Regression/Multiple Linear Regression/Backward Elimination with p-values and Adjusted R Squared.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas  as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(suppress=True,precision = 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>R&amp;D Spend</th>\n",
       "      <th>Administration</th>\n",
       "      <th>Marketing Spend</th>\n",
       "      <th>State</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>165349.20</td>\n",
       "      <td>136897.80</td>\n",
       "      <td>471784.10</td>\n",
       "      <td>New York</td>\n",
       "      <td>192261.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>162597.70</td>\n",
       "      <td>151377.59</td>\n",
       "      <td>443898.53</td>\n",
       "      <td>California</td>\n",
       "      <td>191792.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>153441.51</td>\n",
       "      <td>101145.55</td>\n",
       "      <td>407934.54</td>\n",
       "      <td>Florida</td>\n",
       "      <td>191050.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>144372.41</td>\n",
       "      <td>118671.85</td>\n",
       "      <td>383199.62</td>\n",
       "      <td>New York</td>\n",
       "      <td>182901.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>142107.34</td>\n",
       "      <td>91391.77</td>\n",
       "      <td>366168.42</td>\n",
       "      <td>Florida</td>\n",
       "      <td>166187.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   R&D Spend  Administration  Marketing Spend       State     Profit\n",
       "0  165349.20       136897.80        471784.10    New York  192261.83\n",
       "1  162597.70       151377.59        443898.53  California  191792.06\n",
       "2  153441.51       101145.55        407934.54     Florida  191050.39\n",
       "3  144372.41       118671.85        383199.62    New York  182901.99\n",
       "4  142107.34        91391.77        366168.42     Florida  166187.94"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.read_csv('50_Startups.csv')\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = dataset.drop('Profit',axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = dataset['Profit']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        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>R&amp;D Spend</th>\n",
       "      <th>Administration</th>\n",
       "      <th>Marketing Spend</th>\n",
       "      <th>State</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>165349.20</td>\n",
       "      <td>136897.80</td>\n",
       "      <td>471784.10</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>162597.70</td>\n",
       "      <td>151377.59</td>\n",
       "      <td>443898.53</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>153441.51</td>\n",
       "      <td>101145.55</td>\n",
       "      <td>407934.54</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>144372.41</td>\n",
       "      <td>118671.85</td>\n",
       "      <td>383199.62</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>142107.34</td>\n",
       "      <td>91391.77</td>\n",
       "      <td>366168.42</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>131876.90</td>\n",
       "      <td>99814.71</td>\n",
       "      <td>362861.36</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>134615.46</td>\n",
       "      <td>147198.87</td>\n",
       "      <td>127716.82</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>130298.13</td>\n",
       "      <td>145530.06</td>\n",
       "      <td>323876.68</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>120542.52</td>\n",
       "      <td>148718.95</td>\n",
       "      <td>311613.29</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>123334.88</td>\n",
       "      <td>108679.17</td>\n",
       "      <td>304981.62</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>101913.08</td>\n",
       "      <td>110594.11</td>\n",
       "      <td>229160.95</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>100671.96</td>\n",
       "      <td>91790.61</td>\n",
       "      <td>249744.55</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>93863.75</td>\n",
       "      <td>127320.38</td>\n",
       "      <td>249839.44</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>91992.39</td>\n",
       "      <td>135495.07</td>\n",
       "      <td>252664.93</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>119943.24</td>\n",
       "      <td>156547.42</td>\n",
       "      <td>256512.92</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>114523.61</td>\n",
       "      <td>122616.84</td>\n",
       "      <td>261776.23</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>78013.11</td>\n",
       "      <td>121597.55</td>\n",
       "      <td>264346.06</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>94657.16</td>\n",
       "      <td>145077.58</td>\n",
       "      <td>282574.31</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>91749.16</td>\n",
       "      <td>114175.79</td>\n",
       "      <td>294919.57</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>86419.70</td>\n",
       "      <td>153514.11</td>\n",
       "      <td>0.00</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>76253.86</td>\n",
       "      <td>113867.30</td>\n",
       "      <td>298664.47</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>78389.47</td>\n",
       "      <td>153773.43</td>\n",
       "      <td>299737.29</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>73994.56</td>\n",
       "      <td>122782.75</td>\n",
       "      <td>303319.26</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>67532.53</td>\n",
       "      <td>105751.03</td>\n",
       "      <td>304768.73</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>77044.01</td>\n",
       "      <td>99281.34</td>\n",
       "      <td>140574.81</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>64664.71</td>\n",
       "      <td>139553.16</td>\n",
       "      <td>137962.62</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>75328.87</td>\n",
       "      <td>144135.98</td>\n",
       "      <td>134050.07</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>72107.60</td>\n",
       "      <td>127864.55</td>\n",
       "      <td>353183.81</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>66051.52</td>\n",
       "      <td>182645.56</td>\n",
       "      <td>118148.20</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>65605.48</td>\n",
       "      <td>153032.06</td>\n",
       "      <td>107138.38</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61994.48</td>\n",
