{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The movie Moneyball focuses on the \"quest for the secret of success in baseball\". It follows a low-budget team, the Oakland Athletics, who believed that underused statistics, such as a player's ability to get on base, betterpredict the ability to score runs than typical statistics like home runs, RBIs (runs batted in), and batting average. Obtaining players who excelled in these underused statistics turned out to be much more affordable for the team.\n",
    "\n",
    "### In this lab we'll be looking at data from all 30 Major League Baseball teams and examining the linear relationship between runs scored in a season and a number of other player statistics. Our aim will be to summarize these relationships both graphically and numerically in order to find which variable, if any, helps us best predict a team's runs scored in a season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import io\n",
    "import requests\n",
    "\n",
    "df_url = 'https://raw.githubusercontent.com/akmand/datasets/master/openintro/mlb11.csv'\n",
    "url_content = requests.get(df_url, verify=False).content\n",
    "mlb11 = pd.read_csv(io.StringIO(url_content.decode('utf-8')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>team</th>\n",
       "      <th>runs</th>\n",
       "      <th>at_bats</th>\n",
       "      <th>hits</th>\n",
       "      <th>homeruns</th>\n",
       "      <th>bat_avg</th>\n",
       "      <th>strikeouts</th>\n",
       "      <th>stolen_bases</th>\n",
       "      <th>wins</th>\n",
       "      <th>new_onbase</th>\n",
       "      <th>new_slug</th>\n",
       "      <th>new_obs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Texas Rangers</td>\n",
       "      <td>855</td>\n",
       "      <td>5659</td>\n",
       "      <td>1599</td>\n",
       "      <td>210</td>\n",
       "      <td>0.283</td>\n",
       "      <td>930</td>\n",
       "      <td>143</td>\n",
       "      <td>96</td>\n",
       "      <td>0.340</td>\n",
       "      <td>0.460</td>\n",
       "      <td>0.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Boston Red Sox</td>\n",
       "      <td>875</td>\n",
       "      <td>5710</td>\n",
       "      <td>1600</td>\n",
       "      <td>203</td>\n",
       "      <td>0.280</td>\n",
       "      <td>1108</td>\n",
       "      <td>102</td>\n",
       "      <td>90</td>\n",
       "      <td>0.349</td>\n",
       "      <td>0.461</td>\n",
       "      <td>0.810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Detroit Tigers</td>\n",
       "      <td>787</td>\n",
       "      <td>5563</td>\n",
       "      <td>1540</td>\n",
       "      <td>169</td>\n",
       "      <td>0.277</td>\n",
       "      <td>1143</td>\n",
       "      <td>49</td>\n",
       "      <td>95</td>\n",
       "      <td>0.340</td>\n",
       "      <td>0.434</td>\n",
       "      <td>0.773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Kansas City Royals</td>\n",
       "      <td>730</td>\n",
       "      <td>5672</td>\n",
       "      <td>1560</td>\n",
       "      <td>129</td>\n",
       "      <td>0.275</td>\n",
       "      <td>1006</td>\n",
       "      <td>153</td>\n",
       "      <td>71</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.415</td>\n",
       "      <td>0.744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>St. Louis Cardinals</td>\n",
       "      <td>762</td>\n",
       "      <td>5532</td>\n",
       "      <td>1513</td>\n",
       "      <td>162</td>\n",
       "      <td>0.273</td>\n",
       "      <td>978</td>\n",
       "      <td>57</td>\n",
       "      <td>90</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.425</td>\n",
       "      <td>0.766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>New York Mets</td>\n",
       "      <td>718</td>\n",
       "      <td>5600</td>\n",
       "      <td>1477</td>\n",
       "      <td>108</td>\n",
       "      <td>0.264</td>\n",
       "      <td>1085</td>\n",
       "      <td>130</td>\n",
       "      <td>77</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.391</td>\n",
       "      <td>0.725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>New York Yankees</td>\n",
       "      <td>867</td>\n",
       "      <td>5518</td>\n",
       "      <td>1452</td>\n",
       "      <td>222</td>\n",
       "      <td>0.263</td>\n",
       "      <td>1138</td>\n",
       "      <td>147</td>\n",
       "      <td>97</td>\n",
       "      <td>0.343</td>\n",
       "      <td>0.444</td>\n",
