LinearRegression-By Saumya Pancholi(Machine Learning project)_Final.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error \n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boston House Prediction By linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1:-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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": [
    "# Load the Dataset\n",
    "boston=load_boston()\n",
    "#Description of dataset\n",
    "print(boston.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Put data into Pandas DataFrames\n",
    "features=pd.DataFrame(boston.data, columns=boston.feature_names)\n",
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>28.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>22.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>27.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>18.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>18.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>21.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>20.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>19.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>23.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>13.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>19.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>15.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>14.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>15.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>13.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>16.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>14.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>18.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>16.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>14.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>23.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>25.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>483</th>\n",
       "      <td>21.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>19.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>15.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>13.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>20.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>21.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>24.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>23.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>19.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>18.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>17.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>16.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>23.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Target\n",
       "0      24.0\n",
       "1      21.6\n",
       "2      34.7\n",
       "3      33.4\n",
       "4      36.2\n",
       "5      28.7\n",
       "6      22.9\n",
       "7      27.1\n",
       "8      16.5\n",
       "9      18.9\n",
       "10     15.0\n",
       "11     18.9\n",
       "12     21.7\n",
       "13     20.4\n",
       "14     18.2\n",
       "15     19.9\n",
       "16     23.1\n",
       "17     17.5\n",
       "18     20.2\n",
       "19     18.2\n",
       "20     13.6\n",
       "21     19.6\n",
       "22     15.2\n",
       "23     14.5\n",
       "24     15.6\n",
       "25     13.9\n",
       "26     16.6\n",
       "27     14.8\n",
       "28     18.4\n",
       "29     21.0\n",
       "..      ...\n",
       "476    16.7\n",
       "477    12.0\n",
       "478    14.6\n",
       "479    21.4\n",
       "480    23.0\n",
       "481    23.7\n",
       "482    25.0\n",
       "483    21.8\n",
       "484    20.6\n",
       "485    21.2\n",
       "486    19.1\n",
       "487    20.6\n",
       "488    15.2\n",
       "489     7.0\n",
       "490     8.1\n",
       "491    13.6\n",
       "492    20.1\n",
       "493    21.8\n",
       "494    24.5\n",
       "495    23.1\n",
       "496    19.7\n",
       "497    18.3\n",
       "498    21.2\n",
       "499    17.5\n",
       "500    16.8\n",
       "501    22.4\n",
       "502    20.6\n",
       "503    23.9\n",
       "504    22.0\n",
       "505    11.9\n",
       "\n",
       "[506 rows x 1 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target=pd.DataFrame(boston.target,columns=['Target'])\n",
    "target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(target['Target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(target['Target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>Target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "    <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",
       "      <td>28.7</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",
       "      <td>22.9</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",
       "      <td>27.1</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",
       "      <td>16.5</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",
       "      <td>18.9</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",
       "      <td>15.0</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",
       "      <td>18.9</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",
       "      <td>21.7</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",
       "      <td>20.4</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",
       "      <td>18.2</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",
       "      <td>19.9</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",