       "      <td>115641.28</td>\n",
       "      <td>91131.24</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>61136.38</td>\n",
       "      <td>152701.92</td>\n",
       "      <td>88218.23</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>63408.86</td>\n",
       "      <td>129219.61</td>\n",
       "      <td>46085.25</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>55493.95</td>\n",
       "      <td>103057.49</td>\n",
       "      <td>214634.81</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>46426.07</td>\n",
       "      <td>157693.92</td>\n",
       "      <td>210797.67</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>46014.02</td>\n",
       "      <td>85047.44</td>\n",
       "      <td>205517.64</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>28663.76</td>\n",
       "      <td>127056.21</td>\n",
       "      <td>201126.82</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>44069.95</td>\n",
       "      <td>51283.14</td>\n",
       "      <td>197029.42</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>20229.59</td>\n",
       "      <td>65947.93</td>\n",
       "      <td>185265.10</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>38558.51</td>\n",
       "      <td>82982.09</td>\n",
       "      <td>174999.30</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>28754.33</td>\n",
       "      <td>118546.05</td>\n",
       "      <td>172795.67</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>27892.92</td>\n",
       "      <td>84710.77</td>\n",
       "      <td>164470.71</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>23640.93</td>\n",
       "      <td>96189.63</td>\n",
       "      <td>148001.11</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>15505.73</td>\n",
       "      <td>127382.30</td>\n",
       "      <td>35534.17</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>22177.74</td>\n",
       "      <td>154806.14</td>\n",
       "      <td>28334.72</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1000.23</td>\n",
       "      <td>124153.04</td>\n",
       "      <td>1903.93</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1315.46</td>\n",
       "      <td>115816.21</td>\n",
       "      <td>297114.46</td>\n",
       "      <td>Florida</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.00</td>\n",
       "      <td>135426.92</td>\n",
       "      <td>0.00</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>542.05</td>\n",
       "      <td>51743.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>New York</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.00</td>\n",
       "      <td>116983.80</td>\n",
       "      <td>45173.06</td>\n",
       "      <td>California</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    R&D Spend  Administration  Marketing Spend       State\n",
       "0   165349.20       136897.80        471784.10    New York\n",
       "1   162597.70       151377.59        443898.53  California\n",
       "2   153441.51       101145.55        407934.54     Florida\n",
       "3   144372.41       118671.85        383199.62    New York\n",
       "4   142107.34        91391.77        366168.42     Florida\n",
       "5   131876.90        99814.71        362861.36    New York\n",
       "6   134615.46       147198.87        127716.82  California\n",
       "7   130298.13       145530.06        323876.68     Florida\n",
       "8   120542.52       148718.95        311613.29    New York\n",
       "9   123334.88       108679.17        304981.62  California\n",
       "10  101913.08       110594.11        229160.95     Florida\n",
       "11  100671.96        91790.61        249744.55  California\n",
       "12   93863.75       127320.38        249839.44     Florida\n",
       "13   91992.39       135495.07        252664.93  California\n",
       "14  119943.24       156547.42        256512.92     Florida\n",
       "15  114523.61       122616.84        261776.23    New York\n",
       "16   78013.11       121597.55        264346.06  California\n",
       "17   94657.16       145077.58        282574.31    New York\n",
       "18   91749.16       114175.79        294919.57     Florida\n",
       "19   86419.70       153514.11             0.00    New York\n",
       "20   76253.86       113867.30        298664.47  California\n",
       "21   78389.47       153773.43        299737.29    New York\n",
       "22   73994.56       122782.75        303319.26     Florida\n",
       "23   67532.53       105751.03        304768.73     Florida\n",
       "24   77044.01        99281.34        140574.81    New York\n",
       "25   64664.71       139553.16        137962.62  California\n",
       "26   75328.87       144135.98        134050.07     Florida\n",
       "27   72107.60       127864.55        353183.81    New York\n",
       "28   66051.52       182645.56        118148.20     Florida\n",
       "29   65605.48       153032.06        107138.38    New York\n",
       "30   61994.48       115641.28         91131.24     Florida\n",
       "31   61136.38       152701.92         88218.23    New York\n",
       "32   63408.86       129219.61         46085.25  California\n",
       "33   55493.95       103057.49        214634.81     Florida\n",
       "34   46426.07       157693.92        210797.67  California\n",
       "35   46014.02        85047.44        205517.64    New York\n",
       "36   28663.76       127056.21        201126.82     Florida\n",
       "37   44069.95        51283.14        197029.42  California\n",
       "38   20229.59        65947.93        185265.10    New York\n",
       "39   38558.51        82982.09        174999.30  California\n",
       "40   28754.33       118546.05        172795.67  California\n",
       "41   27892.92        84710.77        164470.71     Florida\n",
       "42   23640.93        96189.63        148001.11  California\n",
       "43   15505.73       127382.30         35534.17    New York\n",
       "44   22177.74       154806.14         28334.72  California\n",
       "45    1000.23       124153.04          1903.93    New York\n",
       "46    1315.46       115816.21        297114.46     Florida\n",
       "47       0.00       135426.92             0.00  California\n",
       "48     542.05        51743.15             0.00    New York\n",
       "49       0.00       116983.80         45173.06  California"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     192261.83\n",
       "1     191792.06\n",
       "2     191050.39\n",
       "3     182901.99\n",
       "4     166187.94\n",
       "5     156991.12\n",
       "6     156122.51\n",
