</th>\n",
       "      <td>9.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>6.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>277</th>\n",
       "      <td>4.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>12.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>5.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>311</th>\n",
       "      <td>5.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>8.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>428</th>\n",
       "      <td>21.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>391</th>\n",
       "      <td>18.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>383</th>\n",
       "      <td>24.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>432</th>\n",
       "      <td>12.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>13.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>14.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>12.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>392</th>\n",
       "      <td>25.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>218</th>\n",
       "      <td>17.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>5.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>366</th>\n",
       "      <td>14.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>345</th>\n",
       "      <td>10.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>5.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>19.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>398</th>\n",
       "      <td>30.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>13.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>348</th>\n",
       "      <td>5.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>13.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>407</th>\n",
       "      <td>12.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>211</th>\n",
       "      <td>23.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>8.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>9.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>16.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>4.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>354 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     LSTAT\n",
       "469  14.76\n",
       "141  34.41\n",
       "454  18.71\n",
       "426  15.69\n",
       "362  10.19\n",
       "162   1.92\n",
       "216  13.51\n",
       "324   6.12\n",
       "238   6.36\n",
       "406  23.34\n",
       "81    7.22\n",
       "487  11.45\n",
       "314   9.28\n",
       "187   6.68\n",
       "425  24.39\n",
       "298   4.97\n",
       "179   5.04\n",
       "438  34.02\n",
       "53    8.43\n",
       "395  17.12\n",
       "139  18.46\n",
       "267   7.44\n",
       "278   7.19\n",
       "66   10.24\n",
       "424  17.16\n",
       "259   6.90\n",
       "365   7.12\n",
       "220   9.71\n",
       "99    6.19\n",
       "277   4.16\n",
       "..     ...\n",
       "6    12.43\n",
       "250   5.90\n",
       "311   5.98\n",
       "75    8.94\n",
       "0     4.98\n",
       "428  21.52\n",
       "391  18.76\n",
       "383  24.56\n",
       "432  12.03\n",
       "68   13.09\n",
       "486  14.98\n",
       "167  12.14\n",
       "392  25.68\n",
       "218  17.92\n",
       "42    5.81\n",
       "366  14.00\n",
       "345  10.53\n",
       "72    5.52\n",
       "23   19.88\n",
       "398  30.59\n",
       "185  13.15\n",
       "348   5.99\n",
       "103  13.44\n",
       "407  12.13\n",
       "211  23.98\n",
       "67    8.10\n",
       "502   9.08\n",
       "25   16.51\n",
       "196   4.08\n",
       "175   5.33\n",
       "\n",
       "[354 rows x 1 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model=LinearRegression()\n",
    "X_train,X_test,Y_train,Y_test = train_test_split(X_new,Y,test_size=0.3,random_state=7)#dividing data into 70% train and 30% test on random seed of 7\n",
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train,Y_train)# give data to model for learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22.26393949, 24.79620654, 22.71245911, 26.94536308, 15.39598272,\n",
       "       16.19023623, 22.41344603, 26.21651869, 30.29991611, 18.63840585,\n",
       "        6.05182386, 28.72075326, 19.16167875, 20.13347127, 31.75760489,\n",
       "       21.24542617, 25.78668738, 30.12237709,  8.77097409, 24.94571308,\n",
       "       17.20874954, 29.3935327 , 31.75760489, 17.41432104,  7.07033718,\n",
