Advanced AIML Lab/Advanced AI-ML Lab 3 23.02.2021.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Abhishek Sharma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CS 2nd Year | Section : \"I\" | Roll no.: 01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Enrollment No.: 12019009001127"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Artificial Intelligence and Machine Learning Lab 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Date : 23.02.2021 | Faculty : PKB, MB, BM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(boston.data, columns = boston.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['MEDV'] = pd.DataFrame(boston.target) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.20</td>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>-0.20</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.57</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.76</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.64</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.38</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.09</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.73</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.59</td>\n",
       "      <td>-0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.57</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.73</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.26</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.66</td>\n",
       "      <td>-0.71</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.77</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>0.63</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.61</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.49</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>0.49</td>\n",
       "      <td>-0.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>0.58</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>0.72</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.67</td>\n",
       "      <td>-0.29</td>\n",
       "      <td>0.51</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>0.91</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>0.54</td>\n",
       "      <td>-0.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.38</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.26</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.46</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-0.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.59</td>\n",
       "      <td>-0.61</td>\n",
       "      <td>0.60</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.37</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MEDV</th>\n",
       "      <td>-0.39</td>\n",
       "      <td>0.36</td>\n",
       "      <td>-0.48</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>0.70</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.25</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>-0.47</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>0.33</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         CRIM    ZN  INDUS  CHAS   NOX    RM   AGE   DIS   RAD   TAX  PTRATIO  \\\n",
       "CRIM     1.00 -0.20   0.41 -0.06  0.42 -0.22  0.35 -0.38  0.63  0.58     0.29   \n",
       "ZN      -0.20  1.00  -0.53 -0.04 -0.52  0.31 -0.57  0.66 -0.31 -0.31    -0.39   \n",
       "INDUS    0.41 -0.53   1.00  0.06  0.76 -0.39  0.64 -0.71  0.60  0.72     0.38   \n",
       "CHAS    -0.06 -0.04   0.06  1.00  0.09  0.09  0.09 -0.10 -0.01 -0.04    -0.12   \n",
       "NOX      0.42 -0.52   0.76  0.09  1.00 -0.30  0.73 -0.77  0.61  0.67     0.19   \n",
       "RM      -0.22  0.31  -0.39  0.09 -0.30  1.00 -0.24  0.21 -0.21 -0.29    -0.36   \n",
       "AGE      0.35 -0.57   0.64  0.09  0.73 -0.24  1.00 -0.75  0.46  0.51     0.26   \n",
       "DIS     -0.38  0.66  -0.71 -0.10 -0.77  0.21 -0.75  1.00 -0.49 -0.53    -0.23   \n",
       "RAD      0.63 -0.31   0.60 -0.01  0.61 -0.21  0.46 -0.49  1.00  0.91     0.46   \n",
       "TAX      0.58 -0.31   0.72 -0.04  0.67 -0.29  0.51 -0.53  0.91  1.00     0.46   \n",
       "PTRATIO  0.29 -0.39   0.38 -0.12  0.19 -0.36  0.26 -0.23  0.46  0.46     1.00   \n",
       "B       -0.39  0.18  -0.36  0.05 -0.38  0.13 -0.27  0.29 -0.44 -0.44    -0.18   \n",
       "LSTAT    0.46 -0.41   0.60 -0.05  0.59 -0.61  0.60 -0.50  0.49  0.54     0.37   \n",
       "MEDV    -0.39  0.36  -0.48  0.18 -0.43  0.70 -0.38  0.25 -0.38 -0.47    -0.51   \n",
       "\n",
       "            B  LSTAT  MEDV  \n",
       "CRIM    -0.39   0.46 -0.39  \n",
       "ZN       0.18  -0.41  0.36  \n",
       "INDUS   -0.36   0.60 -0.48  \n",
       "CHAS     0.05  -0.05  0.18  \n",
       "NOX     -0.38   0.59 -0.43  \n",
       "RM       0.13  -0.61  0.70  \n",
       "AGE     -0.27   0.60 -0.38  \n",
       "DIS      0.29  -0.50  0.25  \n",
       "RAD     -0.44   0.49 -0.38  \n",
       "TAX     -0.44   0.54 -0.47  \n",
       "PTRATIO -0.18   0.37 -0.51  \n",
       "B        1.00  -0.37  0.33  \n",
       "LSTAT   -0.37   1.00 -0.74  \n",