       "7     155752.60\n",
       "8     152211.77\n",
       "9     149759.96\n",
       "10    146121.95\n",
       "11    144259.40\n",
       "12    141585.52\n",
       "13    134307.35\n",
       "14    132602.65\n",
       "15    129917.04\n",
       "16    126992.93\n",
       "17    125370.37\n",
       "18    124266.90\n",
       "19    122776.86\n",
       "20    118474.03\n",
       "21    111313.02\n",
       "22    110352.25\n",
       "23    108733.99\n",
       "24    108552.04\n",
       "25    107404.34\n",
       "26    105733.54\n",
       "27    105008.31\n",
       "28    103282.38\n",
       "29    101004.64\n",
       "30     99937.59\n",
       "31     97483.56\n",
       "32     97427.84\n",
       "33     96778.92\n",
       "34     96712.80\n",
       "35     96479.51\n",
       "36     90708.19\n",
       "37     89949.14\n",
       "38     81229.06\n",
       "39     81005.76\n",
       "40     78239.91\n",
       "41     77798.83\n",
       "42     71498.49\n",
       "43     69758.98\n",
       "44     65200.33\n",
       "45     64926.08\n",
       "46     49490.75\n",
       "47     42559.73\n",
       "48     35673.41\n",
       "49     14681.40\n",
       "Name: Profit, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "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>R&amp;D Spend</th>\n",
       "      <th>Administration</th>\n",
       "      <th>Marketing Spend</th>\n",
       "      <th>State_California</th>\n",
       "      <th>State_Florida</th>\n",
       "      <th>State_New York</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>165349.20</td>\n",
       "      <td>136897.80</td>\n",
       "      <td>471784.10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>162597.70</td>\n",
       "      <td>151377.59</td>\n",
       "      <td>443898.53</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>153441.51</td>\n",
       "      <td>101145.55</td>\n",
       "      <td>407934.54</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>144372.41</td>\n",
       "      <td>118671.85</td>\n",
       "      <td>383199.62</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>142107.34</td>\n",
       "      <td>91391.77</td>\n",
       "      <td>366168.42</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>131876.90</td>\n",
       "      <td>99814.71</td>\n",
       "      <td>362861.36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>134615.46</td>\n",
       "      <td>147198.87</td>\n",
       "      <td>127716.82</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>130298.13</td>\n",
       "      <td>145530.06</td>\n",
       "      <td>323876.68</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>120542.52</td>\n",
       "      <td>148718.95</td>\n",
       "      <td>311613.29</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>123334.88</td>\n",
       "      <td>108679.17</td>\n",
       "      <td>304981.62</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>101913.08</td>\n",
       "      <td>110594.11</td>\n",
       "      <td>229160.95</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>100671.96</td>\n",
       "      <td>91790.61</td>\n",
       "      <td>249744.55</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>93863.75</td>\n",
       "      <td>127320.38</td>\n",
       "      <td>249839.44</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>91992.39</td>\n",
       "      <td>135495.07</td>\n",
       "      <td>252664.93</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>119943.24</td>\n",
       "      <td>156547.42</td>\n",
       "      <td>256512.92</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>114523.61</td>\n",
       "      <td>122616.84</td>\n",
       "      <td>261776.23</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>78013.11</td>\n",
       "      <td>121597.55</td>\n",
       "      <td>264346.06</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>94657.16</td>\n",
       "      <td>145077.58</td>\n",
       "      <td>282574.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>91749.16</td>\n",
       "      <td>114175.79</td>\n",
       "      <td>294919.57</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>86419.70</td>\n",
       "      <td>153514.11</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>76253.86</td>\n",
       "      <td>113867.30</td>\n",
       "      <td>298664.47</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>78389.47</td>\n",
       "      <td>153773.43</td>\n",
       "      <td>299737.29</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>73994.56</td>\n",
       "      <td>122782.75</td>\n",
       "      <td>303319.26</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>67532.53</td>\n",
       "      <td>105751.03</td>\n",
       "      <td>304768.73</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>77044.01</td>\n",
       "      <td>99281.34</td>\n",
       "      <td>140574.81</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>64664.71</td>\n",
       "      <td>139553.16</td>\n",
       "      <td>137962.62</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>75328.87</td>\n",
       "      <td>144135.98</td>\n",
       "      <td>134050.07</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>72107.60</td>\n",
       "      <td>127864.55</td>\n",
       "      <td>353183.81</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>66051.52</td>\n",
       "      <td>182645.56</td>\n",
       "      <td>118148.20</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>65605.48</td>\n",
       "      <td>153032.06</td>\n",
       "      <td>107138.38</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>61994.48</td>\n",
       "      <td>115641.28</td>\n",
       "      <td>91131.24</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>61136.38</td>\n",
       "      <td>152701.92</td>\n",
       "      <td>88218.23</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>63408.86</td>\n",
       "      <td>129219.61</td>\n",
       "      <td>46085.25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>55493.95</td>\n",
       "      <td>103057.49</td>\n",
       "      <td>214634.81</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>46426.07</td>\n",
       "      <td>157693.92</td>\n",
       "      <td>210797.67</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>46014.02</td>\n",
       "      <td>85047.44</td>\n",
       "      <td>205517.64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>28663.76</td>\n",
       "      <td>127056.21</td>\n",
       "      <td>201126.82</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>44069.95</td>\n",