       "       10.56505259, 28.61796752, 28.60862336, 25.89881729, 25.77734322,\n",
       "       21.40427687, 28.99173387, 29.33746775, 17.72267828, 31.7108841 ,\n",
       "       20.30166613, 21.4883743 , 18.36742524, 22.76852407, 24.02998551,\n",
       "       26.43143434, 12.9478131 , 14.7418916 , 27.49666845, 20.92772477,\n",
       "       12.16290376, 27.2817528 , 22.82458902, 20.62871169, 22.20787454,\n",
       "       27.7583049 , 28.50583761, 25.21669369, 29.72057826, 17.79743155,\n",
       "       23.93654393, 19.93724393, 22.31066028, 25.85209649, 22.51623178,\n",
       "       21.9649264 , 24.15145958, 22.37606939, 25.98291472, 23.78703738,\n",
       "       31.97252055, 20.62871169, 24.27293364, 27.46863598, 30.42139018,\n",
       "       28.38436354, 14.00370305, 27.14159042, 30.24385116, 24.29162196,\n",
       "       22.63770584, 13.54583927, 17.17137291, 30.35598106, 22.47885514,\n",
       "       19.02151636, 29.72992242, 24.62801168, 26.36602523, 29.81401985,\n",
       "       25.74931074, 29.27205864, 20.98378972, 30.89794228, 28.25354532,\n",
       "       31.61744251, 31.00072803, 27.87977897, 24.41309603, 28.32829859,\n",
       "        6.65919419, 26.56225257, 15.9005673 ,  9.9950589 , 29.72057826,\n",
       "       18.09644464, 20.82493902, 29.45894181, 19.32052945, 21.23608201,\n",
       "       22.82458902, 18.83463319, 27.7583049 , 28.53387009, 22.09574463,\n",
       "       12.52732595, 26.64635   , 25.07653131, 25.34751191, 12.2656895 ,\n",
       "       24.89899229,  8.68687666, 31.91645559, 19.30184113, 26.04832383,\n",
       "       21.4883743 , 25.49701846, 14.61107338, 31.32777359, 12.91978063,\n",
       "       32.81349485, 25.76799906, 30.14106541, 27.09486962, 29.96352639,\n",
       "       24.50653762, 26.16045373, 22.70311496, 25.60914836, 28.72075326,\n",
       "       22.98343972, 30.37466938, 30.97269555, 16.05007384, 28.37501939,\n",
       "       18.5823409 , 25.1699729 , 25.67455747, 24.17949206, 30.50548761,\n",
       "       19.10561379, 30.40270186, 17.52645094, 26.31930444, 24.06736215,\n",
       "       24.98308972,  9.77079909])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_pred=model.predict(X_test)# now asking the model to answer from the learned experience\n",
    "Y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([21.7, 18.5, 22.2, 20.4,  8.8,  8.3, 21.4, 23.6, 23.5, 19. , 10.2,\n",
       "       31.6, 18.4, 19.4, 44. , 23.2, 22. , 33.1, 13.2, 21.7, 16.7, 23.9,\n",
       "       42.3, 18.5, 14.6,  7.5, 33.4, 22. , 28.1, 24.8, 19.9, 24.8, 28.7,\n",
       "       14.1, 43.5, 20.4, 18.3, 13.4, 21. , 22. , 22.6, 13.9, 13.3, 26.5,\n",
       "       20. ,  9.5, 21.6, 22.6, 15.6, 23.1, 27.1, 25.2, 15. , 21.9,  9.6,\n",
       "       22.7, 18.3, 21.4, 20.5, 21.1, 24.5, 31. , 18.7, 18.7, 22.7, 50. ,\n",
       "       16.7, 23. , 20.4, 22.8, 24.8, 10.5, 18.2, 31.5, 23.8, 19.6, 12.7,\n",
       "       15.2, 31.2, 14.5, 17.8, 25. , 23. , 50. , 23.7, 25.1, 24.7, 16.8,\n",
       "       34.7, 23.3, 50. , 46.7, 43.1, 24.4, 24.1,  6.3, 26.4, 16.3, 17.2,\n",
       "       28. , 15.2, 16.6, 20.6, 16.4, 22. , 17.2, 13.5, 23.3, 26.2, 19.7,\n",
       "       13.1, 23.9, 18.2, 19.3,  7. , 18.5, 13.8, 33.4, 12.6, 19.6, 20.8,\n",
       "       25. , 21.7, 43.8, 13.4, 34.9, 24.5, 26.6, 36.5, 31.1, 22.6, 20.3,\n",
       "       18.4, 28.7, 23.1, 17.6, 35.4, 31.6,  8.5, 22.2, 10.4, 22.8, 23.9,\n",
       "       22.2, 32.9, 15.6, 29.8, 14.3, 28.4, 21.4, 23.1, 10.4])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_test #actual answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5339673849132311"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_train,Y_train) #determinig how good we predicted on training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5677050267960129"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test,Y_test) #determining how good we predicted on testing data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>357</th>\n",
       "      <td>13.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>337</th>\n",
       "      <td>10.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>327</th>\n",
       "      <td>12.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>418</th>\n",
       "      <td>20.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>403</th>\n",