       "      <td>23.1</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",
       "      <td>17.5</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",
       "      <td>20.2</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",
       "      <td>18.2</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",
       "      <td>13.6</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",
       "      <td>19.6</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",
       "      <td>15.2</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",
       "      <td>14.5</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",
       "      <td>15.6</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",
       "      <td>13.9</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",
       "      <td>16.6</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",
       "      <td>14.8</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",
       "      <td>18.4</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",
       "      <td>21.0</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",
       "      <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",
       "      <td>16.7</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",
       "      <td>12.0</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",
       "      <td>14.6</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",
       "      <td>21.4</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",
       "      <td>23.0</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",
       "      <td>23.7</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",
       "      <td>25.0</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",
       "      <td>21.8</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",
       "      <td>20.6</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",
       "      <td>21.2</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",
       "      <td>19.1</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",
       "      <td>20.6</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",
       "      <td>15.2</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",
       "      <td>7.0</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",
       "      <td>8.1</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",
       "      <td>13.6</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",
       "      <td>20.1</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",
       "      <td>21.8</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",
       "      <td>24.5</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",
       "      <td>23.1</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",
       "      <td>19.7</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",
       "      <td>18.3</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",
       "      <td>21.2</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",
       "      <td>17.5</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",
       "      <td>16.8</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",
       "      <td>22.4</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",
       "      <td>20.6</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",
       "      <td>23.9</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",
       "      <td>22.0</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",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>506 rows × 14 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  Target  \n",
       "0       15.3  396.90   4.98    24.0  \n",
       "1       17.8  396.90   9.14    21.6  \n",
       "2       17.8  392.83   4.03    34.7  \n",
       "3       18.7  394.63   2.94    33.4  \n",
       "4       18.7  396.90   5.33    36.2  \n",
       "5       18.7  394.12   5.21    28.7  \n",
       "6       15.2  395.60  12.43    22.9  \n",
       "7       15.2  396.90  19.15    27.1  \n",
       "8       15.2  386.63  29.93    16.5  \n",
       "9       15.2  386.71  17.10    18.9  \n",
       "10      15.2  392.52  20.45    15.0  \n",
       "11      15.2  396.90  13.27    18.9  \n",
       "12      15.2  390.50  15.71    21.7  \n",
       "13      21.0  396.90   8.26    20.4  \n",
       "14      21.0  380.02  10.26    18.2  \n",
       "15      21.0  395.62   8.47    19.9  \n",
       "16      21.0  386.85   6.58    23.1  \n",
       "17      21.0  386.75  14.67    17.5  \n",
       "18      21.0  288.99  11.69    20.2  \n",
       "19      21.0  390.95  11.28    18.2  \n",
       "20      21.0  376.57  21.02    13.6  \n",
       "21      21.0  392.53  13.83    19.6  \n",
       "22      21.0  396.90  18.72    15.2  \n",
       "23      21.0  394.54  19.88    14.5  \n",
       "24      21.0  394.33  16.30    15.6  \n",
       "25      21.0  303.42  16.51    13.9  \n",
       "26      21.0  376.88  14.81    16.6  \n",
       "27      21.0  306.38  17.28    14.8  \n",
       "28      21.0  387.94  12.80    18.4  \n",
       "29      21.0  380.23  11.98    21.0  \n",
       "..       ...     ...    ...     ...  \n",
       "476     20.2  396.21  18.68    16.7  \n",
       "477     20.2  349.48  24.91    12.0  \n",
       "478     20.2  379.70  18.03    14.6  \n",
       "479     20.2  383.32  13.11    21.4  \n",
       "480     20.2  396.90  10.74    23.0  \n",
       "481     20.2  393.07   7.74    23.7  \n",
       "482     20.2  395.28   7.01    25.0  \n",
       "483     20.2  392.92  10.42    21.8  \n",
