Linear Regression.ipynb

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    {
     "name": "stderr",
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     "text": [
      "C:\\Users\\marco\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"data/Advertising.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
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       "      <td>1</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
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       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>44.5</td>\n",
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       "      <td>10.4</td>\n",
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       "      <td>3</td>\n",
       "      <td>17.2</td>\n",
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       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
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       "   Unnamed: 0     TV  radio  newspaper  sales\n",
       "0           1  230.1   37.8       69.2   22.1\n",
       "1           2   44.5   39.3       45.1   10.4\n",
       "2           3   17.2   45.9       69.3    9.3\n",
       "3           4  151.5   41.3       58.5   18.5\n",
       "4           5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Unnamed: 0', 'TV', 'radio', 'newspaper', 'sales'], dtype='object')"
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     "execution_count": 4,
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    "data.columns"
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       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
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       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
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       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
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       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
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       "      <th>4</th>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.7</td>\n",
       "      <td>48.9</td>\n",
       "      <td>75.0</td>\n",
       "      <td>7.2</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>57.5</td>\n",
       "      <td>32.8</td>\n",
       "      <td>23.5</td>\n",
       "      <td>11.8</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>120.2</td>\n",
       "      <td>19.6</td>\n",
       "      <td>11.6</td>\n",
       "      <td>13.2</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.6</td>\n",
       "      <td>2.1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.8</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>199.8</td>\n",
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       "      <td>21.2</td>\n",
       "      <td>10.6</td>\n",
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       "      <th>10</th>\n",
       "      <td>66.1</td>\n",
       "      <td>5.8</td>\n",
       "      <td>24.2</td>\n",
       "      <td>8.6</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>214.7</td>\n",
       "      <td>24.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>17.4</td>\n",
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       "      <th>12</th>\n",
       "      <td>23.8</td>\n",
       "      <td>35.1</td>\n",
       "      <td>65.9</td>\n",
       "      <td>9.2</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>97.5</td>\n",
       "      <td>7.6</td>\n",
       "      <td>7.2</td>\n",
       "      <td>9.7</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>204.1</td>\n",
       "      <td>32.9</td>\n",
       "      <td>46.0</td>\n",
       "      <td>19.0</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>195.4</td>\n",
       "      <td>47.7</td>\n",
       "      <td>52.9</td>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>67.8</td>\n",
       "      <td>36.6</td>\n",
       "      <td>114.0</td>\n",
       "      <td>12.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>281.4</td>\n",
       "      <td>39.6</td>\n",
       "      <td>55.8</td>\n",
       "      <td>24.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>69.2</td>\n",
       "      <td>20.5</td>\n",
       "      <td>18.3</td>\n",
       "      <td>11.3</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>147.3</td>\n",
       "      <td>23.9</td>\n",
       "      <td>19.1</td>\n",
       "      <td>14.6</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>218.4</td>\n",
       "      <td>27.7</td>\n",
       "      <td>53.4</td>\n",
       "      <td>18.0</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>237.4</td>\n",
