Project2_headbrain_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3585</td>\n",
       "      <td>1300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3785</td>\n",
       "      <td>1400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3559</td>\n",
       "      <td>1255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3613</td>\n",
       "      <td>1355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3982</td>\n",
       "      <td>1375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3443</td>\n",
       "      <td>1340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3993</td>\n",
       "      <td>1380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3640</td>\n",
       "      <td>1355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4208</td>\n",
       "      <td>1522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3832</td>\n",
       "      <td>1208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3876</td>\n",
       "      <td>1405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3497</td>\n",
       "      <td>1358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3466</td>\n",
       "      <td>1292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3095</td>\n",
       "      <td>1340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4424</td>\n",
       "      <td>1400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3878</td>\n",
       "      <td>1357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4046</td>\n",
       "      <td>1287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3804</td>\n",
       "      <td>1275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3710</td>\n",
       "      <td>1270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4747</td>\n",
       "      <td>1635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4423</td>\n",
       "      <td>1505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4036</td>\n",
       "      <td>1490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4022</td>\n",
       "      <td>1485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3454</td>\n",
       "      <td>1310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4175</td>\n",
       "      <td>1420</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>207</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3995</td>\n",
       "      <td>1296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>208</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3318</td>\n",
       "      <td>1175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>209</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2720</td>\n",
       "      <td>955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2937</td>\n",
       "      <td>1070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>211</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3580</td>\n",
       "      <td>1320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>212</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2939</td>\n",
       "      <td>1060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>213</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2989</td>\n",
       "      <td>1130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>214</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3586</td>\n",
       "      <td>1250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>215</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3156</td>\n",
       "      <td>1225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>216</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3246</td>\n",
       "      <td>1180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>217</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3170</td>\n",
       "      <td>1178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>218</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3268</td>\n",
       "      <td>1142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>219</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3389</td>\n",
       "      <td>1130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>220</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3381</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>221</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2864</td>\n",
       "      <td>1012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3740</td>\n",
       "      <td>1280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>223</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3479</td>\n",
       "      <td>1103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>224</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3647</td>\n",
       "      <td>1408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>225</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3716</td>\n",
       "      <td>1300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3284</td>\n",
       "      <td>1246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4204</td>\n",
       "      <td>1380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>228</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3735</td>\n",
       "      <td>1350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>229</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3218</td>\n",
       "      <td>1060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>230</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3685</td>\n",
       "      <td>1350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>231</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3704</td>\n",
       "      <td>1220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>232</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3214</td>\n",
       "      <td>1110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3394</td>\n",
       "      <td>1215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>234</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3233</td>\n",