       "MEDV     0.33  -0.74  1.00  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame (data.corr().round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we are trying to figure out the mean squared error value as low as possible using the **``` RM ```** and **``` ZN ```** value with respect to the **``` MEDV ```** values (target values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data[['RM','ZN']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['MEDV']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x,y, test_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "mlr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr.fit(x_train1, y_train1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "yTestPredict = mlr.predict(x_test1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.08804702188216"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(mean_squared_error(y_test1, yTestPredict))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Conclusion* : Mean Squared Error Value is ```5.09```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[24.  21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 15.  18.9 21.7 20.4\n",
      " 18.2 19.9 23.1 17.5 20.2 18.2 13.6 19.6 15.2 14.5 15.6 13.9 16.6 14.8\n",
      " 18.4 21.  12.7 14.5 13.2 13.1 13.5 18.9 20.  21.  24.7 30.8 34.9 26.6\n",
      " 25.3 24.7 21.2 19.3 20.  16.6 14.4 19.4 19.7 20.5 25.  23.4 18.9 35.4\n",
      " 24.7 31.6 23.3 19.6 18.7 16.  22.2 25.  33.  23.5 19.4 22.  17.4 20.9\n",
      " 24.2 21.7 22.8 23.4 24.1 21.4 20.  20.8 21.2 20.3 28.  23.9 24.8 22.9\n",
      " 23.9 26.6 22.5 22.2 23.6 28.7 22.6 22.  22.9 25.  20.6 28.4 21.4 38.7\n",
      " 43.8 33.2 27.5 26.5 18.6 19.3 20.1 19.5 19.5 20.4 19.8 19.4 21.7 22.8\n",
      " 18.8 18.7 18.5 18.3 21.2 19.2 20.4 19.3 22.  20.3 20.5 17.3 18.8 21.4\n",
      " 15.7 16.2 18.  14.3 19.2 19.6 23.  18.4 15.6 18.1 17.4 17.1 13.3 17.8\n",
      " 14.  14.4 13.4 15.6 11.8 13.8 15.6 14.6 17.8 15.4 21.5 19.6 15.3 19.4\n",
      " 17.  15.6 13.1 41.3 24.3 23.3 27.  50.  50.  50.  22.7 25.  50.  23.8\n",
      " 23.8 22.3 17.4 19.1 23.1 23.6 22.6 29.4 23.2 24.6 29.9 37.2 39.8 36.2\n",
      " 37.9 32.5 26.4 29.6 50.  32.  29.8 34.9 37.  30.5 36.4 31.1 29.1 50.\n",
      " 33.3 30.3 34.6 34.9 32.9 24.1 42.3 48.5 50.  22.6 24.4 22.5 24.4 20.\n",
      " 21.7 19.3 22.4 28.1 23.7 25.  23.3 28.7 21.5 23.  26.7 21.7 27.5 30.1\n",
      " 44.8 50.  37.6 31.6 46.7 31.5 24.3 31.7 41.7 48.3 29.  24.  25.1 31.5\n",
      " 23.7 23.3 22.  20.1 22.2 23.7 17.6 18.5 24.3 20.5 24.5 26.2 24.4 24.8\n",
      " 29.6 42.8 21.9 20.9 44.  50.  36.  30.1 33.8 43.1 48.8 31.  36.5 22.8\n",
      " 30.7 50.  43.5 20.7 21.1 25.2 24.4 35.2 32.4 32.  33.2 33.1 29.1 35.1\n",
      " 45.4 35.4 46.  50.  32.2 22.  20.1 23.2 22.3 24.8 28.5 37.3 27.9 23.9\n",
      " 21.7 28.6 27.1 20.3 22.5 29.  24.8 22.  26.4 33.1 36.1 28.4 33.4 28.2\n",
      " 22.8 20.3 16.1 22.1 19.4 21.6 23.8 16.2 17.8 19.8 23.1 21.  23.8 23.1\n",
      " 20.4 18.5 25.  24.6 23.  22.2 19.3 22.6 19.8 17.1 19.4 22.2 20.7 21.1\n",
      " 19.5 18.5 20.6 19.  18.7 32.7 16.5 23.9 31.2 17.5 17.2 23.1 24.5 26.6\n",
      " 22.9 24.1 18.6 30.1 18.2 20.6 17.8 21.7 22.7 22.6 25.  19.9 20.8 16.8\n",
      " 21.9 27.5 21.9 23.1 50.  50.  50.  50.  50.  13.8 13.8 15.  13.9 13.3\n",
      " 13.1 10.2 10.4 10.9 11.3 12.3  8.8  7.2 10.5  7.4 10.2 11.5 15.1 23.2\n",
      "  9.7 13.8 12.7 13.1 12.5  8.5  5.   6.3  5.6  7.2 12.1  8.3  8.5  5.\n",
      " 11.9 27.9 17.2 27.5 15.  17.2 17.9 16.3  7.   7.2  7.5 10.4  8.8  8.4\n",
      " 16.7 14.2 20.8 13.4 11.7  8.3 10.2 10.9 11.   9.5 14.5 14.1 16.1 14.3\n",
      " 11.7 13.4  9.6  8.7  8.4 12.8 10.5 17.1 18.4 15.4 10.8 11.8 14.9 12.6\n",
      " 14.1 13.  13.4 15.2 16.1 17.8 14.9 14.1 12.7 13.5 14.9 20.  16.4 17.7\n",
      " 19.5 20.2 21.4 19.9 19.  19.1 19.1 20.1 19.9 19.6 23.2 29.8 13.8 13.3\n",
      " 16.7 12.  14.6 21.4 23.  23.7 25.  21.8 20.6 21.2 19.1 20.6 15.2  7.\n",
      "  8.1 13.6 20.1 21.8 24.5 23.1 19.7 18.3 21.2 17.5 16.8 22.4 20.6 23.9\n",
      " 22.  11.9]\n"
     ]
    }
   ],
   "source": [
    "print (boston.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  MEDV  \n",
       "0     15.3  396.90   4.98  24.0  \n",
       "1     17.8  396.90   9.14  21.6  \n",
       "2     17.8  392.83   4.03  34.7  \n",
       "3     18.7  394.63   2.94  33.4  \n",
       "4     18.7  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we are trying to figure out the mean squared error value as low as possible using the **``` RM ```** , **``` ZN ```** and **```LSTAT```** value with respect to the **``` MEDV ```** values (target values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x2 = data[['RM','ZN', 'LSTAT']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x2,y, test_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr.fit(x_train1, y_train1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "yTestPredict2 = mlr.predict(x_test1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.651426494186151"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(mean_squared_error(y_test1, yTestPredict2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Conclusion* : Mean Squared Value Error is ```4.65```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Merging both the results in a single table : (Value of Mean Squared Error)\n",
    "\n",
    "|Mean Squared Error depending on the Variables|Value|\n",
    "|:---:|:---:|\n",
    "|RM and ZN | 5.08804702188216|\n",
    "|RM, ZN and LSTAT|4.65142649418615|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**********************************************************************"
   ]
  }
 ],
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