       "      <td>51283.14</td>\n",
       "      <td>197029.42</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>20229.59</td>\n",
       "      <td>65947.93</td>\n",
       "      <td>185265.10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>38558.51</td>\n",
       "      <td>82982.09</td>\n",
       "      <td>174999.30</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>28754.33</td>\n",
       "      <td>118546.05</td>\n",
       "      <td>172795.67</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>27892.92</td>\n",
       "      <td>84710.77</td>\n",
       "      <td>164470.71</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>23640.93</td>\n",
       "      <td>96189.63</td>\n",
       "      <td>148001.11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>15505.73</td>\n",
       "      <td>127382.30</td>\n",
       "      <td>35534.17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>22177.74</td>\n",
       "      <td>154806.14</td>\n",
       "      <td>28334.72</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1000.23</td>\n",
       "      <td>124153.04</td>\n",
       "      <td>1903.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1315.46</td>\n",
       "      <td>115816.21</td>\n",
       "      <td>297114.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.00</td>\n",
       "      <td>135426.92</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>542.05</td>\n",
       "      <td>51743.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.00</td>\n",
       "      <td>116983.80</td>\n",
       "      <td>45173.06</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    R&D Spend  Administration  Marketing Spend  State_California  \\\n",
       "0   165349.20       136897.80        471784.10                 0   \n",
       "1   162597.70       151377.59        443898.53                 1   \n",
       "2   153441.51       101145.55        407934.54                 0   \n",
       "3   144372.41       118671.85        383199.62                 0   \n",
       "4   142107.34        91391.77        366168.42                 0   \n",
       "5   131876.90        99814.71        362861.36                 0   \n",
       "6   134615.46       147198.87        127716.82                 1   \n",
       "7   130298.13       145530.06        323876.68                 0   \n",
       "8   120542.52       148718.95        311613.29                 0   \n",
       "9   123334.88       108679.17        304981.62                 1   \n",
       "10  101913.08       110594.11        229160.95                 0   \n",
       "11  100671.96        91790.61        249744.55                 1   \n",
       "12   93863.75       127320.38        249839.44                 0   \n",
       "13   91992.39       135495.07        252664.93                 1   \n",
       "14  119943.24       156547.42        256512.92                 0   \n",
       "15  114523.61       122616.84        261776.23                 0   \n",
       "16   78013.11       121597.55        264346.06                 1   \n",
       "17   94657.16       145077.58        282574.31                 0   \n",
       "18   91749.16       114175.79        294919.57                 0   \n",
       "19   86419.70       153514.11             0.00                 0   \n",
       "20   76253.86       113867.30        298664.47                 1   \n",
       "21   78389.47       153773.43        299737.29                 0   \n",
       "22   73994.56       122782.75        303319.26                 0   \n",
       "23   67532.53       105751.03        304768.73                 0   \n",
       "24   77044.01        99281.34        140574.81                 0   \n",
       "25   64664.71       139553.16        137962.62                 1   \n",
       "26   75328.87       144135.98        134050.07                 0   \n",
       "27   72107.60       127864.55        353183.81                 0   \n",
       "28   66051.52       182645.56        118148.20                 0   \n",
       "29   65605.48       153032.06        107138.38                 0   \n",
       "30   61994.48       115641.28         91131.24                 0   \n",
       "31   61136.38       152701.92         88218.23                 0   \n",
       "32   63408.86       129219.61         46085.25                 1   \n",
       "33   55493.95       103057.49        214634.81                 0   \n",
       "34   46426.07       157693.92        210797.67                 1   \n",
       "35   46014.02        85047.44        205517.64                 0   \n",
       "36   28663.76       127056.21        201126.82                 0   \n",
       "37   44069.95        51283.14        197029.42                 1   \n",
       "38   20229.59        65947.93        185265.10                 0   \n",
       "39   38558.51        82982.09        174999.30                 1   \n",
       "40   28754.33       118546.05        172795.67                 1   \n",
       "41   27892.92        84710.77        164470.71                 0   \n",
       "42   23640.93        96189.63        148001.11                 1   \n",
       "43   15505.73       127382.30         35534.17                 0   \n",
       "44   22177.74       154806.14         28334.72                 1   \n",
       "45    1000.23       124153.04          1903.93                 0   \n",
       "46    1315.46       115816.21        297114.46                 0   \n",
       "47       0.00       135426.92             0.00                 1   \n",
       "48     542.05        51743.15             0.00                 0   \n",
       "49       0.00       116983.80         45173.06                 1   \n",
       "\n",
       "    State_Florida  State_New York  \n",
       "0               0               1  \n",
       "1               0               0  \n",
       "2               1               0  \n",
       "3               0               1  \n",
       "4               1               0  \n",
       "5               0               1  \n",
       "6               0               0  \n",
       "7               1               0  \n",
       "8               0               1  \n",
       "9               0               0  \n",
       "10              1               0  \n",
       "11              0               0  \n",
       "12              1               0  \n",
       "13              0               0  \n",
       "14              1               0  \n",
       "15              0               1  \n",
       "16              0               0  \n",
       "17              0               1  \n",