       "      <td>5.1</td>\n",
       "      <td>23.5</td>\n",
       "      <td>12.5</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>13.2</td>\n",
       "      <td>15.9</td>\n",
       "      <td>49.6</td>\n",
       "      <td>5.6</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>228.3</td>\n",
       "      <td>16.9</td>\n",
       "      <td>26.2</td>\n",
       "      <td>15.5</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>62.3</td>\n",
       "      <td>12.6</td>\n",
       "      <td>18.3</td>\n",
       "      <td>9.7</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>262.9</td>\n",
       "      <td>3.5</td>\n",
       "      <td>19.5</td>\n",
       "      <td>12.0</td>\n",
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       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>142.9</td>\n",
       "      <td>29.3</td>\n",
       "      <td>12.6</td>\n",
       "      <td>15.0</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>240.1</td>\n",
       "      <td>16.7</td>\n",
       "      <td>22.9</td>\n",
       "      <td>15.9</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>248.8</td>\n",
       "      <td>27.1</td>\n",
       "      <td>22.9</td>\n",
       "      <td>18.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>70.6</td>\n",
       "      <td>16.0</td>\n",
       "      <td>40.8</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170</th>\n",
       "      <td>50.0</td>\n",
       "      <td>11.6</td>\n",
       "      <td>18.4</td>\n",
       "      <td>8.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>164.5</td>\n",
       "      <td>20.9</td>\n",
       "      <td>47.4</td>\n",
       "      <td>14.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>19.6</td>\n",
       "      <td>20.1</td>\n",
       "      <td>17.0</td>\n",
       "      <td>7.6</td>\n",
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       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>168.4</td>\n",
       "      <td>7.1</td>\n",
       "      <td>12.8</td>\n",
       "      <td>11.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>222.4</td>\n",
       "      <td>3.4</td>\n",
       "      <td>13.1</td>\n",
       "      <td>11.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>276.9</td>\n",
       "      <td>48.9</td>\n",
       "      <td>41.8</td>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>248.4</td>\n",
       "      <td>30.2</td>\n",
       "      <td>20.3</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>170.2</td>\n",
       "      <td>7.8</td>\n",
       "      <td>35.2</td>\n",
       "      <td>11.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>276.7</td>\n",
       "      <td>2.3</td>\n",
       "      <td>23.7</td>\n",
       "      <td>11.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>165.6</td>\n",
       "      <td>10.0</td>\n",
       "      <td>17.6</td>\n",
       "      <td>12.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>156.6</td>\n",
       "      <td>2.6</td>\n",
       "      <td>8.3</td>\n",
       "      <td>10.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>218.5</td>\n",
       "      <td>5.4</td>\n",
       "      <td>27.4</td>\n",
       "      <td>12.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>56.2</td>\n",
       "      <td>5.7</td>\n",
       "      <td>29.7</td>\n",
       "      <td>8.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>287.6</td>\n",
       "      <td>43.0</td>\n",
       "      <td>71.8</td>\n",
       "      <td>26.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>253.8</td>\n",
       "      <td>21.3</td>\n",
       "      <td>30.0</td>\n",
       "      <td>17.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>205.0</td>\n",
       "      <td>45.1</td>\n",
       "      <td>19.6</td>\n",
       "      <td>22.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>139.5</td>\n",
       "      <td>2.1</td>\n",
       "      <td>26.6</td>\n",
       "      <td>10.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>191.1</td>\n",
       "      <td>28.7</td>\n",
       "      <td>18.2</td>\n",
       "      <td>17.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>286.0</td>\n",
       "      <td>13.9</td>\n",
       "      <td>3.7</td>\n",
       "      <td>15.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>18.7</td>\n",
       "      <td>12.1</td>\n",
       "      <td>23.4</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>39.5</td>\n",
       "      <td>41.1</td>\n",
       "      <td>5.8</td>\n",
       "      <td>10.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>75.5</td>\n",