       "      <td>19.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>13.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>9.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>4.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>17.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>388</th>\n",
       "      <td>30.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>6.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>442</th>\n",
       "      <td>16.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>15.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>256</th>\n",
       "      <td>3.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>472</th>\n",
       "      <td>14.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>301</th>\n",
       "      <td>9.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>303</th>\n",
       "      <td>4.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>27.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294</th>\n",
       "      <td>10.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>18.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>5.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>3.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>18.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>29.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>416</th>\n",
       "      <td>25.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>306</th>\n",
       "      <td>6.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>213</th>\n",
       "      <td>9.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>289</th>\n",
       "      <td>9.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>221</th>\n",
       "      <td>21.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>3.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>435</th>\n",
       "      <td>23.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>9.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>4.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>264</th>\n",
       "      <td>8.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>5.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>205</th>\n",
       "      <td>10.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>9.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>12.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>217</th>\n",
       "      <td>9.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>347</th>\n",
       "      <td>6.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244</th>\n",
       "      <td>12.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>281</th>\n",
       "      <td>4.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>3.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>397</th>\n",
       "      <td>19.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>6.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>380</th>\n",
       "      <td>17.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>10.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>9.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>11.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>4.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>16.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>4.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>18.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>305</th>\n",
       "      <td>8.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>11.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>318</th>\n",
       "      <td>10.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>417</th>\n",
       "      <td>26.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>152 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     LSTAT\n",
       "357  13.27\n",
       "337  10.56\n",
       "327  12.79\n",
       "13    8.26\n",
       "418  20.62\n",
       "403  19.77\n",
       "479  13.11\n",
       "173   9.04\n",
       "65    4.67\n",
       "466  17.15\n",
       "388  30.62\n",
       "227   6.36\n",
       "442  16.59\n",
       "109  15.55\n",
       "256   3.11\n",
       "472  14.36\n",
       "301   9.50\n",
       "303   4.86\n",
       "32   27.71\n",
       "294  10.40\n",
       "476  18.68\n",
       "503   5.64\n",
       "202   3.11\n",
       "245  18.46\n",
       "147  29.53\n",
       "416  25.79\n",
       "306   6.47\n",
       "504   6.48\n",
       "213   9.38\n",
       "289   9.51\n",
       "..     ...\n",
       "221  21.46\n",
       "98    3.57\n",
       "435  23.27\n",
       "40    1.98\n",
       "248   9.52\n",
       "41    4.84\n",