       "      <td>0.788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Milwaukee Brewers</td>\n",
       "      <td>721</td>\n",
       "      <td>5447</td>\n",
       "      <td>1422</td>\n",
       "      <td>185</td>\n",
       "      <td>0.261</td>\n",
       "      <td>1083</td>\n",
       "      <td>94</td>\n",
       "      <td>96</td>\n",
       "      <td>0.325</td>\n",
       "      <td>0.425</td>\n",
       "      <td>0.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Colorado Rockies</td>\n",
       "      <td>735</td>\n",
       "      <td>5544</td>\n",
       "      <td>1429</td>\n",
       "      <td>163</td>\n",
       "      <td>0.258</td>\n",
       "      <td>1201</td>\n",
       "      <td>118</td>\n",
       "      <td>73</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.410</td>\n",
       "      <td>0.739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Houston Astros</td>\n",
       "      <td>615</td>\n",
       "      <td>5598</td>\n",
       "      <td>1442</td>\n",
       "      <td>95</td>\n",
       "      <td>0.258</td>\n",
       "      <td>1164</td>\n",
       "      <td>118</td>\n",
       "      <td>56</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.374</td>\n",
       "      <td>0.684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Baltimore Orioles</td>\n",
       "      <td>708</td>\n",
       "      <td>5585</td>\n",
       "      <td>1434</td>\n",
       "      <td>191</td>\n",
       "      <td>0.257</td>\n",
       "      <td>1120</td>\n",
       "      <td>81</td>\n",
       "      <td>69</td>\n",
       "      <td>0.316</td>\n",
       "      <td>0.413</td>\n",
       "      <td>0.729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Los Angeles Dodgers</td>\n",
       "      <td>644</td>\n",
       "      <td>5436</td>\n",
       "      <td>1395</td>\n",
       "      <td>117</td>\n",
       "      <td>0.257</td>\n",
       "      <td>1087</td>\n",
       "      <td>126</td>\n",
       "      <td>82</td>\n",
       "      <td>0.322</td>\n",
       "      <td>0.375</td>\n",
       "      <td>0.697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Chicago Cubs</td>\n",
       "      <td>654</td>\n",
       "      <td>5549</td>\n",
       "      <td>1423</td>\n",
       "      <td>148</td>\n",
       "      <td>0.256</td>\n",
       "      <td>1202</td>\n",
       "      <td>69</td>\n",
       "      <td>71</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.401</td>\n",
       "      <td>0.715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Cincinnati Reds</td>\n",
       "      <td>735</td>\n",
       "      <td>5612</td>\n",
       "      <td>1438</td>\n",
       "      <td>183</td>\n",
       "      <td>0.256</td>\n",
       "      <td>1250</td>\n",
       "      <td>97</td>\n",
       "      <td>79</td>\n",
       "      <td>0.326</td>\n",
       "      <td>0.408</td>\n",
       "      <td>0.734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Los Angeles Angels</td>\n",
       "      <td>667</td>\n",
       "      <td>5513</td>\n",
       "      <td>1394</td>\n",
       "      <td>155</td>\n",
       "      <td>0.253</td>\n",
       "      <td>1086</td>\n",
       "      <td>135</td>\n",
       "      <td>86</td>\n",
       "      <td>0.313</td>\n",
       "      <td>0.402</td>\n",
       "      <td>0.714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Philadelphia Phillies</td>\n",
       "      <td>713</td>\n",
       "      <td>5579</td>\n",
       "      <td>1409</td>\n",
       "      <td>153</td>\n",
       "      <td>0.253</td>\n",
       "      <td>1024</td>\n",
       "      <td>96</td>\n",
       "      <td>102</td>\n",
       "      <td>0.323</td>\n",
       "      <td>0.395</td>\n",
       "      <td>0.717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Chicago White Sox</td>\n",
       "      <td>654</td>\n",
       "      <td>5502</td>\n",
       "      <td>1387</td>\n",
       "      <td>154</td>\n",
       "      <td>0.252</td>\n",
       "      <td>989</td>\n",
       "      <td>81</td>\n",
       "      <td>79</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.388</td>\n",
       "      <td>0.706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Cleveland Indians</td>\n",
       "      <td>704</td>\n",
       "      <td>5509</td>\n",
       "      <td>1380</td>\n",
       "      <td>154</td>\n",
       "      <td>0.250</td>\n",
       "      <td>1269</td>\n",
       "      <td>89</td>\n",
       "      <td>80</td>\n",