       "484     20.2  370.73  13.34    20.6  \n",
       "485     20.2  388.62  10.58    21.2  \n",
       "486     20.2  392.68  14.98    19.1  \n",
       "487     20.2  388.22  11.45    20.6  \n",
       "488     20.1  395.09  18.06    15.2  \n",
       "489     20.1  344.05  23.97     7.0  \n",
       "490     20.1  318.43  29.68     8.1  \n",
       "491     20.1  390.11  18.07    13.6  \n",
       "492     20.1  396.90  13.35    20.1  \n",
       "493     19.2  396.90  12.01    21.8  \n",
       "494     19.2  396.90  13.59    24.5  \n",
       "495     19.2  393.29  17.60    23.1  \n",
       "496     19.2  396.90  21.14    19.7  \n",
       "497     19.2  396.90  14.10    18.3  \n",
       "498     19.2  396.90  12.92    21.2  \n",
       "499     19.2  395.77  15.10    17.5  \n",
       "500     19.2  396.90  14.33    16.8  \n",
       "501     21.0  391.99   9.67    22.4  \n",
       "502     21.0  396.90   9.08    20.6  \n",
       "503     21.0  396.90   5.64    23.9  \n",
       "504     21.0  393.45   6.48    22.0  \n",
       "505     21.0  396.90   7.88    11.9  \n",
       "\n",
       "[506 rows x 14 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#concatenate feature & Tareget into a Single DataFrame\n",
    "#axis = 1 makes it concatenate columnwise\n",
    "df=pd.concat([features,target],axis=1)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "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",
       "      <th>Target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "      <td>506.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.61</td>\n",
       "      <td>11.36</td>\n",
       "      <td>11.14</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.55</td>\n",
       "      <td>6.28</td>\n",
       "      <td>68.57</td>\n",
       "      <td>3.80</td>\n",
       "      <td>9.55</td>\n",
       "      <td>408.24</td>\n",
       "      <td>18.46</td>\n",
       "      <td>356.67</td>\n",
       "      <td>12.65</td>\n",
       "      <td>22.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.60</td>\n",
       "      <td>23.32</td>\n",
       "      <td>6.86</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.70</td>\n",
       "      <td>28.15</td>\n",
       "      <td>2.11</td>\n",
       "      <td>8.71</td>\n",
       "      <td>168.54</td>\n",
       "      <td>2.16</td>\n",
       "      <td>91.29</td>\n",
       "      <td>7.14</td>\n",
       "      <td>9.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.38</td>\n",
       "      <td>3.56</td>\n",
       "      <td>2.90</td>\n",
       "      <td>1.13</td>\n",
       "      <td>1.00</td>\n",
       "      <td>187.00</td>\n",
       "      <td>12.60</td>\n",
       "      <td>0.32</td>\n",
       "      <td>1.73</td>\n",
       "      <td>5.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.08</td>\n",
       "      <td>0.00</td>\n",
       "      <td>5.19</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.45</td>\n",
       "      <td>5.89</td>\n",
       "      <td>45.02</td>\n",
       "      <td>2.10</td>\n",
       "      <td>4.00</td>\n",
       "      <td>279.00</td>\n",
       "      <td>17.40</td>\n",
       "      <td>375.38</td>\n",
       "      <td>6.95</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.26</td>\n",
       "      <td>0.00</td>\n",
       "      <td>9.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.54</td>\n",
       "      <td>6.21</td>\n",
       "      <td>77.50</td>\n",
       "      <td>3.21</td>\n",
       "      <td>5.00</td>\n",
       "      <td>330.00</td>\n",
       "      <td>19.05</td>\n",
       "      <td>391.44</td>\n",
       "      <td>11.36</td>\n",
       "      <td>21.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.68</td>\n",
       "      <td>12.50</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.62</td>\n",
       "      <td>6.62</td>\n",
       "      <td>94.07</td>\n",
       "      <td>5.19</td>\n",
       "      <td>24.00</td>\n",
       "      <td>666.00</td>\n",
       "      <td>20.20</td>\n",
       "      <td>396.22</td>\n",
       "      <td>16.96</td>\n",
       "      <td>25.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.98</td>\n",
       "      <td>100.00</td>\n",
       "      <td>27.74</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.87</td>\n",
       "      <td>8.78</td>\n",
       "      <td>100.00</td>\n",
       "      <td>12.13</td>\n",
       "      <td>24.00</td>\n",
       "      <td>711.00</td>\n",
       "      <td>22.00</td>\n",
       "      <td>396.90</td>\n",
       "      <td>37.97</td>\n",
       "      <td>50.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         CRIM      ZN   INDUS    CHAS     NOX      RM     AGE     DIS     RAD  \\\n",
       "count  506.00  506.00  506.00  506.00  506.00  506.00  506.00  506.00  506.00   \n",
       "mean     3.61   11.36   11.14    0.07    0.55    6.28   68.57    3.80    9.55   \n",
       "std      8.60   23.32    6.86    0.25    0.12    0.70   28.15    2.11    8.71   \n",
       "min      0.01    0.00    0.46    0.00    0.38    3.56    2.90    1.13    1.00   \n",
       "25%      0.08    0.00    5.19    0.00    0.45    5.89   45.02    2.10    4.00   \n",
       "50%      0.26    0.00    9.69    0.00    0.54    6.21   77.50    3.21    5.00   \n",
       "75%      3.68   12.50   18.10    0.00    0.62    6.62   94.07    5.19   24.00   \n",
       "max     88.98  100.00   27.74    1.00    0.87    8.78  100.00   12.13   24.00   \n",
       "\n",
       "          TAX  PTRATIO       B   LSTAT  Target  \n",