       "18              1               0  \n",
       "19              0               1  \n",
       "20              0               0  \n",
       "21              0               1  \n",
       "22              1               0  \n",
       "23              1               0  \n",
       "24              0               1  \n",
       "25              0               0  \n",
       "26              1               0  \n",
       "27              0               1  \n",
       "28              1               0  \n",
       "29              0               1  \n",
       "30              1               0  \n",
       "31              0               1  \n",
       "32              0               0  \n",
       "33              1               0  \n",
       "34              0               0  \n",
       "35              0               1  \n",
       "36              1               0  \n",
       "37              0               0  \n",
       "38              0               1  \n",
       "39              0               0  \n",
       "40              0               0  \n",
       "41              1               0  \n",
       "42              0               0  \n",
       "43              0               1  \n",
       "44              0               0  \n",
       "45              0               1  \n",
       "46              1               0  \n",
       "47              0               0  \n",
       "48              0               1  \n",
       "49              0               0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x  = pd.get_dummies(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = x.values\n",
    "y = y.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[165349.2 , 136897.8 , 471784.1 ,      0.  ,      0.  ,      1.  ],\n",
       "       [162597.7 , 151377.59, 443898.53,      1.  ,      0.  ,      0.  ],\n",
       "       [153441.51, 101145.55, 407934.54,      0.  ,      1.  ,      0.  ],\n",
       "       [144372.41, 118671.85, 383199.62,      0.  ,      0.  ,      1.  ],\n",
       "       [142107.34,  91391.77, 366168.42,      0.  ,      1.  ,      0.  ],\n",
       "       [131876.9 ,  99814.71, 362861.36,      0.  ,      0.  ,      1.  ],\n",
       "       [134615.46, 147198.87, 127716.82,      1.  ,      0.  ,      0.  ],\n",
       "       [130298.13, 145530.06, 323876.68,      0.  ,      1.  ,      0.  ],\n",
       "       [120542.52, 148718.95, 311613.29,      0.  ,      0.  ,      1.  ],\n",
       "       [123334.88, 108679.17, 304981.62,      1.  ,      0.  ,      0.  ],\n",
       "       [101913.08, 110594.11, 229160.95,      0.  ,      1.  ,      0.  ],\n",
       "       [100671.96,  91790.61, 249744.55,      1.  ,      0.  ,      0.  ],\n",
       "       [ 93863.75, 127320.38, 249839.44,      0.  ,      1.  ,      0.  ],\n",
       "       [ 91992.39, 135495.07, 252664.93,      1.  ,      0.  ,      0.  ],\n",
       "       [119943.24, 156547.42, 256512.92,      0.  ,      1.  ,      0.  ],\n",
       "       [114523.61, 122616.84, 261776.23,      0.  ,      0.  ,      1.  ],\n",
       "       [ 78013.11, 121597.55, 264346.06,      1.  ,      0.  ,      0.  ],\n",
       "       [ 94657.16, 145077.58, 282574.31,      0.  ,      0.  ,      1.  ],\n",
       "       [ 91749.16, 114175.79, 294919.57,      0.  ,      1.  ,      0.  ],\n",
       "       [ 86419.7 , 153514.11,      0.  ,      0.  ,      0.  ,      1.  ],\n",
       "       [ 76253.86, 113867.3 , 298664.47,      1.  ,      0.  ,      0.  ],\n",
       "       [ 78389.47, 153773.43, 299737.29,      0.  ,      0.  ,      1.  ],\n",
       "       [ 73994.56, 122782.75, 303319.26,      0.  ,      1.  ,      0.  ],\n",
       "       [ 67532.53, 105751.03, 304768.73,      0.  ,      1.  ,      0.  ],\n",
       "       [ 77044.01,  99281.34, 140574.81,      0.  ,      0.  ,      1.  ],\n",
       "       [ 64664.71, 139553.16, 137962.62,      1.  ,      0.  ,      0.  ],\n",
       "       [ 75328.87, 144135.98, 134050.07,      0.  ,      1.  ,      0.  ],\n",
       "       [ 72107.6 , 127864.55, 353183.81,      0.  ,      0.  ,      1.  ],\n",
       "       [ 66051.52, 182645.56, 118148.2 ,      0.  ,      1.  ,      0.  ],\n",
       "       [ 65605.48, 153032.06, 107138.38,      0.  ,      0.  ,      1.  ],\n",
       "       [ 61994.48, 115641.28,  91131.24,      0.  ,      1.  ,      0.  ],\n",
       "       [ 61136.38, 152701.92,  88218.23,      0.  ,      0.  ,      1.  ],\n",
       "       [ 63408.86, 129219.61,  46085.25,      1.  ,      0.  ,      0.  ],\n",
       "       [ 55493.95, 103057.49, 214634.81,      0.  ,      1.  ,      0.  ],\n",
       "       [ 46426.07, 157693.92, 210797.67,      1.  ,      0.  ,      0.  ],\n",
       "       [ 46014.02,  85047.44, 205517.64,      0.  ,      0.  ,      1.  ],\n",
       "       [ 28663.76, 127056.21, 201126.82,      0.  ,      1.  ,      0.  ],\n",
       "       [ 44069.95,  51283.14, 197029.42,      1.  ,      0.  ,      0.  ],\n",
       "       [ 20229.59,  65947.93, 185265.1 ,      0.  ,      0.  ,      1.  ],\n",
       "       [ 38558.51,  82982.09, 174999.3 ,      1.  ,      0.  ,      0.  ],\n",
       "       [ 28754.33, 118546.05, 172795.67,      1.  ,      0.  ,      0.  ],\n",
       "       [ 27892.92,  84710.77, 164470.71,      0.  ,      1.  ,      0.  ],\n",
       "       [ 23640.93,  96189.63, 148001.11,      1.  ,      0.  ,      0.  ],\n",
       "       [ 15505.73, 127382.3 ,  35534.17,      0.  ,      0.  ,      1.  ],\n",
       "       [ 22177.74, 154806.14,  28334.72,      1.  ,      0.  ,      0.  ],\n",
       "       [  1000.23, 124153.04,   1903.93,      0.  ,      0.  ,      1.  ],\n",
       "       [  1315.46, 115816.21, 297114.46,      0.  ,      1.  ,      0.  ],\n",
       "       [     0.  , 135426.92,      0.  ,      1.  ,      0.  ,      0.  ],\n",
       "       [   542.05,  51743.15,      0.  ,      0.  ,      0.  ,      1.  ],\n",
       "       [     0.  , 116983.8 ,  45173.06,      1.  ,      0.  ,      0.  ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([192261.83, 191792.06, 191050.39, 182901.99, 166187.94, 156991.12,\n",
       "       156122.51, 155752.6 , 152211.77, 149759.96, 146121.95, 144259.4 ,\n",
       "       141585.52, 134307.35, 132602.65, 129917.04, 126992.93, 125370.37,\n",
       "       124266.9 , 122776.86, 118474.03, 111313.02, 110352.25, 108733.99,\n",
       "       108552.04, 107404.34, 105733.54, 105008.31, 103282.38, 101004.64,\n",
       "        99937.59,  97483.56,  97427.84,  96778.92,  96712.8 ,  96479.51,\n",
       "        90708.19,  89949.14,  81229.06,  81005.76,  78239.91,  77798.83,\n",