       "      <td>1104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>235</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3352</td>\n",
       "      <td>1170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>236</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3391</td>\n",
       "      <td>1120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>237 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0         1          1             4512                 1530\n",
       "1         1          1             3738                 1297\n",
       "2         1          1             4261                 1335\n",
       "3         1          1             3777                 1282\n",
       "4         1          1             4177                 1590\n",
       "5         1          1             3585                 1300\n",
       "6         1          1             3785                 1400\n",
       "7         1          1             3559                 1255\n",
       "8         1          1             3613                 1355\n",
       "9         1          1             3982                 1375\n",
       "10        1          1             3443                 1340\n",
       "11        1          1             3993                 1380\n",
       "12        1          1             3640                 1355\n",
       "13        1          1             4208                 1522\n",
       "14        1          1             3832                 1208\n",
       "15        1          1             3876                 1405\n",
       "16        1          1             3497                 1358\n",
       "17        1          1             3466                 1292\n",
       "18        1          1             3095                 1340\n",
       "19        1          1             4424                 1400\n",
       "20        1          1             3878                 1357\n",
       "21        1          1             4046                 1287\n",
       "22        1          1             3804                 1275\n",
       "23        1          1             3710                 1270\n",
       "24        1          1             4747                 1635\n",
       "25        1          1             4423                 1505\n",
       "26        1          1             4036                 1490\n",
       "27        1          1             4022                 1485\n",
       "28        1          1             3454                 1310\n",
       "29        1          1             4175                 1420\n",
       "..      ...        ...              ...                  ...\n",
       "207       2          2             3995                 1296\n",
       "208       2          2             3318                 1175\n",
       "209       2          2             2720                  955\n",
       "210       2          2             2937                 1070\n",
       "211       2          2             3580                 1320\n",
       "212       2          2             2939                 1060\n",
       "213       2          2             2989                 1130\n",
       "214       2          2             3586                 1250\n",
       "215       2          2             3156                 1225\n",
       "216       2          2             3246                 1180\n",
       "217       2          2             3170                 1178\n",
       "218       2          2             3268                 1142\n",
       "219       2          2             3389                 1130\n",
       "220       2          2             3381                 1185\n",
       "221       2          2             2864                 1012\n",
       "222       2          2             3740                 1280\n",
       "223       2          2             3479                 1103\n",
       "224       2          2             3647                 1408\n",
       "225       2          2             3716                 1300\n",
       "226       2          2             3284                 1246\n",
       "227       2          2             4204                 1380\n",
       "228       2          2             3735                 1350\n",
       "229       2          2             3218                 1060\n",
       "230       2          2             3685                 1350\n",
       "231       2          2             3704                 1220\n",
       "232       2          2             3214                 1110\n",
       "233       2          2             3394                 1215\n",
       "234       2          2             3233                 1104\n",
       "235       2          2             3352                 1170\n",
       "236       2          2             3391                 1120\n",
       "\n",
       "[237 rows x 4 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df_headbrain=pd.read_csv(\"headbrain.csv\")\n",
    "df_headbrain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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56kAW7egX6JeK0gXtyakEuqbIIokskqyyyLhT78Xwy+uAq2zf2zpQXuHdB9imB58/qXIsga4qskgiiyTHLAZ9SuZEetGpdzoj3w242fbcHnz+pMqyBLqiyCKJLJIss4hOvTNJy1NUQ43dh7TTGHufGvAvZ09FFklkkeSXhedHp96R7ceB1Tsc/5c6nzuVsiyBriiySCKLJMss4kw9XzmWQFcVWSSRRZJlFvnukVF7j9Ijy31IZ0v6gaTlJO0q6SpJ10j6naSNetXYSdFWAr1gutagf2GriiySyCLJMAuPuuvboKncqUtaG3gfMMP25hTVVAcAJwL/XC4N8H3gY71o6GTz/JE0XWvIRRZJZJFklcXoEtwGTN3hl+nAMyQ9DSxPsZCNgZXL51dh0cVtQgihUTlfKK2zScZdwBeAO4B7gIdsnw+8AzhH0lzgbcBxnd7fbxWlIYTh0bs9MvpPneGX1Sh29NgAWAtYQdJbgSOB19teBzgV+FKn9/dbRWlWJdA1RRZJZJFklUUMv3S0G3C77b8BSDoT2AHYsm3f0tOBc+s1cWp4ZBTs4ks76IUVNUUWSWSR5JTFIJ6Bd6vO7Jc7gO0kLV+uyNjao3SVcm9SKAqTbqrZxkmVYwl0VZFFElkkWWYRZ+qLsn2ZpDOAq4D5wNUUWz7NBX4iaRR4EDi4Fw2dLFmWQFcUWSSRRZJjFjmfqdetKP0E8Ikxh88qbwNisL+cvRVZJJFFkl8Wo/ObbsHkGfqK0ixLoCuKLJLIIskyC+f3D1VL3YrSI8pq