       "      <td>10.8</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>17.2</td>\n",
       "      <td>4.1</td>\n",
       "      <td>31.6</td>\n",
       "      <td>5.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>166.8</td>\n",
       "      <td>42.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>19.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>149.7</td>\n",
       "      <td>35.6</td>\n",
       "      <td>6.0</td>\n",
       "      <td>17.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>9.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>13.4</td>\n",
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       "<p>200 rows × 4 columns</p>\n",
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      ],
      "text/plain": [
       "        TV  radio  newspaper  sales\n",
       "0    230.1   37.8       69.2   22.1\n",
       "1     44.5   39.3       45.1   10.4\n",
       "2     17.2   45.9       69.3    9.3\n",
       "3    151.5   41.3       58.5   18.5\n",
       "4    180.8   10.8       58.4   12.9\n",
       "5      8.7   48.9       75.0    7.2\n",
       "6     57.5   32.8       23.5   11.8\n",
       "7    120.2   19.6       11.6   13.2\n",
       "8      8.6    2.1        1.0    4.8\n",
       "9    199.8    2.6       21.2   10.6\n",
       "10    66.1    5.8       24.2    8.6\n",
       "11   214.7   24.0        4.0   17.4\n",
       "12    23.8   35.1       65.9    9.2\n",
       "13    97.5    7.6        7.2    9.7\n",
       "14   204.1   32.9       46.0   19.0\n",
       "15   195.4   47.7       52.9   22.4\n",
       "16    67.8   36.6      114.0   12.5\n",
       "17   281.4   39.6       55.8   24.4\n",
       "18    69.2   20.5       18.3   11.3\n",
       "19   147.3   23.9       19.1   14.6\n",
       "20   218.4   27.7       53.4   18.0\n",
       "21   237.4    5.1       23.5   12.5\n",
       "22    13.2   15.9       49.6    5.6\n",
       "23   228.3   16.9       26.2   15.5\n",
       "24    62.3   12.6       18.3    9.7\n",
       "25   262.9    3.5       19.5   12.0\n",
       "26   142.9   29.3       12.6   15.0\n",
       "27   240.1   16.7       22.9   15.9\n",
       "28   248.8   27.1       22.9   18.9\n",
       "29    70.6   16.0       40.8   10.5\n",
       "..     ...    ...        ...    ...\n",
       "170   50.0   11.6       18.4    8.4\n",
       "171  164.5   20.9       47.4   14.5\n",
       "172   19.6   20.1       17.0    7.6\n",
       "173  168.4    7.1       12.8   11.7\n",
       "174  222.4    3.4       13.1   11.5\n",
       "175  276.9   48.9       41.8   27.0\n",
       "176  248.4   30.2       20.3   20.2\n",
       "177  170.2    7.8       35.2   11.7\n",
       "178  276.7    2.3       23.7   11.8\n",
       "179  165.6   10.0       17.6   12.6\n",
       "180  156.6    2.6        8.3   10.5\n",
       "181  218.5    5.4       27.4   12.2\n",
       "182   56.2    5.7       29.7    8.7\n",
       "183  287.6   43.0       71.8   26.2\n",
       "184  253.8   21.3       30.0   17.6\n",
       "185  205.0   45.1       19.6   22.6\n",
       "186  139.5    2.1       26.6   10.3\n",
       "187  191.1   28.7       18.2   17.3\n",
       "188  286.0   13.9        3.7   15.9\n",
       "189   18.7   12.1       23.4    6.7\n",
       "190   39.5   41.1        5.8   10.8\n",
       "191   75.5   10.8        6.0    9.9\n",
       "192   17.2    4.1       31.6    5.9\n",
       "193  166.8   42.0        3.6   19.6\n",
       "194  149.7   35.6        6.0   17.3\n",
       "195   38.2    3.7       13.8    7.6\n",
       "196   94.2    4.9        8.1    9.7\n",
       "197  177.0    9.3        6.4   12.8\n",
       "198  283.6   42.0       66.2   25.5\n",
       "199  232.1    8.6        8.7   13.4\n",
       "\n",
       "[200 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.drop(['Unnamed: 0'], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple linear regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x196ee27c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 8))\n",
    "plt.scatter(\n",
    "    data['TV'],\n",
    "    data['sales'],\n",
    "    c='black'\n",
    ")\n",
    "plt.xlabel(\"Money spent on TV ads ($)\")\n",
    "plt.ylabel(\"Sales ($)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data['TV'].values.reshape(-1,1)\n",
    "y = data['sales'].values.reshape(-1,1)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.047536640433019764\n",
      "7.032593549127693\n",
      "The linear model is: Y = 7.0326 + 0.047537X\n"
     ]
    }
   ],
   "source": [
    "print(reg.coef_[0][0])\n",
    "print(reg.intercept_[0])\n",