       "count  506.00   506.00  506.00  506.00  506.00  \n",
       "mean   408.24    18.46  356.67   12.65   22.53  \n",
       "std    168.54     2.16   91.29    7.14    9.20  \n",
       "min    187.00    12.60    0.32    1.73    5.00  \n",
       "25%    279.00    17.40  375.38    6.95   17.02  \n",
       "50%    330.00    19.05  391.44   11.36   21.20  \n",
       "75%    666.00    20.20  396.22   16.96   25.00  \n",
       "max    711.00    22.00  396.90   37.97   50.00  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#use round(decimals=2) to set the precison to 2 Decimal\n",
    "df.describe().round(decimals=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#calculate the correlation between every columns the data\n",
    "corr=df.corr('pearson')\n",
    "#take absolute values of correlation \n",
    "corrs=[abs(corr[attr]['Target']) for attr in list(features)]\n",
    "\n",
    "#make a list of pairs [(corr, features)]\n",
    "l=list(zip(corrs,list(features)))\n",
    "\n",
    "#Sort the list of pairs in reverse/descending order,\n",
    "#with the correlation value as the key for sorting\n",
    "l.sort(key=lambda x:x[0],reverse=True)\n",
    "\n",
    "#\"unzip\" the pairs to two lists\n",
    "corrs,labels=list(zip((*l)))\n",
    "\n",
    "#Now plotting the correlation w.r.t the target variable as bar graph\n",
    "index=np.arange(len(labels))\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(index,corrs,width=0.75)\n",
    "plt.xlabel('Attributes')\n",
    "plt.ylabel('correlation with the target variable')\n",
    "plt.xticks(index,labels)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normalization of Data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=df['RM'].values #Will indicate mostly of -ve slope \n",
    "Y=df['Target'].values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[24.  21.6 34.7 33.4 36.2]\n"
     ]
    }
   ],
   "source": [
    "#before normalization\n",
    "print(Y[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_scaler=MinMaxScaler()\n",
    "X=x_scaler.fit_transform(X.reshape(-1,1))\n",
    "X=X[:,-1]\n",
    "y_scaler=MinMaxScaler()\n",
    "Y=y_scaler.fit_transform(Y.reshape(-1,1))\n",
    "Y=Y[:,-1]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.42222222 0.36888889 0.66       0.63111111 0.69333333]\n"
     ]
    }
   ],
   "source": [
    "#after normalisation\n",
    "print(Y[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Splitting Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#0.2 indicating 20% of data is Randomly Sampled as Testing data\n",
    "xtrain, xtest, ytrain, ytest = train_test_split(X,Y,test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loss Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Error Function\n",
    "def error(m,x,c,t):\n",
    "    N=x.size\n",
    "    e=sum(((m * x + c) - t)**2)\n",
    "    return e * 1/(2 * N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying Gradiant Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(m,x,c,t,learning_rate):\n",
    "    grad_m = sum (2 * ( (m * x + c) - t) * x)\n",
    "    grad_c = sum (2 * ( (m * x + c) - t))\n",
    "    m=m- grad_m * learning_rate\n",
    "    c = c- grad_c * learning_rate\n",
    "    return [m, c];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(init_m,init_c,x,t,learning_rate,iterations,error_threshold):\n",
    "    m = init_m\n",
    "    c = init_c\n",
    "    error_values = list()\n",
    "    mc_values = list()\n",
    "    for i in range (iterations):\n",
    "        e=error(m, x, c, t)\n",
    "        #print(\"Iteration :\"+str(i)+\"Error :\"+str(e))\n",
    "        if e<error_threshold:\n",
    "            print('Error less that the threshold,Stoping Gradient Descent')\n",
    "            break\n",
    "        \n",
    "        error_values.append(e)\n",
    "        m, c = update(m, x, c, t, learning_rate) \n",
    "        mc_values.append((m, c))\n",
    "        \n",
    "        return [m, c, error_values, mc_values];    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Training Visulization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1e+03 µs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "init_m = 0.9\n",
    "init_c = 0\n",
    "learning_rate=0.001\n",
    "iterations=250\n",
    "error_threshold=0.001\n",
    "\n",
    "m, c, error_values, mc_values = gradient_descent(init_m, init_c, xtrain, ytrain, learning_rate, iterations, error_threshold)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x8b71fd0>]"
      ]
     },
     "execution_count": 31,
     "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": [
    "import matplotlib.animation\n",
    "plt.scatter(xtrain,ytrain,color='g')\n",
    "plt.plot(xtrain,(m*xtrain+c),color='b')\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Iterations')"
      ]
     },
     "execution_count": 32,
     "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.plot(np.arange(len(error_values)),error_values)\n",
    "plt.ylabel('Error')\n",