0hskvb88tqWkSyRdL+lnklZe3Oc0aaES6NIgVpH1QmSRRBZJjlnElMYOJG0OvBPYFtgS2EPSxsBJwFG2X0wxDPOhXjR00mRYAl1ZZJFEFkmGWXhUXd8GTZ0z9RcCl9p+3PZ84DfAm4BNgYvL11wA7FuviVMjqxLomiKLJLJIcsoiztQ7mw28UtLq5brqrwfWLY/vWb5m//LYIqKiNITQlNERdX0bNHWWCbgJ+BzF2fi5wLUUUxsPBg6TdCWwEtDhKkv/VZSGEIZHzsMvdac0ngycDCDps8Bc2zcDrymPbQK8oW4jp0I25c89EFkkkUWSUxaDPnlnInW3s1vD9jxJ61FsNL1927GlKJbd/UYvGjrZciqBriuySCKLJKcsBvEMvFt156n/RNLqwNPAYbYfLKc5HlY+fybFol59K8sS6IoiiySySHLMIjr1cdjescOxE4AT6nzuVMqxBLqqyCKJLJIcs4jhl6wN9peztyKLJLJI8stidKRW3WVfW+yfTNIpkuZJmt12bP+yinRU0owxrz9a0hxJt0h67WQ0upeyLIGuKLJIIoskxyyGfZ76t4DdxxybTXFh9OL2g5I2o9in9EXle/5bUl9fMs+xBLqqyCKJLJIcsxi1ur4NmsUOv9i+WNL6Y47dBKBFx9X2An5o+0ngdklzKJYRuKQXjZ0UbSXQCwz4F7ayyCKJLJIMs/AAdtbd6vXA0trAnW2P55bHFtFvFaU5lUDXFVkkkUWSUxY5Fx/1ulPvlEDHf9KjojSE0BS7+9ug6fXsl7ksvNbLOsDdPf4ZIYRQy8gwz35ZQmcDB0haVtIGwMbA5T3+GZMiq53Sa4osksgiySkLW13fBk03Uxp/QHGhc1NJcyUdIulNkuYC2wO/kHQegO0bgB9RbEB9LkWV6UAMwnlkNI0XDnhhRV2RRRJZJDll0cvhF0m7l1O450g6qsPzy0o6vXz+svaJJ5MxBbyb2S8HjvNUx31IbX8G+EydRk2lHEugq4osksgiyTGLXk1VLKdsfx14NcXw8xWSzrZ9Y9vLDgEetL2RpAMoVrd985gp4GsBv5K0Sd0T4XwHlrqUYwl0VZFFElkkOWbRw+GXbYE5tm+z/RTwQ4qp3e32Ak4r758B7KpiPviCKeC2bwdaU8BrqVpRerykmyVdJ+ksSauWx1eX9GtJj0r6Wt3GTY3B/nL2VmSRRBZJflmMjKrr22J0M417wWvKXeIeAlbv8r1LrGpF6QXA5ra3AP4IHF0efwL4d+CDdRs2VXIsga4qskgiiyTHLJbkTL29pqa8Hdr2Ud1M4x7vNV1PAV8SVStKz297eCmwX3n8MeB3kjaq27CpslAJdPlFHfQS6KoiiySySHLMYknG1G3PBGaO83Q307hbr5kraTqwCvBAl+9dYr0YUz8Y+GUPPqcZGe6UXllkkUQWSYZZeAlui3EFsLGkDSQtQ3Hh8+wxrzkbOKi8vx/wf7bNJE0Br9WpSzqGYl/S71V4bywT0KciiySySHLKolcLepVj5IcD5wE3AT+yfYOkYyXtWb7sZGD1ci2sDwBHle+dlCnglStKJR0E7AHsWv6rs0Taf6WZtc7eg/3PfghhoPSyqMj2OcA5Y459vO3+E8D+47y351PAK3XqknYHPgK8yvbjvWxQCCFMtpEMZ/S0LLZTLytKdwKeVVaRfoJitsuywAXl8ruX2n53+fo/AysDy0jaG3jNmIn4fSmX8udeiCySyCLJKYsBvyQwoaoVpSdP8Pr16zSoKTntlF5XZJFEFklOWYwO85l67nIsga4qskgiiyTHLJxxp161ovTTZTXpNZLOl7RWefyfy+PXSfqDpC0ns/G9kGMJdFWRRRJZJDlmMboEt0FTtaL0eNtb2N4K+DnQutJ7O8XF0y2ATzP+hP0+Mthfzt6KLJLIIskvC6Oub4OmakXpw20PV6Cco2/7D23HL6WokOprOZZAVxVZJJFFkmMW85tuwCSqM0/9M8D/o1icZucOLzmEAag0zbEEuqrIIokskhyzGMQz8G5Vrii1fYztdSmqSQ9vf07SzhSd+kfGe3/fVJRmWAJdWWSRRBZJhlmMqvvboOnF2i/fB/ZtPZC0BXASsJft+8d7U79tPJ1TCXRdkUUSWSQ5ZTGKur4NmkqduqSN2x7uCdxcHl8POBN4m+0/1m9eCCH0Xg8X9Oo7VStKXy9pU4oZP38B3l2+/OMUi7//d1lpOt/2jElodwghVDZ/wKdkTqSnFaW23wG8o26jmpBTCXRdkUUSWSQ5ZTGIZ+DdGvqK0pacSqDriiySyCLJKYtBLCrqVldj6p2qStue+6AkS3pW+XivtmrTWZJe0etG91KOJdBVRRZJZJHkmEXMfulcVYqkdYFXA3e0Hb4Q2LKsNj2YYiZM38qxBLqqyCKJLJIcsxj62S+2L6bYU2+sLwMfpm2IyvajbZtmrEDfD18N3v9pkyeySCKLJL8shnr2y3jKrZrusn2txvyrLelNwH8CawBvqNXCSZZjCXRVkUUSWSQ5ZjE/v3+nFqg6T3154BjSQl4LsX2W7RcAe1Ms7NXpM/qionShEujSoJdAVxVZJJFFkmMWOZ+pV60ofT6wAXBtudPROsBVkp7b/qJy2Ob5rYuoY57rj4rSDEugK4ssksgiyTCLnC+UVhp+sX09xdAKsGALuxm275O0EfAn25b0EmAZYNzlAvpFq/w5p7m4VUUWSWSR5JRFTGksqkovATaVNFfSIRO8fF9gtqRrgK8Db267cBpCCI3LeZOMrs7Ux6kqbX9+/bb7nwM+V69ZIYQweTyAwyrdiorSUg6/UvZKZJFEFklOWeS8SUbVPUo/Kemusmr0GkmvH/Oe9SQ9KumDk9HoyeCR0bSs6IAXVtQVWSSRRZJTFsM+++VbdKgmBb5se6vyds7Y5xiAXY8gzxLoqiKLJLJIcsxiqGe/dNqjdCKS9gZuAx6r3qypk2MJdFWRRRJZJDlmMYgXQLtVZ+ejw8uFu06RtBqApBUotrD7VE9aNyUG+8vZW5FFElkk+WWR8+yXqp36iRQFSFsB9wBfLI9/imJY5tHFfUC/VJTmWAJdVWSRRBZJjlmMqPvboKlafHRv676kbwI/Lx++DNhP0ueBVYFRSU/Y/lqHz5gJzASYtc7ejX1DctwpvarIIokskhyzGMQz8G5V6tQlrWn7nvLhm4DZALZ3bHvNJ4FHO3XofaWtBHqBAf/CVhZZJJFFkmEWg936iVXdo3QnSVtRZPNn4F2T2MYpkVMJdF2RRRJZJDllMZpxt97TPUrHvO+TVRoUQgiTLYZfQgghI/mep0envkAOv1L2SmSRRBZJTlkM9SYZ4206Lem9km6RdEM52wVJ60v6R9vyAd+YrIb3Wk4l0HVFFklkkeSUxSju+laHpGdKukDSreV/VxvndQeVr7lV0kEdnj97bB88nkrLBEjaGdgL2ML2i4AvtD39p7blA97dTSOalGMJdFWRRRJZJDlmMYVrvxwFXGh7Y+DC8vFCJD2TYgLKy4BtgU+0d/6S9gEWW/vTsthOfZxNp98DHGf7yfI187r9gf0mxxLoqiKLJLJIcsxiCitK9wJOK++fRrHF51ivBS6w/YDtB4ELKE+kJa0IfAD4j25/YNWK0k2AHSVdJuk3kl7a9twGkq4uj+843gf0S0VpjiXQ1UUWSWSR5JfFkgy/tPdV5e3QJfhRz2nV9JT/XaPDa9YG7mx7PLc8BsUez18EHu/2B1a9UDodWA3YDngp8CNJG1IsGbCe7fslbQP8VNKLbD889gP6paI0xxLoqiKLJLJIcsxiZAle295XdSLpV8BzOzx1TJc/otO/mi5rgTayfeSSLKpYtVOfC5xZblN3uaRR4Fm2/wa0hmSulPQnirP6WRV/zqTLsQS6qsgiiSySHLPoZfGR7d3Ge07Sva0KfElrAp2GqudSFHi2rANcBGwPbFPuAT0dWEPSRbZ3YgJVh19+CuxSNnoTis2l75P0bEnTyuMbAhtTLMPbvzLcKb2yyCKJLJIMs5jCC6VnA63ZLAcB/9vhNecBr5G0WnmB9DXAebZPtL1WuV3oK4A/Lq5Dh+rLBJwCnFJOsXkKOMi2Jb0SOFbSfIrfcN5te+xF1r6UUwl0XZFFElkkOWUxhRWlx1EMTx8C3AHsDyBpBkX/+A7bD0j6NHBF+Z5j6/SbVZcJAHhrh9f+BPhJ1caEEMJU8BTVlNq+H9i1w/FZwDvaHp9CcbI83uf8Gdi8m58ZFaUhhKEz1Gu/SDoF2AOYZ3vz8tjpwKblS1YF/m57q/K5LYD/AVamyO6ltp+YhLaHEEIlIxmv/tLNmfq3gK8B324dsP3m1n1JXwQeKu9PB74LvM32tZJWB57uZYMnSw7jhL0SWSSRRZJTFsO+9O64G09LEvBPlDNhKK7aXmf72vK99/emmZPPI6NgF1/cAa+WqyuySCKLJKcsch5+qbPxNMCOwL22by0fb0Ixaf48SVdJ+vB4b+yXitIc17WoKrJIIoskxyy8BP8bNHUvlB4I/GDM572Cosr0ceBCSVfavnDsG/ulojTHdS2qiiySyCLJMYs4U++gHD/fBzi97fBc4De277P9OHAO8JJ6TZxsg/3l7K3IIokskvyyyPlMvc7wy27Azbbnth07D9hC0vJlp/8q4MY6DZxsOa5rUVVkkUQWSY5ZzLe7vg2abjbJ+AFwCbCppLllZRTAASw89EK5bOSXKCqjrgGusv2L3ja5txZa16I06OtaVBVZJJFFkmMWU7hMwJSrXFFq+1/GOf5dimmNg6FtXYsFBvwLW1lkkUQWSYZZDPWUxmGR07oWdUUWSWSR5JTFII6Vd6vSHqWStpJ0abkP6SxJ25bHP9S2P+lsSSPlVk0hhNA3pnDnoylXaY9S4PPAp8qlAT5ePsb28a39SYGjKWbCDMQqjSGE4THCaNe3QVO1otQUa7sArALc3eGtY+ew97UcfqXslcgiiSySnLIYvK66e1WnNL4fOF7SncAXKM7KF5C0PMXZ/bjL8PZLRWmLR0YXjBkOemFFXZFFElkkOWVhu+vboKnaqb8HONL2usCRwMljnn8j8PuJhl5sz7Q9w/aMfVZYv2Iz6suxBLqqyCKJLJIcs1iSjacHTdVO/SDgzPL+j4Ftxzy/yBz2fpVjCXRVkUUSWSQ5ZjHsF0o7uZuiWhSKFRpbC3ohaZXyuU578fWhwf5y9lZkkUQWSX5Z5LxMQNU9St8JnFAuBfAEcGjbW94EnG/7sd43t/dyLIGuKrJIIoskxyxGPIjn4N2ps0fpNuO8/lsU0yAHwkIl0OUXddBLoKuKLJLIIskxi3y79KgozbIEurLIIokskgyzGMRhlW4/kdigAAAZK0lEQVRVrSjdUtIlkq6X9DNJK5fHl5Z0Wnn8JklHj//J/cXzR9J0rSEXWSSRRZJTFsM+++VbLFpRehJwlO0XA2cBHyqP7w8sWx7fBnjXeFvhhRBCU4Z6nrrti4Gx8803BS4u718A7Nt6ObBCeQH1GcBTwMO9aWoIIfTGsJ+pdzIb2LO8vz+wbnn/DOAx4B7gDuAL4xUg9VtFqaZPy6oMuo7IIokskpyyGPFo17dBU7VTPxg4TNKVwEoUZ+RQFCGNAGsBGwD/JmnDTh/QLxWlC9qTUQl0XZFFElkkOWUx1JtkdGL7ZuA1AJI2Ad5QPvUW4FzbTwPzJP0emAHc1oO2ToocS6CriiySyCLJMYtBHFbpVqUzdUlrlP9dCvgY8I3yqTuAXVRYAdgOuLkXDZ0sOZZAVxVZJJFFkmMWQz2mPs4epQdK+iNFh303cGr58q8DK1KMuV8BnGr7uklpec8M9peztyKLJLJI8ssi59kvdSpKT+jw2kcpLpwOjBxLoKuKLJLIIskxi0Hc/KJbQ19RmmMJdFWRRRJZJDlmMYhn4N3qZvhlXUm/LitEb5B0RHn8mZIukHRr+d/VyuOrSTpL0nWSLpe0+WT/IWppK4FeMF1rwL+wlUUWSWSRZJjFUI+pA/OBf7P9QooLn4dJ2gw4CrjQ9sbAheVjgI8C19jeAvh/dBim6Uc5lUDXFVkkkUWSUxY5j6l3U1F6j+2ryvuPADcBawN7AaeVLzsN2Lu8vxlFJ9+a+ri+pOf0uN0hhFDZsJ+pL1Cu47I1cBnwHNv3QNHxA2uUL7sW2Kd8/bbA84B1OnxWX1WUhhCGx1RtkjHeMHWH1x1UvuZWSQe1HT+wXCDxOknnSnrW4n5m1526pBUpNpJ+v+2J1nM5DlhN0jXAe4GrKYZwFtJvFaU5lUDXFVkkkUWSUxZTuEzAeMPUC0h6JsXmQy+jqMr/RHltcjrF8PXO5XD2dcDhi/uBXXXqkpam6NC/Z7u1N+m9ktYsn18TmAdg+2Hbb7e9FcWY+rOB27v5OU3KqQS6rsgiiSySnLIYtbu+1TTeMHW71wIX2H7A9oMUiyTuTlEgIIpFEgWsTFEXNKFuZr8IOBm4yfaX2p46m2IDasr//m/5+lUltUrQ3gFcvJgz+0blWAJdVWSRRBZJjllM4R6l4w1Tt1sbuLPt8Vxg7XK5lfcA11N05ptR9MUT6mae+g7A24DryyEVKGa4HAf8qKwwvYNUdPRC4NuSRoAbgUO6+BmNybEEuqrIIokskhyzWJIzcEmHsvA+zDNtz2x7/lfAczu89Zhuf0SHYy5HSN5DcR3zNuCrwNHAf0z0Yd1UlP5unB8KsGuH118CbLy4z+0fg/3l7K3IIokskvyyWJIz8LIDnznB87uN95ykeyWtafue9mHqMeYCO7U9Xge4CNiq/Pw/lZ/1IzqMyY9VdendbORYAl1VZJFEFkmOWUzhmHrHYeoxzgNeU14cXY1iBdzzgLuAzSQ9u3zdqymmlE+oTkXp8ZJuLqfanCVp1bb3HC1pjqRbJL12cT+jSQuVQJcGvQS6qsgiiSySHLMY9UjXt5qOA14t6VaKTvk4AEkzJJ0EUG4k9GmKRRCvAI4tL5reDXwKuFjSdRRn7p9d3A/sZky9VVF6laSVgCslXUBxhfZo2/MlfY5irOcjZbXpAcCLKDbL+JWkTez66UyKDHdKryyySCKLJMMspqqoyPb9dB6mnkUxkaT1+BTglA6v+wZpafOuVK4otX2+7db880tJBUZ7AT+0/aTt24E5FHMv+1pOJdB1RRZJZJHklMVQLxPQbkxFabuDgV+W9ztOz+nwWVFRGkJoRM7LBHS99O54FaWSjqEYovle61CHty+STPsV5Vnr7D14yYUQBtYgnoF3q6tOfZyKUso1CvYAdnVKaS6wbtvb16GLKqim5VL+3AuRRRJZJDll0YPy/75VuaJU0u7AR4A9bT/e9pazgQMkLStpA4o565f3ttm9l1MJdF2RRRJZJDllkfOYep2K0v8ClgUuKPp9LrX9bts3lJPkb6QYljmsb2e+kGcJdFWRRRJZJDlmMYhj5d2qU1F6zgTv+QzwmRrtmjI5lkBXFVkkkUWSYxaDeAberaHfozTHEujqIoskskjyy6IHlaJ9q05F6afLatJrJJ0vaa3y+AskXSLpSUkfnOw/QF05lkBXFVkkkUWSYxY5j6nX2aP0eNtblOum/xz4ePn6B4D3AV+YjAb3Wo4l0FVFFklkkeSYxRRukjHluhlTvwdorQf8iKRWRemNbS9bgXIuuu15wDxJb5iE9vZehiXQlUUWSWSRZJhFzsMvSzSmPraiVNJnKHY3egjYucdtm1KtqVo5zcWtKrJIIoskpyx6sPlF36q1R6ntY2yvS1FNuti988Z8XiwTEEJoxBQuvTvl6uxR2u77wL5L8oP7bePpp+c9yFN33dd0M/pCZJFEFklOWeR8oXSxwy8TVJRubPvW8uGewM2T08QpMlL8aumR0YG/sl9bZJFEFklGWYwO4AXQbtWpKD1E0qbAKPAX4N0Akp4LzKLY+XpU0vuBzfp18+n5Dz6y8HJjo2b0iScba0+TIoskskhyzGIQz8C71fOKUtt/Ja2t3vf+8cc7Fz7rGB3lqb/e31yDGhRZJJFFkmMW+XbpoJz/xerSK4ALgbv+/ve/r7jqqqsuRzHcdGSzzWpEZJFEFklkMUCGfuNpil2bHgB45JFHVgYeA05qtEXNiSySyCKJLAZIdOpFxewh5X8Bvgbc0FxzGhVZJJFFElkMkBh+aSNplu0ZTbejH0QWSWSRRBb9L87UFzaz6Qb0kcgiiSySyKLPxZl6CCFkJM7UQwghI9GphxBCRmLnoxDGkLQUsCWwFvAP4Abb9zbbqmZIWoOiqryVxWxglp1xnf2AG9oxdUnTgPNs79Z0W/qBpOcAnwXWsv26ciOU7W2f3HDTpoyk5wMfAXYDbgX+BiwHbAI8DvwPcNowdGiSdgaOAp4JXA3MI2XxfOAM4Iv9uvzHMBvaTh1A0tnA22w/1HRbmibpl8CpwDG2t5Q0Hbja9osbbtqUkfQD4ETgtx7zF6M8Y30L8KDt05po31SSdDzwVdt3dHhuOrAHMM32T6a8cWFCw96p/4hii74LKKrkALD9vsYa1RBJV9h+qaSrbW9dHrum3K4whDAghn1M/RflLcBjklanXOtI0nYUO1oNFUnbArZ9RTkEtTtws+2OC9jlrtxo/lTgEYqlAbYGjrJ9fqMNC+Ma6jN1AEnPANazfUvTbWmSpJcAXwU2p7gY9mxgP9vXNdqwKSTpE8DrKE52LgBeBlxEMcZ+nu3PNNe6Zki6thyOey1wGPDvwKm2X9Jw08I4hrpTl/RG4AvAMrY3kLQVcKztPRtuWiPKsdJNKZZavsX20w03aUpJuh7YClgW+Cuwju2Hy3/4L7O9RaMNbICk62xvIekE4CLbZ7UP0YX+M+zDL58EtqU4G8P2NZI2aLJBTZG0z5hDm0h6CLje9rwm2tSA+bZHgMcl/altL95/SMp+xss4rpR0PrABcLSklSg2xgl9atg79fm2Hyp27FtgWH91OQTYHvh1+XgniiVXN5F0rO3vNNWwKfSUpOVtPw5s0zooaRWGtyM7hOK3l9tsP15ed3l7w20KExj2Tn22pLcA0yRtDLwP+EPDbWrKKPDCVpFNOW/9RIpx5YuBYejUX2n7SYAxc9GXBg5qpknNsj0qaT7wynJ4rmVorrUMmmHv1N8LHAM8CfwAOA/4dKMtas76Y6om5wGb2H5A0lCMrbc69A7H7wPum+Lm9AVJpwBbUKyf3vqHzsCZjTUqTGioL5SGRNJ/A+sBPy4P7QvMBT4E/Nz2zk21bapJ+qTtTzbdjn4g6UbbmzXdjtC9oTxTl/QzJhg7H9LZL4dRdOQ7UMx++Tbwk7Kycig69HLNl29S/JYSCpdI2sz2jU03JHRnKM/UJb2qvLsP8Fzgu+XjA4E/2/5oIw0LjZL0C+BG2x9qui39QtIrgZ9RTPF8kuIffA/j9M5BMZSdeouki22/cnHHhkE5pfFzwBoUf3Fbf3lXbrRhU0jSvcCbbA/rxfJFSJoDfAC4nrYZQLb/0lijwoSGcvilzbMlbWj7NoByjvqzG25TUz4PvNH2TU03pEE7A6dLeofty5puTJ+4w/bZTTcidG/YO/UjgYsk3VY+Xh94V3PNadS9Q96hY/vGshz+h8DQ/bY2jpslfZ9iCGbB7CDbMfulTw318AuApGWBF5QPbx5vWlvuyjLw5wI/Zcj/8kpayfYjTbejH0g6tcNh2z54yhsTuhKduvRyijP0Bb+12P52Yw1qSPzlDSEPQ92pS/oOxS4u1wAj5WEP43rqIZE0g6Io7XkU/9gP7YwPSctRLBXwIoqdjwCIf+z717CPqc8ANhu7y80wir+8C/keRdHVQjM+htR3gJuB1wLHAv8MDPW1l363VNMNaNhsinHkUPzlfS7FX97fAOtQbIwwjP5m+2zbt9v+S+vWdKMaspHtfwceK7fxewMwNFscDqJhP1N/FnCjpMtZ+OLgMFaUbmR7f0l72T6tnPFwXtONasgnJJ0EXMiQXzQGWuv+/F3S5hRFSOs315ywOMPeqX+y6Qb0kfjLm7ydYkbU0sQiVjMlrQZ8DDgbWJFi96PQp4a6U7f9G0nPAza2/StJywPTmm5XQzr95f14s01qzJa2h36IoVwL52HbD1Isv7xhw00KXRj22S/vBA4Fnmn7+eWa6t+wvWvDTQsNkvRN4MuxiNXwLpsxyIb9QulhFKsStrYtu5Vi7ZOhImmapGe1PV5G0jslDessh1cA10i6RdJ1kq6XNKybQlwg6YOS1pX0zNat6UaF8Q318AvwpO2nWtvZlTu7DNWvLpIOAP4HeEzSrRTXGb4DXEExfW0Y7d50A/pIa0rrYW3HTAzF9K1h79R/I+mjwDMkvRr4V4o1LobJx4BtbM+R9BLgEuAA22c13K4mrQnc0FoqoNxseTNg6KY12h7KjdgH2bCPqS9FUXDzmvLQebZParBJU07SVbZf0vb4ZtsvmOg9uZN0NfCSVlFa+T2Z1Z7TsCiXZB7rIeB627GZSB8ayjN1SXsB69j+OvDN8oLps4FtJP3d9hnNtnBKrSHpA22PV2x/bPtLDbSpaWqvMi43Xx7KvysUJz3bA78uH+8EXApsIulY28OwIflAGdYLpR+mmLbXsgywDcUX9j1NNKhB3wRWaruNfTyMbpP0PklLl7cjgNsW+648jQIvtL2v7X0phqGeBF4GfKTRloWOhvXsYxnbd7Y9/p3tB4AHJK3QVKOaYPtTTbehD70b+C+K6w2mqCw9tNEWNWd92/e2PZ4HbGL7AUlPj/em0Jxh7dRXa39g+/C2h8O681EolWPFBzTdjj7xW0k/B35cPt4XuLg8+fl7c80K4xnW4ZfLynH0hUh6F3B5A+0JfUDSxyaagy1pF0l7TGWb+sBhwKnAVsDWwLeBw2w/ZnvnRlsWOhrK2S+S1iDt8HNVeXgbYFlg7zG/boYhUV5A/zDwBMX34m8UyxBvTNGp/Qr4rO2/NdbIKSJpoYvFVV8Tpt5QduotknahWD8cinnJ/9dke5ok6TnAZ4G1bL9O0mbA9rZPbrhpU65cLmIHivnq/6BYP/xi2/9otGFTSNJFwE+A/7V9R9vxZSgqbg8Cfm37W400MIxrqDv1kEj6JcWv2cfY3rKcwnf1MC9sJWkF24813Y4mlJumHExRVbwBxfj5MyiGbM8Hvm77muZaGMYTnXoAQNIVtl8q6WrbW5fHrrG9VdNtm2qStgdOBla0vZ6kLYF32f7XhpvWCElLU+w98A/bcXG0zw3rhdKwqMckrU659o2k7SgqB4fRVyh2gLofwPa1wFCuVCjpO7aftn1Pq0Mv9/YNfWpYpzSGRX2AoiDr+ZJ+TzG1c79mm9Qc23e2FnorjYz32sy9qP1BOSy3TUNtCV2ITj0AYPsqSa8CNgUE3GJ7WItL7pT0csDlhcH3MWSbLUs6Gmgtdvdw6zDwFDCzsYaFxYox9QDEwk3tyrXlTwB2o+jIzgeOsH1/ow1rgKT/tH100+0I3YtOPQAg6ReMs3ATMFQLN0lad8wyEkh6ru2/NtWmJklaG3gebb/Z2764uRaFicTwS2hpLdx0LyyYt34ixcJNF1NsnDEsbpf0Y+Dgtrnp5wDDuPTucRRLJtxIuq5giu9E6EPRqYeWWLgpuR74LfA7Sf9k+08UwzDD6E3AprafbLohoTvRqYeWsQs37VceG8aFm2z7vyVdC/xM0kcYsm0O29wGLE2xpEYYADGmHoBiHQ9gH4oScFEsRzxMm4UsMKYAa03gdGCG7eWbbdnUkfRVin/I1ga2pFh+eEHHbvt9DTUtLEZ06qEjSa8ADrR92GJfnBlJa9q+p+3xdODlw3RxUNJBEz1v+7SpaktYMjH8EhaQtBVwIPBm4HbgzGZbNLUkvdX2d4EDxxQetQxNpx6d9uCKTn3ISdqEYnbDgRRl8adT/AY3jGtlt3a9GtZt/BYh6XoWvZ7wEDAL+I9hnLvf72L4ZchJGqWY6XGI7Tnlsdtsb9hsy0I/kPR5iqmM3y8PHUBxzeUh4BW239hU20JnsaBX2Bf4K/BrSd+UtCtDOn1P0jvLtdRR4RRJD0m6TtLWTbevITvYPtr29eXtGOBVtj8HrN9w20IH0akPOdtn2X4z8ALgIuBI4DmSTpT0mkYbN/WOAP5c3j+QYtbHhhSLnf1XQ21q2oqSXtZ6IGlbYMXy4fxmmhQmEsMvYRHlPp37A2+2vUvT7Zkq7evHS/o+cJntE8rHV9kexorSlwKnUHTkAh4G3gHcALzB9o8abF7oIDr1EEqSrgLeADwI/AXYxfYN5XM32X5hk+1rkqRVKPqLYStEGzgx+yWE5OMUszqmAWe3deivoqisHBqt6Z2SPjDmOAC2v9RIw8JiRaceQsn2zyU9D1jJ9oNtT82imLs/TGJ654CK4ZcQQshIzH4JIYxL0iaSLpQ0u3y8haSPNd2uML7o1EMIE/kmcDTwNIDt6ygKkEKfijH1EEqSJpyyaPuqqWpLH1ne9uVj1sKJ+el9LDr1EJIvlv9dDpgBXEsxN3sL4DKKZYmHzX2Snk+5/ouk/YB7Jn5LaFJ06iGUWouYSfohcKjt68vHmwMfbLJtDToMmAm8QNJdFKt3/nOzTQoTidkvIYzRXlk60bFhUu6AtZTtR5puS5hYnKmHsKibJJ0EfJdi2OGtwE3NNmlqSbofuBT4A/B74PLo0AdDnKmHMIak5YD3AK8sD10MnGj7ieZaNbUkrQxsB7y8vG1DUVX7B+D3seZL/4pOPYSwWOXwy9uB9wMb2J7WcJPCOKJTD2GMck31/wQ2o5gJA8AwbRwiaS3SWfpLy8NXUgzJXGL7L021LUwsxtRDWNSpwCeALwM7U5yhDtvGIXOBqygyOMr2Uw23J3QpztRDGEPSlba3kXS97ReXx35re8em2zZVJG0PbE9xpr4BxeYhl5S3WbafbK51YSJxph7Cop6QtBRwq6TDgbuANRpu05Sy3erAvwQgaX3gjcBpwDq0DUuF/hJn6iGMUe72cxOwKvBpYGXgeNuXNtqwKSbpBaRx9R2A1Sg6+t/b/kKTbQvji049hHFIWsH2Y023owmS7qNYDuAPpGmMc5ptVehGdOohjFGOJ58MrGh7PUlbAu+y/a8NN23KSFrF9kNNtyMsuVh6N4RFfQV4LXA/gO1rSYVIQyE69MEVnXoIHdi+c8yhkUYaEsISitkvISzqTkkvByxpGeB9DNnaL2FwxZh6CGNIehZwArAbRdHR+cARtu9vtGENkLQssC+wPm0ngbaPbapNYWLRqYcQxiXpXOAhiiUCFgxB2f7iuG8KjYpOPYSSpK9S7vDTie33TWFz+oKk2bY3b7odoXsxph5CMqvt/qco1n8Zdn+Q9OLWLlCh/8WZeggdSLra9tZNt6Npkm4ENqLYxu5JimsMtr1Fow0L44oz9RA6i7OdwuuabkBYMtGphxAWIWll2w8DsYXdgInhlxBKkh4hnaEvDzzeeopiyGHlRhrWAEk/t72HpNspMmlfT97DtGHIoIlOPYQQMhLDLyGECUlaDdiYhbf2u7i5FoWJRKceQhiXpHcAR1BsjHENsB3Fmuq7NNmuML5Y0CuEMJEjKDae/ovtnYGtgb8126QwkejUQwgTecL2E1CsA2P7ZmDThtsUJhDDLyGEicyVtCrwU+ACSQ8CdzfcpjCBmP0SQuiKpFcBqwDn2n6q6faEzqJTDyF0JGkp4LpY0GuwxJh6CKEj26PAtZLWa7otoXsxph5CmMiawA2SLgceax20vWdzTQoTiU49hDCRTzXdgLBkYkw9hNCVcpu/+x2dRl+LMfUQwiIkbSfpIklnStpa0mxgNnCvpN2bbl8YX5yphxAWIWkW8FGKKYwzgdfZvlTSC4AfxAYi/SvO1EMInUy3fb7tHwN/tX0pQFlRGvpYdOohhE5G2+7/Y8xz8et9H4vhlxDCIiSNUExhFPAMFt4wZDnbSzfVtjCx6NRDCCEjMfwSQggZiU49hBAyEp16CCFkJDr1EELISHTqIYSQkejUQwghI/8ftvqCTjmIwIcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#lets check whether the null values are present in the dataset or not using heatmap\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "sns.heatmap(df_headbrain.isnull(),annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Gender                 0\n",
       "Age Range              0\n",
       "Head Size(cm^3)        0\n",
       "Brain Weight(grams)    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#lets check the null vales without usig visualisation\n",
    "df_headbrain.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(237, 4)\n",
      "(236, 4)\n"
     ]
    }
   ],
   "source": [
    "#Lets check whether their are outliers present in the dataset or not\n",
    "from scipy.stats import zscore\n",
    "z_score=abs(zscore(df_headbrain))\n",
    "print(df_headbrain.shape)\n",
    "df_headbrain_final=df_headbrain.loc[(z_score<3).all(axis=1)]\n",
    "print(df_headbrain_final.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Lets check the how Brain Weight(grams) is changing with respect to Head Size(cm^3)\n",
    "sns.lineplot(x=df_headbrain[\"Head Size(cm^3)\"],y=df_headbrain[\"Brain Weight(grams)\"],data=df_headbrain)\n",
    "plt.show()\n",
    "#The below graph clearly shows that with increase in head size their is increase in brain weight too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qRoHLgBOBY6rqoek4YFXdkeSWJM+pqh8CBwLXNJ+VwPHN95nNLmuAdyb5MrAvsHFsSEuSNPN6Bcf+wEuB1wFHJ/kRcFHzWVtVP5/Ccd8FfDHJdsANwNvonP18NckRwM3AG5u+ZwGHAuuBB5q+kqQh6fWQw7GQOAEgyVI67xdfTWe4aPvJHrSqLgeWj7PpwHH6Fp17SSRJs0DPFzkleS7wm81nf2AXOmHyd4MvTZI0G/V6kdPddB4t8h/Ad4Djq2r9TBUmSZqdep1xPLOqNs5YJZKkOaHXfRyGhiRpC/085FCSpEcYHJKkVnpeVQWQ5PHA64Gl3f2r6kODK0uSNFttNTjo3MG9EVgHTOWmP0nSY0A/wbG4qg4eeCWSpDmhnzmO/0jywoFXIkmaE/o543gZ8NYkN9IZqgqdJ4HsNdDKJEmzUj/BccjAq5AkzRm9HjnypKq6D5jy62IlSY8dvc44vgS8hs7VVMWvvomvmNrLnCRJc1Svx6q/pvnec+bKkSTNdv3McZBkF2AZXe/gqKoLB1WUJGn26ufO8XcAR9F5edPlwH503snxysGWJkmajfq5j+Mo4CXATVX1CmBvYMNAq5IkzVr9BMeDVfUgdJ5bVVXXAc8ZbFmSpNmqnzmO0SQ7A98Azk1yL3DbYMuSJM1WWw2Oqnpds/jnSS4Angx8a6BVSZJmrZ7BkeRxwBVV9QKAqvq3GalKkjRr9ZzjqKqHgR8k2WO6D5xkmyTfT/LNZn3PJJckuT7JV5Js17Q/vllf32xfOt21SJL618/k+O7A1UnOS7Jm7DMNxz4KuLZr/aPAiVW1DLgXOKJpPwK4t6qeBZzY9JMkDUk/k+N/Md0HTbIYeDXwEeDoJKFzX8jvN11WA38OnASsaJYBzgA+lSRVVdNdlyRp6/qZHH9kXiPJQuDH0/CP9v8F3gvs1Kw/BfhJVW1q1keBRc3yIuCWppZNSTY2/e/u/sEkq4BVAHvsMe0ja5KkxoRDVUn2S/LtJF9PsneSq4CrgDuTTPqNgEleA9xVVeu6m8fpWn1se7Sh6uSqWl5Vy0dGRiZbniRpK3qdcXwKeD+dy2/PBw6pqouTPBc4nclfkrs/8Nokh9J59tWT6JyB7JxkQXPWsZhH7xUZBZbQuZ9kQVPPPZM8tiRpinpNji+oqnOq6h+BO6rqYoDmzvFJq6pjq2pxVS0FDgfOr6o/AC4A3tB0Wwmc2SyvadZptp/v/IYkDU+v4Hi4a/lnm20bxD/c76MzUb6ezhzGKU37KcBTmvajgWMGcGxJUp96DVX9RpL76MwxPKFZplnffuLd+ldV3wa+3SzfAOwzTp8HgTdOx/EkSVPX60VO28xkIZKkuaGfGwAlSXqEwSFJasXgkCS1YnBIkloxOCRJrRgckqRWDA5JUisGhySpFYNDktSKwSFJasXgkCS1YnBIkloxOCRJrRgckqRWDA5JUisGhySpFYNDktSKwSFJasXgkCS1YnBIklqZ8eBIsiTJBUmuTXJ1kqOa9l2TnJvk+uZ7l6Y9ST6ZZH2SK5K8aKZrliQ9ahhnHJuA/1VVvw7sBxyZ5HnAMcB5VbUMOK9ZBzgEWNZ8VgEnzXzJkqQxMx4cVXV7VV3WLN8PXAssAlYAq5tuq4HDmuUVwGnVcTGwc5LdZ7hsSVJjqHMcSZYCewOXALtV1e3QCRfgqU23RcAtXbuNNm2SpCEYWnAk2RH4GvDuqrqvV9dx2mqc31uVZG2StRs2bJiuMiVJmxlKcCTZlk5ofLGqvt403zk2BNV839W0jwJLunZfDNy2+W9W1clVtbyqlo+MjAyueEma54ZxVVWAU4Brq+qErk1rgJXN8krgzK72tzRXV+0HbBwb0pIkzbwFQzjm/sCbgSuTXN60vR84HvhqkiOAm4E3NtvOAg4F1gMPAG+b2XIlSd1mPDiq6t8Zf94C4MBx+hdw5ECLkiT1zTvHJUmtGBySpFYMDklSKwaHJKkVg0OS1IrBIUlqxeCQJLVicEiSWjE4JEmtGBySpFYMDklSKwaHJKkVg0OS1IrBIUlqxeCQJLVicEiSWjE4JEmtGBySpFYMDklSKwaHJKkVg0OS1IrBIUlqZc4ER5KDk/wwyfokxwy7Hkmar+ZEcCTZBvg0cAjwPOBNSZ433KokaX6aE8EB7AOsr6obquoh4MvAiiHXJEnz0lwJjkXALV3ro02bJGmGLRh2AX3KOG31Kx2SVcCqZvU/k/xw4FXNHwuBu4ddxGyQv1457BK0Jf9+jjluvH8qW/m1fjrNleAYBZZ0rS8GbuvuUFUnAyfPZFHzRZK1VbV82HVI4/Hv58ybK0NVlwLLkuyZZDvgcGDNkGuSpHlpTpxxVNWmJO8Ezga2AU6tqquHXJYkzUtzIjgAquos4Kxh1zFPOQSo2cy/nzMsVbX1XpIkNebKHIckaZYwODShJKcmuSvJVcOuReqWZEmSC5Jcm+TqJEcNu6b5xKEqTSjJy4H/BE6rqhcMux5pTJLdgd2r6rIkOwHrgMOq6pohlzYveMahCVXVhcA9w65D2lxV3V5VlzXL9wPX4tMkZozBIWlOS7IU2Bu4ZLiVzB8Gh6Q5K8mOwNeAd1fVfcOuZ74wOCTNSUm2pRMaX6yqrw+7nvnE4JA05yQJcApwbVWdMOx65huDQxNKcjpwEfCcJKNJjhh2TVJjf+DNwCuTXN58Dh12UfOFl+NKklrxjEOS1IrBIUlqxeCQJLVicEiSWjE4JEmtGBxSC0l2S/KlJDckWZfkoiSvm4bfPSDJN6ejRmnQDA6pT81NZ98ALqyqZ1TVi4HDgcVDqGXOvL1Tjz0Gh9S/VwIPVdXfjTVU1U1V9TdJtkny8SSXJrkiyX+HR84kvp3kjCTXJfliE0AkObhp+3fgd8d+M8kOzbtQLk3y/SQrmva3JvnHJP8EnDOjf3Kpi/+vRerf84HLJth2BLCxql6S5PHAd5OM/eO+d7PvbcB3gf2TrAU+SyeM1gNf6fqtDwDnV9Xbk+wMfC/JvzbbXgrsVVU+7l5DY3BIk5Tk08DLgIeAm4C9kryh2fxkYFmz7XtVNdrsczmwlM4Lsm6squub9n8AVjX7HgS8Nsl7mvXtgT2a5XMNDQ2bwSH172rg9WMrVXVkkoXAWuBm4F1VdXb3DkkOAH7e1fRLHv3f3UTP+wnw+qr64Wa/tS/w06n8AaTp4ByH1L/zge2T/HFX2xOb77OBP24e9U2SZyfZocdvXQfsmeSZzfqburadDbyray5k72mpXpomBofUp+o8EfQw4LeS3Jjke8Bq4H3A3wPXAJcluQr4DD3O6KvqQTpDU//cTI7f1LX5w8C2wBXNb314EH8eabJ8Oq4kqRXPOCRJrRgckqRWDA5JUisGhySpFYNDktSKwSFJasXgkCS1YnBIklr5/6db2daKUj87AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#lets