    "\n",
    "print(\"The linear model is: Y = {:.5} + {:.5}X\".format(reg.intercept_[0], reg.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x196ee27ccc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = reg.predict(X)\n",
    "\n",
    "plt.figure(figsize=(16, 8))\n",
    "plt.scatter(\n",
    "    data['TV'],\n",
    "    data['sales'],\n",
    "    c='black'\n",
    ")\n",
    "plt.plot(\n",
    "    data['TV'],\n",
    "    predictions,\n",
    "    c='blue',\n",
    "    linewidth=2\n",
    ")\n",
    "plt.xlabel(\"Money spent on TV ads ($)\")\n",
    "plt.ylabel(\"Sales ($)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.612\n",
      "Model:                            OLS   Adj. R-squared:                  0.610\n",
      "Method:                 Least Squares   F-statistic:                     312.1\n",
      "Date:                Wed, 28 Nov 2018   Prob (F-statistic):           1.47e-42\n",
      "Time:                        22:06:58   Log-Likelihood:                -519.05\n",
      "No. Observations:                 200   AIC:                             1042.\n",
      "Df Residuals:                     198   BIC:                             1049.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          7.0326      0.458     15.360      0.000       6.130       7.935\n",
      "TV             0.0475      0.003     17.668      0.000       0.042       0.053\n",
      "==============================================================================\n",
      "Omnibus:                        0.531   Durbin-Watson:                   1.935\n",
      "Prob(Omnibus):                  0.767   Jarque-Bera (JB):                0.669\n",
      "Skew:                          -0.089   Prob(JB):                        0.716\n",
      "Kurtosis:                       2.779   Cond. No.                         338.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = data['TV']\n",
    "y = data['sales']\n",
    "\n",
    "X2 = sm.add_constant(X)\n",
    "est = sm.OLS(y, X2)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple linear regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marco\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:2: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xs = data.drop(['sales', 'Unnamed: 0'], axis=1)\n",
    "y = data['sales'].values.reshape(-1,1)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(Xs, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.04576465  0.18853002 -0.00103749]]\n",
      "[2.93888937]\n"
     ]
    }
   ],
   "source": [
    "print(reg.coef_)\n",
    "print(reg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: Y = 2.9389 + 0.045765*TV + 0.18853*radio + -0.0010375*newspaper\n"
     ]
    }
   ],
   "source": [
    "print(\"The linear model is: Y = {:.5} + {:.5}*TV + {:.5}*radio + {:.5}*newspaper\".format(reg.intercept_[0], reg.coef_[0][0], reg.coef_[0][1], reg.coef_[0][2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8972106381789521"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(Xs, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.897\n",
      "Model:                            OLS   Adj. R-squared:                  0.896\n",
      "Method:                 Least Squares   F-statistic:                     570.3\n",
      "Date:                Wed, 28 Nov 2018   Prob (F-statistic):           1.58e-96\n",
      "Time:                        22:06:58   Log-Likelihood:                -386.18\n",
      "No. Observations:                 200   AIC:                             780.4\n",
      "Df Residuals:                     196   BIC:                             793.6\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          2.9389      0.312      9.422      0.000       2.324       3.554\n",
      "x1             0.0458      0.001     32.809      0.000       0.043       0.049\n",
      "x2             0.1885      0.009     21.893      0.000       0.172       0.206\n",
      "x3            -0.0010      0.006     -0.177      0.860      -0.013       0.011\n",
      "==============================================================================\n",
      "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
      "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
      "Kurtosis:                       6.332   Cond. No.                         454.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = np.column_stack((data['TV'], data['radio'], data['newspaper']))\n",
    "y = data['sales']\n",
    "\n",
    "X2 = sm.add_constant(X)\n",
    "est = sm.OLS(y, X2)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  }
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