    "plt.xlabel('Iterations')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc_values_anim=mc_values[0:250:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Zl0YYNgz23dePrx81SsMti5gCvkiEwqpSmS5Nk+qCAP7O/r+2Hso1v3nM392PHw/PPAPf/nZGbZHCoRy+SESCjJYJKt3onFQXhK3q4KsN58KlV8G//zs89xwcdFCbji2FS3f4IhEJOlomiHSjc5LNni3/EOZPxQ+zPP10WLxYwb7EKOCLRCToJKkgkpVHaF57vvkFwRrgrPmwaDJ8e/02MGMGTJ7sJ1RJSVFKRyQiQSZJtUX14OqUqaCm52fNm8zUBxo48h/wasXu7DdrAXzzmxkdTwqf7vBFIhJkklSYqr8cyLt/3ZEj12wLNTXs9+JbCvYlTgFfJEtBR96kS8OEdtzPP4eRI+G442CvvXyufvRoDbeU9NUyc0XVMqUYtBx50yTXa7mmOu5VHY7lvJol8Pbb8Nvfwrhx0L59ztoh0cumWqYCvkgWQlsfNsvjltXDJU/CRc9C4lt7+sVKDjkkZ8eX+OR6TVsRSSHMkTcttZYqar7/fT6C52+C3z0Dtx6AnzGrYC9JKOCLZCHVCJtMR940SbeSVcIS4GD0Qlh8A+z1KfzseKj8jwTssENWx5bipYAvkoW2jrwJ2sGbbpLWuXsNZ9YdUDMbntkD9h8D95XnbsSPFAeNwxfJQvOFQ+pdfdLyxE3aUlqh1VTRzJn8+Zw5bFiX4OyjGvjLgY52iQRjUhxXpIk6bUUi0pYO3mTbbvcVXPuIcfoiB717w9/+Bj175rTNkn/UaStSANrSwdsyNdN/NSyeDKNecnDBBX6NWQV7aSOldEQi0pbSCk2pmZtenMyFTzfw+6dhXeeOtJv3IBx2WM7bKsVJd/giEWlrB291j3P4au6BjH8Syk4cTuf/Wa1gL1lRwBeJSODSCs75pQZ794YVK2DaND+RqlOnGFotxUSdtiL5ZO1aX6t+xgwYMABuuQW6d4+7VZJH1GkrUgzmzIH994eHHoJrroFHH1Wwl1Ap4Is0Cmu92TZbvx7GjoXBg6FrV1i4EM45B9rpz1PCpU+UCOlLGQR5fUYXi0WL+KBHN6iu5prvwnbHLqfq3Rsy/WeItEoBX4Ts1pvN6GJRXw9XXEH9Qf2pW/cZA0fAeUfC+rKGNl1oRNpCAV+E7KpetvlisWqVH1558cXcu6+j1xh4Yq+ArxXJgiZeSVGpml2Vtq5Nsm2yWW+2tYtFz0k9WfHxCupdPebgF0vgL3PAGdx/7kBGdnwckixEFUZ5ZZGWdIcvRSNIaiXVNj0690i6zyDVJ1u7KCz/aDn1rp6d1sNdd8OtD8DiXaDXGBi5/eNYimUHsy2vLJKMAr4UjSCplVTbrPh4Rcbrzaa6WDT50T9gaQ0MfR0u+BEMOBne2dH/zpF8HkyDa4h+tJAUPaV0pGgEycO3tk314Oo2lxeuml3F8o+WJ/3dNl/DHx+DXy2A5V3gJyfCy7sE22/ThaC1EsoibaU7fCkaQVafCnuFqlTfGHp9AAun+GA/sT/0OyN9sE9YImU71IkrYVDAl6IRpDhZWwuYpdPyG0O7BjjvOR/sO/8LjhwOZx8NX7YPtq9crpErooAvkcvVjNbqwdWUdynf7LnyLuWbpUICFzALqPkdeffP4LHb4KpHYVYP6F3VjtUHl2/cxpINx8ngOCKZCpTDN7NBwH8DCWCqc+5PKbY7DrgbONA5p8posoW2LPOXyb5b5tOXf7ScqtlVWwT9sPLhlf0qqamtYdhSqJ4NCQcjh8K2p43mnz+pSfqaluegOcOSduRqrVoJQ9o7fDNLAJOAo4ByYJiZlSfZbnvgl8CCsBspxSObGa1h7TvMbxjV3/sDL877NnfcB8t2hr5j2rHt6WOoThHsofULm8OF+g1EpLkgKZ3+wErn3JvOuQ3AncDQJNtdBlwJfBli+6TI5DJHHWTf2dbM2cy8eXDAARz43Ftw2WVMu/4MVu1k1NTWpL2QtNZ5XD24mrpxdbhLHHXj6hTsJTRBAn434N1mj1c3PreRmfUBujvnHmxtR2ZWaWa1Zla7du3aNjdWCl/Yo2Tauu8wvmH88oEzuOaQdjQMGMCK9e/y5yuHUtVnDZMWTw58IQm781gkiCABP1lP08Yko5m1A64Fzk23I+fcFOdchXOuomvXrsFbKUUjl4EuyL5b+xYQJL1z2aSfM2r0FM593jG5AvqeARd+fm/KnHyqC0nYncciQQTptF0NNF+FYTdgTbPH2wP7AU82ThP/JjDTzIao41Zaagpo6erd5GrfqWrmQJoO5IYGmDiR88+bzrpt4CfDYHbrE2w37rO19irAS5TSLnFoZmXAG8BA4D1gIXCic25Ziu2fBM5LF+y1xKHEobURMk0SlqBuXN2mJ957D045BR57jJn7wGlDYG3HYMfbYl8iWcrpEofOuTrgTGAu8Bow3Tm3zMwmmNmQTA4qEpcgd9Sb3ZXffbdfdvD552HyZIYOCx7sQTl5yS+BJl455+Y45/Zxzv27c+4Pjc+Nc87NTLLt4UrlSD5L10GcsATnTB/Fbb3bwfHH82KHT7n02qFQWZm8R6uRcvKS79KmdHJFKR3JVs9JPTebaFXepZxlY5NmGjeTLq0z/LM9uOyvb9P9c7j8B/6/uoQP6EDS1yq4S1RymtIRaU1cC3+3DPbgZ9X2nNQz7WubRsi0LHXQvg7+8Bjcet3b1LeDQ0+FS3/ogz34zmCNrpFCpjt8yViqO+UoAqCNb70uTZDVrprbdy387T7o9z5M7QO/HgRfbL3lft0l8fy9iDTRHb7EIpdlErIVZLUrABxUvQgvTYY9PoNjfw6nD00e7FXATAqdAr5krBBK+ba22tU3/hdm/x0mzYEnvwX7V8GM76TeV6YjbuJKe4m0pIAvGctlmYR0WpZBTiXValfHvgavVsMP34Kqo+Hok+CD7Te9rnl+P5s8fai1e0SypIAvGYuzHkyQ0Tiw5WpXHb+CG2fA/XfB2zv60gg1/dliuGVTieIxFWMyLmDW2migfEh7SelRwJeMFcKIleYXnz92GMLLN8Cpi+GKQ+G7o+D1NCWdMg3M6YZ+5lPaS0qHFjGXrMRZDybVYiHQYpTO11/D5Zdz/uUz+LjL9gw49f94avcGEpagvHMPVny8IvT+iHQXCnUASxwU8CVvNR9CmWyY5eiK0emHhb7xBgwfDgsXwogRdJ44kSc7ddriNWUTypIG90wDc7oLhUouSByU0pG8FKSzsyml1FJNbQ12qTF6SDu+6tUTVq6E6dPh1luhRbBvGkGTKkBnGphbu1DkW9pLSocCvuSlbMb4d/0CZkyDG2Y5nu5Wxw/P7ULZa8O2GBaZdFx+o2z7I1JdKBTsJU5K6UheCppTb3kBGLwCbpoJnb6EXx0JEw8CV/c/m72+KQ2U6uKRaUnjlimo8i7lG/sHwqz7L5IpBXzJS6kWKmmZKmnapsMGuPoRGFMLS74BA0fAsm+k3n+y8got99kWLUfl1Lt6ln+0XHf0kleU0pG80XxGaoNrSLpNy1RJwhJUvOdLI5xRC1d9D/qf3nqwBzbedSeTSUdtPpeZEGmigJ8HNPV+y3x6y+GWSXPqdXXc9z/9eP4m6PA1DDwZfvNj2BDge2tTiiWZIB21Ld+zQigzIaKUTsySpQJSrqtaxNqcT//HP+AXv2DICy9yx34wdjB8tm3w4zXPpycb+tnakNBk71lrqmZXldR7KflL5ZFj1tr472JdCzVZMG1tVupmJYmdg1tugV/+EhIJqK6mbOWIlEG3vEs5r3302mbfGNLl1dOVfW7tjj6ZYn4vJXoqj1zASi0VkGp8fSqb5dM/+giOOw5OPRX69ePia49JG+yXf7Q85WzcVNLl49v63hTreymFRwE/ZnFWnIxDWzsxN+bT5871i4nPmgVXXsnYc/blinf+1uoY+hUfr8ioDekuwm19b4r1vZTCo4AfszgrTsYh3d3uFoXYBlzj0zeDBkHnzvDii3D++Ux+eWrK1zdVt8z021O6i3Cq9yZVyeZifS+l8Cjgx6wQKk6GKd3dbt24OtwlzgftXU+Hfv3gL3+Bs8/29XB69waCpcJaO1ZrI6HSXYRTvWfLxi4rqfdSCo86bSVSrZUN3ti5WV8PV18Nv/89dO3qO2mPOGKzbYN0dqcrUdxaME5XuE0kLuq0laxFNRegenB166mPt9+GAQPgwgth6FBYunSLYL9x21T7aHasZMXVmrSWy68eXL35t42Ig73mZkguKOAXsaBBI+pl+JKmPvqNpvrT70GvXrB4sa9sOX26z9snETQV1lqgzrSEQq4DsZZFlFxRSqdIpRtL3lzscwE+/RTGjIG77oJDDoHbb4c99wxt92H9+9pyTrMR+/sheU0pHdlCW2q7xDoX4PHH/XDLe++FP/wBnnoq1GAP4Y2EiqpeTqnNzZDoqLRCkWpL0AhamTJUX34JF18M//Vf0KMHzJjhR+RkqbXO1mw7YaMKxLG8H1ISdIdfpNoyJDHyuQCvvAL9+/tgP3YsvPRSaME+Ve47jE7YqCbJldrcDImOAn6Rai04pFoqMMzx40k7NxsafJCvqIAPP4TZs+H666FDh1Zfb+ONduPbpe0ozSblEqQzNqpAXGpzMyQ66rQtYoHGvEd03G7r4LHHu7Hv0vf8cMsbb/Rj7AO+vqVkAdDGW8rtNyvAFvB4yY4R5fh8zQWQZLLptFXAL3KZBsFstBxlcvyrcMOD0L4BOlZP9cXPLHW7glSjTHbBynR0Sz6OiolqRJAUHo3SkZTiKM7WFDx3+BJuuw/uugdWdIbeZwCjRrUa7Ju/vq3bZJpyycdRMVpBS3JBAb/IxdEBmLAEP3gLltbAsFfgksPh0FPhrS7BLjJBLkbJtsk09x32RTGMyVn5eBGSwhco4JvZIDNbYWYrzezCJL8/x8yWm9lSM3vczPYIv6mSicg7ADdsYPYrvZh3C2xIwCGjYMLhUJ8IfpEJsl2qbTIZjRPmRTGsWbKlVjZbopE24JtZApgEHAWUA8PMrGUxlMVAhXOuF3APcGXYDc2lYq9bElldmOXL4aCDOPKexTw3qJyK0e14cbe2X2RaXqQADJ8GytUFq2n/TTI9RqapmJafwR6deyTdTkMzJRtBJl71B1Y6594EMLM7gaHA8qYNnHPzmm0/HxgeZiNzSWvKhqChASZNgt/8Bjp2hBkz+P6QIazLYpfVg6sjOf9BRgS1RSapmGSfweUfLae8SzkrPl6hUToSmrSjdMzsOGCQc+60xse/AA5yzp2ZYvvrgQ+cc5cn+V0lUAmw++6793v77bezbH728nGERkFZs8aPupk7F44+Gm66Cb75zbhbFVjY738m+9NnUNoi16N0kg2pSHqVMLPhQAVwVbLfO+emOOcqnHMVXVOMwY6aOseycN99vg7O009DTQ08+GBBBXsI//3PpD9An0GJSpCAvxro3uzxbsCalhuZ2Y+Ai4Ehzrmvwmle7qlzLAOffw4jR8LPfuYLnS1eDKNHpx1umY/Cfv8z6STXZ1CiEiTgLwT2NrM9zWwr4ARgZvMNzKwPMBkf7D8Mv5m5o7olbfTcc36Zwdtu88XPXnjBFz8rULl4/9vaSa7PoEQlbcB3ztUBZwJzgdeA6c65ZWY2wcyGNG52FdARuNvMXjazmSl2l3dUtySgr7/2Sw7+4Af+8dNPw+WXQ/v2OTlclCtwxf3+50MbpDSotIKkt2IFDB8OtbU+lXPddbDDDjk7nMoKiKSm0gqSG875ztg+feDNN+Gee+Dmm3Ma7EFlBURyRQGf4p94lZF//hOOOQaqquD73/c17H/2s0jOlUatiORGyQf8YlkwOtRAPHOmH275+OMwcSI89BDsumtk50qjVkRyo+QDfjGkD0ILxF98AZWVvl59t24+Z3/WWdDOf0yiOlcatSKSGyUf8IshfRBKIF6wwOfqp06FCy6A+fOhZ8/NNonqXGnUikhulPwi5sWwYHRWgbiuDq64AiZM8Hf18+bBYYcl3TTKcxVVLR2RUlLyd/jFkD7IOOe9cqXvkL3kEhg2DJYuTRnsoTjOVRDqxJdiVfIBvxjSB20OxM75Ime9e8Prr8O0aXD77dCpU6vHKYZzlU6xdOKLJKOJV0Ui8ILXa9f6jtkHHoABA+CWW6B79y23K1GqXCn5LpuJVyWfwy8WgXLeDz3kZ8p++imDOer9AAAH5ElEQVRccw386lcbR+CIVwyd+CKp6K+9FKxfD2PH+nr1XbvCwoVwzjkK9kloDoAUM/3FF7tFi6BvX6iu9kF+4ULo1SvuVuWtUumYltKkgF+s6uvhj3+Egw/2E6oee8yncbbZJu6W5bVS6JiW0qVO22K0ahWMGAHPPgvHH+8LoO20U9ytEpEQqFqmeM75hUkOOMCPqb/9drjzTgV7EQEU8IvHJ5/Az38OJ5/sSyQsXepr2BfgsoMikhsK+FnKi1mZjz7qq1s+8AD86U/wxBOwxx7Rt0NE8poCfhZin5X55Zfw61/Dj3/sZ8kuWOALnyU0hLCt8uLCLZJjCvhZiLW08pIlUFHhlxs86yw//LJPn9wfN0OZBtQoAnHsF26RiCjgZyGWWZkNDXD11dC/P3z8MTz8sF+kZNttc3fMLGUaUKMKxMWwJoJIEAr4WYh8VuY778DAgXD++TB4sF928MgjM9pVlCmMTANqVIFY5RSkVCjgZyHSWZnTpvkZsrW1fiHxe++FLl0y2lXUKYxMA2pUgVjlFKRUKOBnIZJZmZ99Biee6P/r2dPn7keOzGq4ZdQpjEwDalSBWOUUpFQo4GepenA1dePqcJc46sbVhRvs583zd/V33w2XXQZPPQV77ZX1bqNOYWQaUKMKxCqnIKVC5ZHz0Vdfwe9/7ztn994bnn8eDjwwtN1HvaxjU+AMVK8/hNdl2kYFeCl2qqWTb1591c+QXbIERo/2QX+77UI9RFMOvyXd1YrkP9XSKQYNDX5MfUUFvP8+zJrli56FHOxBKQyRUqU7/Hzw3ntwyim+hPExx8DUqbDzznG3SkTykO7wC9k99/g6OM8/D5Mnw4wZCvYikhMK+HH5/HNf2fI//9N3zC5e7BcXV3VLEckRBfw4PPOMr1n/t7/BuHF+oZJ99om7VSJS5BTwo7RhA1x8MRx+uF9A/NlnYfx4aN8+7paJSAnQOPyovP46nHQSvPQSjBoF114L228fd6tEpIToDj/XnINJk6BvX3j7bbj/fj8KR8FeRCKmO/xc+uADOPVUeOghGDTIFz3bZZe4WyUiJSrQHb6ZDTKzFWa20swuTPL7rc3srsbfLzCzb4Xd0ILzwAN+uOW8eXD99TBnjoJ9AFp5SiR30gZ8M0sAk4CjgHJgmJmVt9hsFPCpc+7bwLXAn8NuaMH44gs47TT4j/+A3Xf3OfuxYzXcMgCtPCWSW0Hu8PsDK51zbzrnNgB3AkNbbDMUuLXx53uAgWYlGOHmz4fevX3q5qKL4IUX4DvfibtVBUMrT4nkVtrSCmZ2HDDIOXda4+NfAAc5585sts2rjdusbnz8j8ZtPmqxr0qgqbbtfsCrYf1DClwX4KO0WxW7XejHeqBDkt+9z6Kom5MH9LnYROdikx7OuYxGfQTptE12p97yKhFkG5xzU4ApAGZWm2k9iGKjc7GJmdW6z3QuQJ+L5nQuNjGzjIuQBUnprAa6N3u8G7Am1TZmVgZ0Aj7JtFEiIhK+IAF/IbC3me1pZlsBJwAzW2wzEzi58efjgCdcXGU4RUQkqbQpHedcnZmdCcwFEsDNzrllZjYBqHXOzQRuAm43s5X4O/sTAhxbPXGb6FxsonOxic7FJjoXm2R8LmKrhy8iItFSaQURkRKhgC8iUiJyHvBVlmGTAOfiHDNbbmZLzexxM9sjjnZGId25aLbdcWbmzKxoh+QFORdmdnzjZ2OZmd0RdRujEuBvZHczm2dmixv/To6Oo525ZmY3m9mHjXOckv3ezGxi43laamZ9A+3YOZez//CdvP8A9gK2ApYA5S22qQJuaPz5BOCuXLYprv8CnosfAh0afx5TyueicbvtgaeB+UBF3O2O8XOxN7AY+LfGxzvH3e4Yz8UUYEzjz+XAW3G3O0fn4gdAX+DVFL8/GngIPwfqYGBBkP3m+g5fZRk2SXsunHPznHPrGx/Ox895KEZBPhcAlwFXAl9G2biIBTkXpwOTnHOfAjjnPoy4jVEJci4csEPjz53Yck5QUXDOPU3rc5mGArc5bz6wo5mlrc6Y64DfDXi32ePVjc8l3cY5VwesAzrnuF1xCHIumhuFv4IXo7Tnwsz6AN2dcw9G2bAYBPlc7APsY2bPmdl8MxsUWeuiFeRcXAoMN7PVwBzgrGialnfaGk+A3NfDD60sQxEI/O80s+FABXBYTlsUn1bPhZm1w1ddPSWqBsUoyOeiDJ/WORz/re8ZM9vPOfdZjtsWtSDnYhhwi3PuGjP7Ln7+z37OuYbcNy+vZBQ3c32Hr7IMmwQ5F5jZj4CLgSHOua8ialvU0p2L7fHF9Z40s7fwOcqZRdpxG/RvZIZz7mvn3CpgBf4CUGyCnItRwHQA59wLwDb4wmqlJlA8aSnXAV9lGTZJey4a0xiT8cG+WPO0kOZcOOfWOee6OOe+5Zz7Fr4/Y4hzLuOiUXksyN/IA/gOfcysCz7F82akrYxGkHPxDjAQwMy+gw/4ayNtZX6YCYxoHK1zMLDOOfd+uhflNKXjcleWoeAEPBdXAR2Buxv7rd9xzg2JrdE5EvBclISA52Iu8GMzWw7UA+c75z6Or9W5EfBcnAvcaGa/xqcwTinGG0Qzm4ZP4XVp7K+4BGgP4Jy7Ad9/cTSwElgPjAy03yI8VyIikoRm2oqIlAgFfBGREqGALyJSIhTwRURKhAK+iEiJUMAXESkRCvgiIiXi/wFceqYcmcPLIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig,ax=plt.subplots()\n",
    "ln,=plt.plot([],[],'ro-',animated=True)\n",
    "\n",
    "def init():\n",
    "    plt.scatter(xtest,ytest,color='g')\n",
    "    ax.set_xlim(0,1.0)\n",
    "    ax.set_ylim(0,1.0)\n",
    "    return ln,\n",
    "\n",
    "def update_frame(frame):\n",
    "    m,c=mc_values_anim[frame]\n",
    "    x1,y1=(-0.5), m* (-0.5 )+c\n",
    "    x2,y2=(1.5),m*(1.5)+c\n",
    "    ln.set_data([x1,x2],[y1,y2])\n",
    "    return ln,\n",
    "\n",
    "anim =FuncAnimation(fig, update_frame, frames=range(len(mc_values_anim)),interval=50, init_func=init, blit=True)\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction and Evalution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculate the perdiction on test as vectorised operation\n",
    "predicted = (m * xtest + c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.023115387686320942"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Compute MSE for the predicted values on testing set\n",
    "mean_squared_error(ytest, predicted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "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>x</th>\n",
       "      <th>target_y</th>\n",
       "      <th>predicted_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.494922</td>\n",
       "      <td>0.693333</td>\n",
       "      <td>0.364112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.333972</td>\n",
       "      <td>0.155556</td>\n",
       "      <td>0.224355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.452002</td>\n",
       "      <td>0.348889</td>\n",
       "      <td>0.326844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.606821</td>\n",
       "      <td>0.220000</td>\n",
       "      <td>0.461277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.922399</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.735301</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x  target_y  predicted_y\n",
       "0  0.494922  0.693333     0.364112\n",
       "1  0.333972  0.155556     0.224355\n",
       "2  0.452002  0.348889     0.326844\n",
       "3  0.606821  0.220000     0.461277\n",
       "4  0.922399  1.000000     0.735301"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p=pd.DataFrame(list(zip(xtest, ytest, predicted)),columns=['x','target_y','predicted_y'])\n",
    "p.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x8ec53f0>]"
      ]
     },
     "execution_count": 42,
     "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.scatter(xtest, ytest, color ='b')\n",
    "plt.plot(xtest, predicted, color ='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "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>X_Test</th>\n",