       "264   8.10\n",
       "193   5.03\n",
       "205  10.87\n",
       "79    9.10\n",
       "28   12.80\n",
       "217   9.69\n",
       "347   6.36\n",
       "244  12.50\n",
       "281   4.59\n",
       "57    3.95\n",
       "397  19.92\n",
       "62    6.73\n",
       "380  17.21\n",
       "111  10.16\n",
       "84    9.62\n",
       "242  11.22\n",
       "200   4.45\n",
       "146  16.65\n",
       "188   4.56\n",
       "129  18.34\n",
       "305   8.93\n",
       "96   11.34\n",
       "318  10.36\n",
       "417  26.64\n",
       "\n",
       "[152 rows x 1 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_test['LSTAT'], Y_test,  color='gray') #plotting the points in form of dots through scatter function\n",
    "plt.plot(X_test['LSTAT'], Y_pred, color='red', linewidth=2)# determinig the best fit line\n",
    "plt.show()# function to display after pllot creaion on screen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.93441589])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_ # determining coeffiecents(a1,a2,....)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.663638300161935"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_# determining intercepts(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Regression\n",
    "   \n",
    "   using all the features to determine how the end target is depended on all attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "# similar step as explained earlier\n",
    "model=LinearRegression()\n",
    "X_train,X_test,Y_train,Y_test = train_test_split(X,Y,test_size=0.3,random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28.64896005, 36.49501384, 15.4111932 , 25.40321303, 18.85527988,\n",
       "       23.14668944, 17.3921241 , 14.07859899, 23.03692679, 20.59943345,\n",
       "       24.82286159, 18.53057049, -6.86543527, 21.80172334, 19.22571177,\n",
       "       26.19191985, 20.27733882,  5.61596432, 40.44887974, 17.57695918,\n",
       "       27.44319095, 30.1715964 , 10.94055823, 24.02083139, 18.07693812,\n",
       "       15.934748  , 23.12614028, 14.56052142, 22.33482544, 19.3257627 ,\n",
       "       22.16564973, 25.19476081, 25.31372473, 18.51345025, 16.6223286 ,\n",
       "       17.50268505, 30.94992991, 20.19201752, 23.90440431, 24.86975466,\n",
       "       13.93767876, 31.82504715, 42.56978796, 17.62323805, 27.01963242,\n",
       "       17.19006621, 13.80594006, 26.10356557, 20.31516118, 30.08649576,\n",
       "       21.3124053 , 34.15739602, 15.60444981, 26.11247588, 39.31613646,\n",
       "       22.99282065, 18.95764781, 33.05555669, 24.85114223, 12.91729352,\n",
       "       22.68101452, 30.80336295, 31.63522027, 16.29833689, 21.07379993,\n",
       "       16.57699669, 20.36362023, 26.15615896, 31.06833034, 11.98679953,\n",
       "       20.42550472, 27.55676301, 10.94316981, 16.82660609, 23.92909733,\n",
       "        5.28065815, 21.43504661, 41.33684993, 18.22211675,  9.48269245,\n",
       "       21.19857446, 12.95001331, 21.64822797,  9.3845568 , 23.06060014,\n",
       "       31.95762512, 19.16662892, 25.59942257, 29.35043558, 20.13138581,\n",
       "       25.57297369,  5.42970803, 20.23169356, 15.1949595 , 14.03241742,\n",
       "       20.91078077, 24.82249135, -0.47712079, 13.70520524, 15.69525576,\n",
       "       22.06972676, 24.64152943, 10.7382866 , 19.68622564, 23.63678009,\n",
       "       12.07974981, 18.47894211, 25.52713393, 20.93461307, 24.6955941 ,\n",
       "        7.59054562, 19.01046053, 21.9444339 , 27.22319977, 32.18608828,\n",
       "       15.27826455, 34.39190421, 12.96314168, 21.01681316, 28.57880911,\n",
       "       15.86300844, 24.85124135,  3.37937111, 23.90465773, 25.81792146,\n",
       "       23.11020547, 25.33489201, 33.35545176, 20.60724498, 38.4772665 ,\n",
       "       13.97398533, 25.21923987, 17.80946626, 20.63437371,  9.80267398,\n",
       "       21.07953576, 22.3378417 , 32.32381854, 31.48694863, 15.46621287,\n",
       "       16.86242766, 28.99330526, 24.95467894, 16.73633557,  6.12858395,\n",
       "       26.65990044, 23.34007187, 17.40367164, 13.38594123, 39.98342478,\n",
       "       16.68286302, 18.28561759])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_pred=model.predict(X_test)\n",
    "Y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7434997532004697"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.711226005748496"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test,Y_test)\n",
    "\n",