       "        71498.49,  69758.98,  65200.33,  64926.08,  49490.75,  42559.73,\n",
       "        35673.41,  14681.4 ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[     1.  , 165349.2 , 136897.8 , 471784.1 ,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  , 162597.7 , 151377.59, 443898.53,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 153441.51, 101145.55, 407934.54,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 144372.41, 118671.85, 383199.62,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  , 142107.34,  91391.77, 366168.42,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 131876.9 ,  99814.71, 362861.36,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  , 134615.46, 147198.87, 127716.82,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 130298.13, 145530.06, 323876.68,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 120542.52, 148718.95, 311613.29,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  , 123334.88, 108679.17, 304981.62,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 101913.08, 110594.11, 229160.95,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 100671.96,  91790.61, 249744.55,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  93863.75, 127320.38, 249839.44,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  91992.39, 135495.07, 252664.93,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 119943.24, 156547.42, 256512.92,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  , 114523.61, 122616.84, 261776.23,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  78013.11, 121597.55, 264346.06,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  94657.16, 145077.58, 282574.31,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  91749.16, 114175.79, 294919.57,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  86419.7 , 153514.11,      0.  ,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  76253.86, 113867.3 , 298664.47,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  78389.47, 153773.43, 299737.29,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  73994.56, 122782.75, 303319.26,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  67532.53, 105751.03, 304768.73,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  77044.01,  99281.34, 140574.81,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  64664.71, 139553.16, 137962.62,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  75328.87, 144135.98, 134050.07,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  72107.6 , 127864.55, 353183.81,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  66051.52, 182645.56, 118148.2 ,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  65605.48, 153032.06, 107138.38,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  61994.48, 115641.28,  91131.24,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  61136.38, 152701.92,  88218.23,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  63408.86, 129219.61,  46085.25,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  55493.95, 103057.49, 214634.81,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  46426.07, 157693.92, 210797.67,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  46014.02,  85047.44, 205517.64,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  28663.76, 127056.21, 201126.82,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  44069.95,  51283.14, 197029.42,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  20229.59,  65947.93, 185265.1 ,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  38558.51,  82982.09, 174999.3 ,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  28754.33, 118546.05, 172795.67,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  27892.92,  84710.77, 164470.71,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  23640.93,  96189.63, 148001.11,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,  15505.73, 127382.3 ,  35534.17,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,  22177.74, 154806.14,  28334.72,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,   1000.23, 124153.04,   1903.93,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,   1315.46, 115816.21, 297114.46,      0.  ,      1.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,      0.  , 135426.92,      0.  ,      1.  ,      0.  ,\n",
       "             0.  ],\n",
       "       [     1.  ,    542.05,  51743.15,      0.  ,      0.  ,      0.  ,\n",
       "             1.  ],\n",
       "       [     1.  ,      0.  , 116983.8 ,  45173.06,      1.  ,      0.  ,\n",
       "             0.  ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.append(arr = np.ones((50,1)).astype(int),values=x,axis=1)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "sl = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[     1.  , 165349.2 , 136897.8 , 471784.1 ,      0.  ,      0.  ],\n",
       "       [     1.  , 162597.7 , 151377.59, 443898.53,      1.  ,      0.  ],\n",
       "       [     1.  , 153441.51, 101145.55, 407934.54,      0.  ,      1.  ],\n",
       "       [     1.  , 144372.41, 118671.85, 383199.62,      0.  ,      0.  ],\n",
       "       [     1.  , 142107.34,  91391.77, 366168.42,      0.  ,      1.  ],\n",
       "       [     1.  , 131876.9 ,  99814.71, 362861.36,      0.  ,      0.  ],\n",
       "       [     1.  , 134615.46, 147198.87, 127716.82,      1.  ,      0.  ],\n",
       "       [     1.  , 130298.13, 145530.06, 323876.68,      0.  ,      1.  ],\n",
       "       [     1.  , 120542.52, 148718.95, 311613.29,      0.  ,      0.  ],\n",
       "       [     1.  , 123334.88, 108679.17, 304981.62,      1.  ,      0.  ],\n",
       "       [     1.  , 101913.08, 110594.11, 229160.95,      0.  ,      1.  ],\n",
       "       [     1.  , 100671.96,  91790.61, 249744.55,      1.  ,      0.  ],\n",
       "       [     1.  ,  93863.75, 127320.38, 249839.44,      0.  ,      1.  ],\n",
       "       [     1.  ,  91992.39, 135495.07, 252664.93,      1.  ,      0.  ],\n",
       "       [     1.  , 119943.24, 156547.42, 256512.92,      0.  ,      1.  ],\n",
       "       [     1.  , 114523.61, 122616.84, 261776.23,      0.  ,      0.  ],\n",
       "       [     1.  ,  78013.11, 121597.55, 264346.06,      1.  ,      0.  ],\n",
       "       [     1.  ,  94657.16, 145077.58, 282574.31,      0.  ,      0.  ],\n",
       "       [     1.  ,  91749.16, 114175.79, 294919.57,      0.  ,      1.  ],\n",
       "       [     1.  ,  86419.7 , 153514.11,      0.  ,      0.  ,      0.  ],\n",
       "       [     1.  ,  76253.86, 113867.3 , 298664.47,      1.  ,      0.  ],\n",