       "      <th>Y_Test</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.144</td>\n",
       "      <td>36.2</td>\n",
       "      <td>21.385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.304</td>\n",
       "      <td>12.0</td>\n",
       "      <td>15.096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.920</td>\n",
       "      <td>20.7</td>\n",
       "      <td>19.708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.728</td>\n",
       "      <td>14.9</td>\n",
       "      <td>25.757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8.375</td>\n",
       "      <td>50.0</td>\n",
       "      <td>38.089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.849</td>\n",
       "      <td>28.2</td>\n",
       "      <td>26.663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.138</td>\n",
       "      <td>11.9</td>\n",
       "      <td>6.366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6.513</td>\n",
       "      <td>20.2</td>\n",
       "      <td>24.148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7.148</td>\n",
       "      <td>37.3</td>\n",
       "      <td>28.902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.138</td>\n",
       "      <td>13.8</td>\n",
       "      <td>6.366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.713</td>\n",
       "      <td>15.1</td>\n",
       "      <td>18.158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>6.059</td>\n",
       "      <td>20.6</td>\n",
       "      <td>20.749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6.122</td>\n",
       "      <td>22.1</td>\n",
       "      <td>21.220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6.701</td>\n",
       "      <td>16.4</td>\n",
       "      <td>25.555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6.113</td>\n",
       "      <td>21.0</td>\n",
       "      <td>21.153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8.725</td>\n",
       "      <td>50.0</td>\n",
       "      <td>40.709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6.431</td>\n",
       "      <td>18.0</td>\n",
       "      <td>23.534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>6.083</td>\n",
       "      <td>22.2</td>\n",
       "      <td>20.928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.973</td>\n",
       "      <td>16.1</td>\n",
       "      <td>12.618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.731</td>\n",
       "      <td>19.3</td>\n",
       "      <td>18.293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>6.169</td>\n",
       "      <td>25.3</td>\n",
       "      <td>21.572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>6.193</td>\n",
       "      <td>11.0</td>\n",
       "      <td>21.752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>6.474</td>\n",
       "      <td>19.8</td>\n",
       "      <td>23.856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6.980</td>\n",
       "      <td>29.8</td>\n",
       "      <td>27.644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>5.594</td>\n",
       "      <td>17.4</td>\n",
       "      <td>17.267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5.933</td>\n",
       "      <td>18.9</td>\n",
       "      <td>19.805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>5.856</td>\n",
       "      <td>17.3</td>\n",
       "      <td>19.229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>6.009</td>\n",
       "      <td>18.9</td>\n",
       "      <td>20.374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>5.454</td>\n",
       "      <td>15.2</td>\n",
       "      <td>16.219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>7.088</td>\n",
       "      <td>32.2</td>\n",
       "      <td>28.453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>6.064</td>\n",
       "      <td>24.4</td>\n",
       "      <td>20.786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>6.120</td>\n",
       "      <td>20.6</td>\n",
       "      <td>21.205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>7.185</td>\n",
       "      <td>34.7</td>\n",
       "      <td>29.179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>6.065</td>\n",
       "      <td>22.8</td>\n",
       "      <td>20.794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>5.924</td>\n",
       "      <td>15.6</td>\n",
       "      <td>19.738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>5.531</td>\n",
       "      <td>8.5</td>\n",
       "      <td>16.796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>6.375</td>\n",
       "      <td>28.1</td>\n",
       "      <td>23.115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>6.842</td>\n",
       "      <td>30.1</td>\n",
       "      <td>26.611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>6.874</td>\n",
       "      <td>31.2</td>\n",
       "      <td>26.851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>5.850</td>\n",
       "      <td>21.0</td>\n",
       "      <td>19.184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>5.713</td>\n",
       "      <td>12.7</td>\n",
       "      <td>18.158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>6.389</td>\n",
       "      <td>23.9</td>\n",
       "      <td>23.219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>7.853</td>\n",
       "      <td>48.5</td>\n",
       "      <td>34.180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>6.130</td>\n",
       "      <td>13.8</td>\n",
       "      <td>21.280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>5.747</td>\n",