    "# What is this score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so it is\n",
    "\n",
    "# 1-mse(predicted model)/mse(average_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted=np.mean(Y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_avg_test=[predicted]*len(Y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.711226005748496"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-(mean_squared_error(Y_test,Y_pred)/mean_squared_error(Y_test,Y_avg_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.33470103e-01,  3.58089136e-02,  4.95226452e-02,  3.11983512e+00,\n",
       "       -1.54170609e+01,  4.05719923e+00, -1.08208352e-02, -1.38599824e+00,\n",
       "        2.42727340e-01, -8.70223437e-03, -9.10685208e-01,  1.17941159e-02,\n",
       "       -5.47113313e-01])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31.631084035694585"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot to show how much importance eaach feature has in determinig the target\n",
    "plt.bar(boston.feature_names,model.coef_)\n",
    "plt.xticks(rotation= 60)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scalability as a factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "#standardizing the attributes\n",
    "\n",
    "model=LinearRegression()\n",
    "scalar=StandardScaler()\n",
    "X_train,X_test,Y_train,Y_test = train_test_split(X,Y,test_size=0.3,random_state=42)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_scaled=scalar.fit_transform(X_train)\n",
    "X_test_scaled=scalar.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.140251946943885"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_scaled.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train_scaled,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_new_predicted=model.predict(X_test_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7434997532004697"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_train_scaled,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7112260057484934"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test_scaled,Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularization and Issues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Regularization\n",
    "\n",
    "b= 10\n",
    "a = 5\n",
    "error = 20\n",
    "\n",
    "\n",
    "b=10\n",
    "a=50  => lead to over-fitting\n",
    "error = 19.5 \n",
    "\n",
    "\n",
    "Error_Term = Sum of squared errors\n",
    "           =  sigma_i (yi - ai -b)^2\n",
    "    \n",
    "    \n",
    "Error Terms = Sum of squared errors + regularization term * sum of square of corefficients\n",
    "         = sigma_i (yi - ai -b)^2+     alpha * sigma_j(a_j^2)\n",
    "\n",
    "    \n",
    "    \n",
    "alpha = 0.01\n",
    "b= 10\n",
    "a = 5\n",
    "error = 20 + 0.01 (5^2)= 20.25\n",
    "\n",
    " \n",
    "\n",
    "b=10\n",
    "a=50  => lead to over-fitting\n",
    "error = 19.5 + 0.01(50^2) = 34.5\n",
    "\n",
    "\n",
    "b=10\n",
    "a= 10\n",
    "error = 19.8 + 0.01(10^2) = 20.8\n",
    "\n",
    "b=10\n",
    "a= 6\n",
    "erorr = 19.85 + 0.01(6^2)= 20.21\n",
    "error  -0.15\n",
    "reglarization +0.11\n",
    "\n",
    "\n",
    "Ridge regularization or L2 Regularization\n",
    " sigma_i (yi - ai -b)^2+     alpha * sigma_j(a_j^2)\n",
    "    \n",
    "Lasso regularizatior or L1 regularization\n",
    "sigma_i (yi - ai -b)^2+     alpha * sigma_j(|a_j|)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge Regularization (L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1=Ridge(alpha=.0001)\n",
    "\n",
    "model1.fit(X_train,Y_train)\n",
    "Y_reg=model1.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21.517511858968156"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(Y_test,Y_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7434997531265819"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.score(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7112250981524468"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.score(X_test,Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lasso Regularization (L1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2=Lasso(alpha=.000001)\n",
    "model2.fit(X_train,Y_train)\n",
    "\n",
    "Y_reg2=model2.predict(X_test)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7112258251516046"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "+"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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