       "       [     1.  ,  78389.47, 153773.43, 299737.29,      0.  ,      0.  ],\n",
       "       [     1.  ,  73994.56, 122782.75, 303319.26,      0.  ,      1.  ],\n",
       "       [     1.  ,  67532.53, 105751.03, 304768.73,      0.  ,      1.  ],\n",
       "       [     1.  ,  77044.01,  99281.34, 140574.81,      0.  ,      0.  ],\n",
       "       [     1.  ,  64664.71, 139553.16, 137962.62,      1.  ,      0.  ],\n",
       "       [     1.  ,  75328.87, 144135.98, 134050.07,      0.  ,      1.  ],\n",
       "       [     1.  ,  72107.6 , 127864.55, 353183.81,      0.  ,      0.  ],\n",
       "       [     1.  ,  66051.52, 182645.56, 118148.2 ,      0.  ,      1.  ],\n",
       "       [     1.  ,  65605.48, 153032.06, 107138.38,      0.  ,      0.  ],\n",
       "       [     1.  ,  61994.48, 115641.28,  91131.24,      0.  ,      1.  ],\n",
       "       [     1.  ,  61136.38, 152701.92,  88218.23,      0.  ,      0.  ],\n",
       "       [     1.  ,  63408.86, 129219.61,  46085.25,      1.  ,      0.  ],\n",
       "       [     1.  ,  55493.95, 103057.49, 214634.81,      0.  ,      1.  ],\n",
       "       [     1.  ,  46426.07, 157693.92, 210797.67,      1.  ,      0.  ],\n",
       "       [     1.  ,  46014.02,  85047.44, 205517.64,      0.  ,      0.  ],\n",
       "       [     1.  ,  28663.76, 127056.21, 201126.82,      0.  ,      1.  ],\n",
       "       [     1.  ,  44069.95,  51283.14, 197029.42,      1.  ,      0.  ],\n",
       "       [     1.  ,  20229.59,  65947.93, 185265.1 ,      0.  ,      0.  ],\n",
       "       [     1.  ,  38558.51,  82982.09, 174999.3 ,      1.  ,      0.  ],\n",
       "       [     1.  ,  28754.33, 118546.05, 172795.67,      1.  ,      0.  ],\n",
       "       [     1.  ,  27892.92,  84710.77, 164470.71,      0.  ,      1.  ],\n",
       "       [     1.  ,  23640.93,  96189.63, 148001.11,      1.  ,      0.  ],\n",
       "       [     1.  ,  15505.73, 127382.3 ,  35534.17,      0.  ,      0.  ],\n",
       "       [     1.  ,  22177.74, 154806.14,  28334.72,      1.  ,      0.  ],\n",
       "       [     1.  ,   1000.23, 124153.04,   1903.93,      0.  ,      0.  ],\n",
       "       [     1.  ,   1315.46, 115816.21, 297114.46,      0.  ,      1.  ],\n",
       "       [     1.  ,      0.  , 135426.92,      0.  ,      1.  ,      0.  ],\n",
       "       [     1.  ,    542.05,  51743.15,      0.  ,      0.  ,      0.  ],\n",
       "       [     1.  ,      0.  , 116983.8 ,  45173.06,      1.  ,      0.  ]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=x[:,:-1]\n",
    "x_opt = x\n",
    "x_opt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "regressor_ols = sm.OLS(endog = y,exog = x_opt).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.945</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   169.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 10 Aug 2020</td> <th>  Prob (F-statistic):</th> <td>1.34e-27</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>09:59:32</td>     <th>  Log-Likelihood:    </th> <td> -525.38</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   1063.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    44</td>      <th>  BIC:               </th> <td>   1074.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td> 5.008e+04</td> <td> 6952.587</td> <td>    7.204</td> <td> 0.000</td> <td> 3.61e+04</td> <td> 6.41e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.8060</td> <td>    0.046</td> <td>   17.369</td> <td> 0.000</td> <td>    0.712</td> <td>    0.900</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -0.0270</td> <td>    0.052</td> <td>   -0.517</td> <td> 0.608</td> <td>   -0.132</td> <td>    0.078</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.0270</td> <td>    0.017</td> <td>    1.574</td> <td> 0.123</td> <td>   -0.008</td> <td>    0.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   41.8870</td> <td> 3256.039</td> <td>    0.013</td> <td> 0.990</td> <td>-6520.229</td> <td> 6604.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>  240.6758</td> <td> 3338.857</td> <td>    0.072</td> <td> 0.943</td> <td>-6488.349</td> <td> 6969.701</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>14.782</td> <th>  Durbin-Watson:     </th> <td>   1.283</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  21.266</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.948</td> <th>  Prob(JB):          </th> <td>2.41e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.572</td> <th>  Cond. No.          </th> <td>1.47e+06</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.47e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.951\n",
       "Model:                            OLS   Adj. R-squared:                  0.945\n",
       "Method:                 Least Squares   F-statistic:                     169.9\n",
       "Date:                Mon, 10 Aug 2020   Prob (F-statistic):           1.34e-27\n",
       "Time:                        09:59:32   Log-Likelihood:                -525.38\n",
       "No. Observations:                  50   AIC:                             1063.\n",
       "Df Residuals:                      44   BIC:                             1074.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       5.008e+04   6952.587      7.204      0.000    3.61e+04    6.41e+04\n",
       "x1             0.8060      0.046     17.369      0.000       0.712       0.900\n",
       "x2            -0.0270      0.052     -0.517      0.608      -0.132       0.078\n",
       "x3             0.0270      0.017      1.574      0.123      -0.008       0.062\n",
       "x4            41.8870   3256.039      0.013      0.990   -6520.229    6604.003\n",
       "x5           240.6758   3338.857      0.072      0.943   -6488.349    6969.701\n",
       "==============================================================================\n",
       "Omnibus:                       14.782   Durbin-Watson:                   1.283\n",
       "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.266\n",
       "Skew:                          -0.948   Prob(JB):                     2.41e-05\n",
       "Kurtosis:                       5.572   Cond. No.                     1.47e+06\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.47e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor_ols.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.      , 0.      , 0.607737, 0.122677, 0.989794, 0.942862])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor_ols.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9897941241607429"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mx = max(regressor_ols.pvalues)\n",