check what is the average brain size according to gender\n",
    "sns.barplot(x=df_headbrain[\"Gender\"],y=df_headbrain[\"Brain Weight(grams)\"],data=df_headbrain)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now lets check what is the average brain size according to age range\n",
    "sns.barplot(x=df_headbrain[\"Age Range\"],y=df_headbrain[\"Brain Weight(grams)\"],data=df_headbrain)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LXZI6YaFLUif+H2Ud+i7eOdPQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Lets draw histogram for brain weight\n",
    "plt.hist(x=\"Brain Weight(grams)\",bins=10,data=df_headbrain)\n",
    "plt.show()\n",
    "#we can say it shows almost normal distribution based on below output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Gender                 0.265554\n",
       "Age Range             -0.144748\n",
       "Head Size(cm^3)        0.238807\n",
       "Brain Weight(grams)    0.265478\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#lets hcek skewnesss of the dataset\n",
    "df_headbrain.skew()\n",
    "#Below shows acceptable level of skewness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now let seprate input and output variable to be used for the linear regression problem\n",
    "x=df_headbrain[[\"Head Size(cm^3)\"]]\n",
    "y=df_headbrain[[\"Brain Weight(grams)\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\data.py:645: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "F:\\anaconda3\\lib\\site-packages\\sklearn\\base.py:464: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 2.40886829],\n",
       "       [ 0.28535333],\n",
       "       [ 1.72023489],\n",
       "       [ 0.39235214],\n",
       "       [ 1.4897759 ],\n",
       "       [-0.13441126],\n",
       "       [ 0.41430062],\n",
       "       [-0.2057438 ],\n",
       "       [-0.05759159],\n",
       "       [ 0.95478182],\n",
       "       [-0.52399669],\n",
       "       [ 0.98496097],\n",
       "       [ 0.01648451],\n",
       "       [ 1.57482624],\n",
       "       [ 0.54324791],\n",
       "       [ 0.66396452],\n",
       "       [-0.37584448],\n",
       "       [-0.46089482],\n",
       "       [-1.47875536],\n",
       "       [ 2.16743507],\n",
       "       [ 0.66945164],\n",
       "       [ 1.13036962],\n",
       "       [ 0.46642825],\n",
       "       [ 0.20853367],\n",
       "       [ 3.05360475],\n",
       "       [ 2.16469151],\n",
       "       [ 1.10293403],\n",
       "       [ 1.06452419],\n",
       "       [-0.49381754],\n",
       "       [ 1.48428878],\n",
       "       [ 0.41978774],\n",
       "       [ 0.44447977],\n",
       "       [ 1.28675251],\n",
       "       [ 1.44587895],\n",
       "       [ 1.43764827],\n",
       "       [ 0.49386384],\n",
       "       [-0.2935377 ],\n",
       "       [ 0.31278892],\n",
       "       [-0.82304466],\n",
       "       [-0.38956228],\n",
       "       [ 0.89991063],\n",
       "       [-0.35389601],\n",
       "       [ 1.8683871 ],\n",
       "       [ 0.46642825],\n",
       "       [ 0.62829825],\n",
       "       [ 1.09744691],\n",
       "       [ 1.84918218],\n",
       "       [-1.2867062 ],\n",
       "       [ 0.01922807],\n",
       "       [ 0.02745875],\n",
       "       [ 0.70511792],\n",
       "       [ 0.4362491 ],\n",
       "       [ 1.74492692],\n",
       "       [ 1.17701013],\n",
       "       [ 1.0370886 ],\n",
       "       [-0.4828433 ],\n",
       "       [ 0.70237436],\n",
       "       [ 1.45959675],\n",
       "       [ 0.82583453],\n",
       "       [ 0.09604773],\n",
       "       [ 0.63652893],\n",
       "       [-0.66117466],\n",
       "       [ 2.21681914],\n",
       "       [ 1.69828641],\n",
       "       [ 0.25517418],\n",
       "       [-0.83676246],\n",
       "       [-0.60081635],\n",
       "       [-0.71878941],\n",
       "       [ 2.18389643],\n",
       "       [ 2.04946202],\n",
       "       [ 1.02611436],\n",
       "       [ 0.61458046],\n",
       "       [ 1.33613657],\n",
       "       [ 1.16054877],\n",
       "       [ 0.52129944],\n",
       "       [-0.6584311 ],\n",
       "       [-0.20848736],\n",
       "       [-0.746225  ],\n",
       "       [ 0.81211673],\n",
       "       [ 0.55147859],\n",
       "       [ 0.53776079],\n",
       "       [ 0.60909334],\n",
       "       [-1.05624721],\n",
       "       [-0.15635973],\n",
       "       [ 0.82034741],\n",
       "       [ 0.59263198],\n",
       "       [-0.89163365],\n",
       "       [-0.62550839],\n",
       "       [-0.35115245],\n",
       "       [ 0.74901487],\n",
       "       [ 1.44313539],\n",
       "       [-0.86694161],\n",
       "       [ 0.07684282],\n",
       "       [ 0.72706639],\n",
       "       [ 0.18109807],\n",
       "       [ 0.39783926],\n",
       "       [-0.44168991],\n",
       "       [-0.3950494 ],\n",
       "       [ 0.05489434],\n",
       "       [-0.42797211],\n",
       "       [-0.3813316 ],\n",
       "       [ 0.54873503],\n",
       "       [ 0.66396452],\n",
       "       [ 0.07409926],\n",