       "      <td>8.5</td>\n",
       "      <td>18.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>6.546</td>\n",
       "      <td>29.4</td>\n",
       "      <td>24.395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>6.335</td>\n",
       "      <td>18.1</td>\n",
       "      <td>22.815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>6.167</td>\n",
       "      <td>20.1</td>\n",
       "      <td>21.557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>5.362</td>\n",
       "      <td>20.8</td>\n",
       "      <td>15.530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>5.990</td>\n",
       "      <td>17.5</td>\n",
       "      <td>20.232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>5.155</td>\n",
       "      <td>16.3</td>\n",
       "      <td>13.980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>7.645</td>\n",
       "      <td>46.0</td>\n",
       "      <td>32.623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>6.549</td>\n",
       "      <td>27.1</td>\n",
       "      <td>24.417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6.398</td>\n",
       "      <td>25.0</td>\n",
       "      <td>23.287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>6.433</td>\n",
       "      <td>24.5</td>\n",
       "      <td>23.549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>7.163</td>\n",
       "      <td>31.6</td>\n",
       "      <td>29.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>5.880</td>\n",
       "      <td>19.1</td>\n",
       "      <td>19.408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>7.923</td>\n",
       "      <td>50.0</td>\n",
       "      <td>34.704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>5.757</td>\n",
       "      <td>15.0</td>\n",
       "      <td>18.488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>5.572</td>\n",
       "      <td>23.1</td>\n",
       "      <td>17.103</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>102 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     X_Test  Y_Test  Predicted\n",
       "0     6.144    36.2     21.385\n",
       "1     5.304    12.0     15.096\n",
       "2     5.920    20.7     19.708\n",
       "3     6.728    14.9     25.757\n",
       "4     8.375    50.0     38.089\n",
       "5     6.849    28.2     26.663\n",
       "6     4.138    11.9      6.366\n",
       "7     6.513    20.2     24.148\n",
       "8     7.148    37.3     28.902\n",
       "9     4.138    13.8      6.366\n",
       "10    5.713    15.1     18.158\n",
       "11    6.059    20.6     20.749\n",
       "12    6.122    22.1     21.220\n",
       "13    6.701    16.4     25.555\n",
       "14    6.113    21.0     21.153\n",
       "15    8.725    50.0     40.709\n",
       "16    6.431    18.0     23.534\n",
       "17    6.083    22.2     20.928\n",
       "18    4.973    16.1     12.618\n",
       "19    5.731    19.3     18.293\n",
       "20    6.169    25.3     21.572\n",
       "21    6.193    11.0     21.752\n",
       "22    6.474    19.8     23.856\n",
       "23    6.980    29.8     27.644\n",
       "24    5.594    17.4     17.267\n",
       "25    5.933    18.9     19.805\n",
       "26    5.856    17.3     19.229\n",
       "27    6.009    18.9     20.374\n",
       "28    5.454    15.2     16.219\n",
       "29    7.088    32.2     28.453\n",
       "..      ...     ...        ...\n",
       "72    6.064    24.4     20.786\n",
       "73    6.120    20.6     21.205\n",
       "74    7.185    34.7     29.179\n",
       "75    6.065    22.8     20.794\n",
       "76    5.924    15.6     19.738\n",
       "77    5.531     8.5     16.796\n",
       "78    6.375    28.1     23.115\n",
       "79    6.842    30.1     26.611\n",
       "80    6.874    31.2     26.851\n",
       "81    5.850    21.0     19.184\n",
       "82    5.713    12.7     18.158\n",
       "83    6.389    23.9     23.219\n",
       "84    7.853    48.5     34.180\n",
       "85    6.130    13.8     21.280\n",
       "86    5.747     8.5     18.413\n",
       "87    6.546    29.4     24.395\n",
       "88    6.335    18.1     22.815\n",
       "89    6.167    20.1     21.557\n",
       "90    5.362    20.8     15.530\n",
       "91    5.990    17.5     20.232\n",
       "92    5.155    16.3     13.980\n",
       "93    7.645    46.0     32.623\n",
       "94    6.549    27.1     24.417\n",
       "95    6.398    25.0     23.287\n",
       "96    6.433    24.5     23.549\n",
       "97    7.163    31.6     29.014\n",
       "98    5.880    19.1     19.408\n",
       "99    7.923    50.0     34.704\n",
       "100   5.757    15.0     18.488\n",
       "101   5.572    23.1     17.103\n",
       "\n",
       "[102 rows x 3 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#reshaping the array and reverting normalisation\n",
    "predicted=predicted.reshape(-1,1)\n",
    "xtest=xtest.reshape(-1,1)\n",
    "ytest=ytest.reshape(-1,1)\n",
    "\n",
    "xtest_scaled=x_scaler.inverse_transform(xtest)\n",
    "ytest_scaled=y_scaler.inverse_transform(ytest)\n",
    "predicted_scaled=y_scaler.inverse_transform(predicted)\n",
    "\n",
    "#getting rid of extra dimension by slicing \n",
    "xtest_scaled=xtest_scaled[:,-1]\n",
    "ytest_scaled=ytest_scaled[:,-1]\n",
    "predicted_scaled=predicted_scaled[:,-1]\n",
    "\n",
    "p=pd.DataFrame(list(zip(xtest_scaled,ytest_scaled,predicted_scaled)),columns=[\"X_Test\",\"Y_Test\",\"Predicted\"])\n",
    "p.round(decimals=3)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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