    "mx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.950\n",
      "Model:                            OLS   Adj. R-squared:                  0.948\n",
      "Method:                 Least Squares   F-statistic:                     450.8\n",
      "Date:                Mon, 10 Aug 2020   Prob (F-statistic):           2.16e-31\n",
      "Time:                        09:59:33   Log-Likelihood:                -525.54\n",
      "No. Observations:                  50   AIC:                             1057.\n",
      "Df Residuals:                      47   BIC:                             1063.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const       4.698e+04   2689.933     17.464      0.000    4.16e+04    5.24e+04\n",
      "x1             0.7966      0.041     19.266      0.000       0.713       0.880\n",
      "x2             0.0299      0.016      1.927      0.060      -0.001       0.061\n",
      "==============================================================================\n",
      "Omnibus:                       14.677   Durbin-Watson:                   1.257\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.161\n",
      "Skew:                          -0.939   Prob(JB):                     2.54e-05\n",
      "Kurtosis:                       5.575   Cond. No.                     5.32e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.32e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "def backwardElimination(x, SL):\n",
    "    numVars = len(x[0])\n",
    "    temp = np.zeros((50,6)).astype(int)\n",
    "    for i in range(0, numVars):\n",
    "        regressor_OLS = sm.OLS(y, x).fit()\n",
    "        maxVar = max(regressor_OLS.pvalues).astype(float)\n",
    "        adjR_before = regressor_OLS.rsquared_adj.astype(float)\n",
    "        if maxVar > SL:\n",
    "            for j in range(0, numVars - i):\n",
    "                if (regressor_OLS.pvalues[j].astype(float) == maxVar):\n",
    "                    temp[:,j] = x[:, j]\n",
    "                    x = np.delete(x, j, 1)\n",
    "                    tmp_regressor = sm.OLS(y, x).fit()\n",
    "                    adjR_after = tmp_regressor.rsquared_adj.astype(float)\n",
    "                    if (adjR_before >= adjR_after):\n",
    "                        x_rollback = np.hstack((x, temp[:,[0,j]]))\n",
    "                        x_rollback = np.delete(x_rollback, j, 1)\n",
    "                        print (regressor_OLS.summary())\n",
    "                        return x_rollback\n",
    "                    else:\n",
    "                        continue\n",
    "    regressor_OLS.summary()\n",
    "    return x\n",
    " \n",
    "SL = 0.05\n",
    "X_opt = x[:, [0, 1, 2, 3, 4, 5]]\n",
    "X_Modeled = backwardElimination(X_opt, SL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[     1.  , 165349.2 , 471784.  ],\n",
       "       [     1.  , 162597.7 , 443898.  ],\n",
       "       [     1.  , 153441.51, 407934.  ],\n",
       "       [     1.  , 144372.41, 383199.  ],\n",
       "       [     1.  , 142107.34, 366168.  ],\n",
       "       [     1.  , 131876.9 , 362861.  ],\n",
       "       [     1.  , 134615.46, 127716.  ],\n",
       "       [     1.  , 130298.13, 323876.  ],\n",
       "       [     1.  , 120542.52, 311613.  ],\n",
       "       [     1.  , 123334.88, 304981.  ],\n",
       "       [     1.  , 101913.08, 229160.  ],\n",
       "       [     1.  , 100671.96, 249744.  ],\n",
       "       [     1.  ,  93863.75, 249839.  ],\n",
       "       [     1.  ,  91992.39, 252664.  ],\n",
       "       [     1.  , 119943.24, 256512.  ],\n",
       "       [     1.  , 114523.61, 261776.  ],\n",
       "       [     1.  ,  78013.11, 264346.  ],\n",
       "       [     1.  ,  94657.16, 282574.  ],\n",
       "       [     1.  ,  91749.16, 294919.  ],\n",
       "       [     1.  ,  86419.7 ,      0.  ],\n",
       "       [     1.  ,  76253.86, 298664.  ],\n",
       "       [     1.  ,  78389.47, 299737.  ],\n",
       "       [     1.  ,  73994.56, 303319.  ],\n",
       "       [     1.  ,  67532.53, 304768.  ],\n",
       "       [     1.  ,  77044.01, 140574.  ],\n",
       "       [     1.  ,  64664.71, 137962.  ],\n",
       "       [     1.  ,  75328.87, 134050.  ],\n",
       "       [     1.  ,  72107.6 , 353183.  ],\n",
       "       [     1.  ,  66051.52, 118148.  ],\n",
       "       [     1.  ,  65605.48, 107138.  ],\n",
       "       [     1.  ,  61994.48,  91131.  ],\n",
       "       [     1.  ,  61136.38,  88218.  ],\n",
       "       [     1.  ,  63408.86,  46085.  ],\n",
       "       [     1.  ,  55493.95, 214634.  ],\n",
       "       [     1.  ,  46426.07, 210797.  ],\n",
       "       [     1.  ,  46014.02, 205517.  ],\n",
       "       [     1.  ,  28663.76, 201126.  ],\n",
       "       [     1.  ,  44069.95, 197029.  ],\n",
       "       [     1.  ,  20229.59, 185265.  ],\n",
       "       [     1.  ,  38558.51, 174999.  ],\n",
       "       [     1.  ,  28754.33, 172795.  ],\n",
       "       [     1.  ,  27892.92, 164470.  ],\n",
       "       [     1.  ,  23640.93, 148001.  ],\n",
       "       [     1.  ,  15505.73,  35534.  ],\n",
       "       [     1.  ,  22177.74,  28334.  ],\n",
       "       [     1.  ,   1000.23,   1903.  ],\n",
       "       [     1.  ,   1315.46, 297114.  ],\n",
       "       [     1.  ,      0.  ,      0.  ],\n",
       "       [     1.  ,    542.05,      0.  ],\n",
       "       [     1.  ,      0.  ,  45173.  ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_Modeled "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split as tts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train,x_test,y_train,y_test = tts(X_Modeled[:,1:],y,test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(x_train,y_train)\n",
    "y_pred = regressor.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([162312.556081,  76279.971197, 127969.511403, 111951.153749,\n",
       "        49832.392209, 117090.074234, 170547.26899 ,  90217.572496,\n",
       "       100329.565736, 118204.608609])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([156991.12,  90708.19, 134307.35, 105733.54,  14681.4 , 126992.93,\n",
       "       166187.94,  96479.51,  99937.59, 111313.02])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Score:  0.9648986870282177\n",
      "Test Score:  0.8903604405412001\n"
     ]
    }
   ],
   "source": [
    "print('Train Score: ', regressor.score(x_train, y_train))  \n",
    "print('Test Score: ', regressor.score(x_test, y_test))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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