       "       [-0.0438738 ],\n",
       "       [ 0.03843298],\n",
       "       [ 1.09195979],\n",
       "       [-0.6447133 ],\n",
       "       [ 0.7737069 ],\n",
       "       [ 2.18389643],\n",
       "       [ 0.16738028],\n",
       "       [-0.30176838],\n",
       "       [-0.17282109],\n",
       "       [-0.10971922],\n",
       "       [-0.68861025],\n",
       "       [-0.37035736],\n",
       "       [-0.12343702],\n",
       "       [ 0.72980995],\n",
       "       [ 1.31693166],\n",
       "       [ 0.83132165],\n",
       "       [-0.6447133 ],\n",
       "       [ 1.55287777],\n",
       "       [ 2.34302287],\n",
       "       [-0.05484804],\n",
       "       [ 1.14408742],\n",
       "       [ 0.40606994],\n",
       "       [-0.66666178],\n",
       "       [-1.39919214],\n",
       "       [ 1.14957454],\n",
       "       [-0.14264194],\n",
       "       [ 0.08781705],\n",
       "       [-0.27981991],\n",
       "       [ 1.13036962],\n",
       "       [ 0.09056061],\n",
       "       [-2.13172249],\n",
       "       [-0.54320161],\n",
       "       [ 0.43076198],\n",
       "       [-0.91083856],\n",
       "       [-1.45406332],\n",
       "       [-1.27024484],\n",
       "       [-0.17007753],\n",
       "       [-0.28530702],\n",
       "       [-1.25927061],\n",
       "       [-0.53771449],\n",
       "       [ 0.73804063],\n",
       "       [ 0.72706639],\n",
       "       [-0.63922618],\n",
       "       [-1.00686314],\n",
       "       [-0.50204822],\n",
       "       [-1.49247315],\n",
       "       [-0.60630347],\n",
       "       [-0.85322382],\n",
       "       [ 0.12622688],\n",
       "       [-0.53497093],\n",
       "       [ 0.60086266],\n",
       "       [-1.31139823],\n",
       "       [-0.97394043],\n",
       "       [ 0.20030299],\n",
       "       [ 1.02062724],\n",
       "       [-1.00137602],\n",
       "       [-1.54460078],\n",
       "       [ 0.39783926],\n",
       "       [-0.23592295],\n",
       "       [-0.93827416],\n",
       "       [-0.37584448],\n",
       "       [-1.51442163],\n",
       "       [-1.05899077],\n",
       "       [-0.75719924],\n",
       "       [ 0.46368469],\n",
       "       [-0.18653889],\n",
       "       [-1.34157739],\n",
       "       [-0.35938313],\n",
       "       [-0.17282109],\n",
       "       [ 0.2469435 ],\n",
       "       [-0.05210448],\n",
       "       [-1.18245094],\n",
       "       [-0.06856583],\n",
       "       [-0.20025668],\n",
       "       [ 0.94655114],\n",
       "       [-0.27707635],\n",
       "       [ 0.15091892],\n",
       "       [-1.30591112],\n",
       "       [ 1.01788369],\n",
       "       [-1.24280925],\n",
       "       [-0.42522855],\n",
       "       [ 0.02197163],\n",
       "       [-0.00546397],\n",
       "       [-1.5500879 ],\n",
       "       [-0.6584311 ],\n",
       "       [ 0.18932875],\n",
       "       [-1.2867062 ],\n",
       "       [-0.76817348],\n",
       "       [-1.7393935 ],\n",
       "       [ 0.1454318 ],\n",
       "       [-0.21397448],\n",
       "       [-2.36218148],\n",
       "       [-1.58026705],\n",
       "       [-0.79560907],\n",
       "       [-0.38681872],\n",
       "       [-0.92455636],\n",
       "       [-0.75171212],\n",
       "       [-1.11386196],\n",
       "       [-0.97942755],\n",
       "       [ 0.59537554],\n",
       "       [-1.55557502],\n",
       "       [ 0.1591496 ],\n",
       "       [-0.63648263],\n",
       "       [ 0.99044809],\n",
       "       [-0.86694161],\n",
       "       [-2.50759013],\n",
       "       [-1.91223774],\n",
       "       [-0.14812905],\n",
       "       [-1.90675062],\n",
       "       [-1.76957265],\n",
       "       [-0.1316677 ],\n",
       "       [-1.31139823],\n",
       "       [-1.06447789],\n",
       "       [-1.2729884 ],\n",
       "       [-1.00411958],\n",
       "       [-0.6721489 ],\n",
       "       [-0.69409737],\n",
       "       [-2.11251758],\n",
       "       [ 0.29084045],\n",
       "       [-0.42522855],\n",
       "       [ 0.03568942],\n",
       "       [ 0.22499502],\n",
       "       [-0.96022263],\n",
       "       [ 1.563852  ],\n",
       "       [ 0.27712265],\n",
       "       [-1.14129755],\n",
       "       [ 0.13994468],\n",
       "       [ 0.19207231],\n",
       "       [-1.15227179],\n",
       "       [-0.6584311 ],\n",
       "       [-1.10014416],\n",
       "       [-0.77366059],\n",
       "       [-0.66666178]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#scaling down using standardscaler\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()\n",
    "x = sc.fit_transform(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2_score corresponding to random state:  42  is:  0.7149168473012075\n",
      "r2_score corresponding to random state:  43  is:  0.6404165530671617\n",
      "r2_score corresponding to random state:  44  is:  0.653010968876236\n",
      "r2_score corresponding to random state:  45  is:  0.6939862623941999\n",
      "r2_score corresponding to random state:  46  is:  0.5332650244375814\n",
      "r2_score corresponding to random state:  47  is:  0.6201411206780885\n",
      "r2_score corresponding to random state:  48  is:  0.6851449361873334\n",
      "r2_score corresponding to random state:  49  is:  0.6433491336855989\n",
      "r2_score corresponding to random state:  50  is:  0.7683161771318532\n",
      "r2_score corresponding to random state:  51  is:  0.5935686929145347\n",
      "r2_score corresponding to random state:  52  is:  0.6342022687682457\n",
      "r2_score corresponding to random state:  53  is:  0.5909146568147448\n",
      "r2_score corresponding to random state:  54  is:  0.6130331905389369\n",
      "r2_score corresponding to random state:  55  is:  0.5884150240645216\n",
      "r2_score corresponding to random state:  56  is:  0.7399588791116045\n",
      "r2_score corresponding to random state:  57  is:  0.5071803243347979\n",
      "r2_score corresponding to random state:  58  is:  0.6123621922042879\n",
      "r2_score corresponding to random state:  59  is:  0.7318498972427991\n",
      "r2_score corresponding to random state:  60  is:  0.670702983531536\n",
      "r2_score corresponding to random state:  61  is:  0.6107719657611239\n",
      "r2_score corresponding to random state:  62  is:  0.5886035640681522\n",
      "r2_score corresponding to random state:  63  is:  0.6677040991373102\n",
      "r2_score corresponding to random state:  64  is:  0.6296914854979072\n",
      "r2_score corresponding to random state:  65  is:  0.71647493474892\n",
      "r2_score corresponding to random state:  66  is:  0.6203738753194059\n",
      "r2_score corresponding to random state:  67  is:  0.712612390279983\n",
      "r2_score corresponding to random state:  68  is:  0.657656658919509\n",
      "r2_score corresponding to random state:  69  is:  0.6703630883745614\n",
      "r2_score corresponding to random state:  70  is:  0.5891175986445862\n",
      "r2_score corresponding to random state:  71  is:  0.6417613976759238\n",
      "r2_score corresponding to random state:  72  is:  0.5463136037595998\n",
      "r2_score corresponding to random state:  73  is:  0.5045543063528727\n",
      "r2_score corresponding to random state:  74  is:  0.6908546939589804\n",
      "r2_score corresponding to random state:  75  is:  0.5839986897763758\n",
      "r2_score corresponding to random state:  76  is:  0.5842914878403354\n",
      "r2_score corresponding to random state:  77  is:  0.66166348734816\n",
      "r2_score corresponding to random state:  78  is:  0.6473967116879223\n",
      "r2_score corresponding to random state:  79  is:  0.7378058902454341\n",
      "r2_score corresponding to random state:  80  is:  0.31163981871623503\n",
      "r2_score corresponding to random state:  81  is:  0.6287492712541896\n",
      "r2_score corresponding to random state:  82  is:  0.5498061635931804\n",
      "r2_score corresponding to random state:  83  is:  0.7426892680367267\n",
      "r2_score corresponding to random state:  84  is:  0.6841481547920669\n",
      "r2_score corresponding to random state:  85  is:  0.6839611629631983\n",
      "r2_score corresponding to random state:  86  is:  0.5705188355104969\n",
      "r2_score corresponding to random state:  87  is:  0.5235044952071041\n",
      "r2_score corresponding to random state:  88  is:  0.5212182362300138\n",
      "r2_score corresponding to random state:  89  is:  0.6647722042837871\n",
      "r2_score corresponding to random state:  90  is:  0.6925914283710493\n",
      "r2_score corresponding to random state:  91  is:  0.7602597914098644\n",
      "r2_score corresponding to random state:  92  is:  0.7279273279367926\n",
      "r2_score corresponding to random state:  93  is:  0.6673454912138065\n",
      "r2_score corresponding to random state:  94  is:  0.680198003060743\n",
      "r2_score corresponding to random state:  95  is:  0.449616958785648\n",
      "r2_score corresponding to random state:  96  is:  0.6854497779131984\n",
      "r2_score corresponding to random state:  97  is:  0.5090577072170099\n",
      "r2_score corresponding to random state:  98  is:  0.4944064453867718\n",
      "r2_score corresponding to random state:  99  is:  0.531293315126045\n",
      "r2_score corresponding to random state:  100  is:  0.6887976995086573\n",
      "\n",
      "\n",
      "max r2 score corresponding to  50  is  0.7683161771318532\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn import linear_model\n",
    "max_r_score=0\n",
    "for r_state in range(42,101):\n",
    "    x_train, x_test, y_train, y_test = train_test_split(x, y,random_state = r_state,test_size=0.20)\n",
    "    regr = linear_model.LinearRegression()\n",
    "    regr.fit(x_train,y_train)\n",
    "    y_pred = regr.predict(x_test)\n",
    "    r2_scr=r2_score(y_test,y_pred)\n",
    "    print(\"r2_score corresponding to random state: \",r_state,\" is: \",r2_scr)\n",
    "    if r2_scr>max_r_score:\n",
    "        max_r_score=r2_scr\n",
    "        final_r_state=r_state\n",
    "print()\n",
    "print()\n",
    "print(\"max r2 score corresponding to \",final_r_state,\" is \",max_r_score)\n",
    "#The belwo output shows that we are getting acceptable level of r2 score in most of the cases and max value is also shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4936984443261272"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Lets do the cross validation\n",
    "from sklearn.model_selection import cross_val_score\n",
    "cross_val_score(linear_model.LinearRegression(), x, y, cv=5,scoring=\"r2\").mean()\n",
    "#the Below cross validation score is less and it shows that we further need to improve our model using more data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "#since maximum r2 score is comming around random state 50 we will use that to create our final model\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y,random_state = 50,test_size=0.20)\n",
    "lr=linear_model.LinearRegression()\n",
    "lr.fit(x_train,y_train)\n",
    "y_pred=lr.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 score is:  0.7683161771318532\n",
      "RMSE is :  60.36773435476799\n"
     ]
    }
   ],
   "source": [
    "#Lets evaluate RMSE and r2 score using sklearn library\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score\n",
    "import numpy as np\n",
    "print(\"r2 score is: \",r2_score(y_test,y_pred))\n",
    "print(\"RMSE is : \",np.sqrt(mean_squared_error(y_test,y_pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['lr_headbrain.pkl']"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Lets save the model using joblib\n",
    "from sklearn.externals import joblib \n",
    "# Save the model as a pickle in a file \n",
    "joblib.dump(lr, 'lr_headbrain.pkl')"
   ]
  }
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