       "      <td>0.317</td>\n",
       "      <td>0.396</td>\n",
       "      <td>0.714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Arizona Diamondbacks</td>\n",
       "      <td>731</td>\n",
       "      <td>5421</td>\n",
       "      <td>1357</td>\n",
       "      <td>172</td>\n",
       "      <td>0.250</td>\n",
       "      <td>1249</td>\n",
       "      <td>133</td>\n",
       "      <td>94</td>\n",
       "      <td>0.322</td>\n",
       "      <td>0.413</td>\n",
       "      <td>0.736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Toronto Blue Jays</td>\n",
       "      <td>743</td>\n",
       "      <td>5559</td>\n",
       "      <td>1384</td>\n",
       "      <td>186</td>\n",
       "      <td>0.249</td>\n",
       "      <td>1184</td>\n",
       "      <td>131</td>\n",
       "      <td>81</td>\n",
       "      <td>0.317</td>\n",
       "      <td>0.413</td>\n",
       "      <td>0.730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Minnesota Twins</td>\n",
       "      <td>619</td>\n",
       "      <td>5487</td>\n",
       "      <td>1357</td>\n",
       "      <td>103</td>\n",
       "      <td>0.247</td>\n",
       "      <td>1048</td>\n",
       "      <td>92</td>\n",
       "      <td>63</td>\n",
       "      <td>0.306</td>\n",
       "      <td>0.360</td>\n",
       "      <td>0.666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Florida Marlins</td>\n",
       "      <td>625</td>\n",
       "      <td>5508</td>\n",
       "      <td>1358</td>\n",
       "      <td>149</td>\n",
       "      <td>0.247</td>\n",
       "      <td>1244</td>\n",
       "      <td>95</td>\n",
       "      <td>72</td>\n",
       "      <td>0.318</td>\n",
       "      <td>0.388</td>\n",
       "      <td>0.706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>Pittsburgh Pirates</td>\n",
       "      <td>610</td>\n",
       "      <td>5421</td>\n",
       "      <td>1325</td>\n",
       "      <td>107</td>\n",
       "      <td>0.244</td>\n",
       "      <td>1308</td>\n",
       "      <td>108</td>\n",
       "      <td>72</td>\n",
       "      <td>0.309</td>\n",
       "      <td>0.368</td>\n",
       "      <td>0.676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Oakland Athletics</td>\n",
       "      <td>645</td>\n",
       "      <td>5452</td>\n",
       "      <td>1330</td>\n",
       "      <td>114</td>\n",
       "      <td>0.244</td>\n",
       "      <td>1094</td>\n",
       "      <td>117</td>\n",
       "      <td>74</td>\n",
       "      <td>0.311</td>\n",
       "      <td>0.369</td>\n",
       "      <td>0.680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Tampa Bay Rays</td>\n",
       "      <td>707</td>\n",
       "      <td>5436</td>\n",
       "      <td>1324</td>\n",
       "      <td>172</td>\n",
       "      <td>0.244</td>\n",
       "      <td>1193</td>\n",
       "      <td>155</td>\n",
       "      <td>91</td>\n",
       "      <td>0.322</td>\n",
       "      <td>0.402</td>\n",
       "      <td>0.724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Atlanta Braves</td>\n",
       "      <td>641</td>\n",
       "      <td>5528</td>\n",
       "      <td>1345</td>\n",
       "      <td>173</td>\n",
       "      <td>0.243</td>\n",
       "      <td>1260</td>\n",
       "      <td>77</td>\n",
       "      <td>89</td>\n",
       "      <td>0.308</td>\n",
       "      <td>0.387</td>\n",
       "      <td>0.695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Washington Nationals</td>\n",
       "      <td>624</td>\n",
       "      <td>5441</td>\n",
       "      <td>1319</td>\n",
       "      <td>154</td>\n",
       "      <td>0.242</td>\n",
       "      <td>1323</td>\n",
       "      <td>106</td>\n",
       "      <td>80</td>\n",
       "      <td>0.309</td>\n",
       "      <td>0.383</td>\n",
       "      <td>0.691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>San Francisco Giants</td>\n",
       "      <td>570</td>\n",
       "      <td>5486</td>\n",
       "      <td>1327</td>\n",
       "      <td>121</td>\n",
       "      <td>0.242</td>\n",
       "      <td>1122</td>\n",
       "      <td>85</td>\n",
       "      <td>86</td>\n",
       "      <td>0.303</td>\n",
       "      <td>0.368</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>San Diego Padres</td>\n",
       "      <td>593</td>\n",
       "      <td>5417</td>\n",
       "      <td>1284</td>\n",
       "      <td>91</td>\n",
       "      <td>0.237</td>\n",
       "      <td>1320</td>\n",
       "      <td>170</td>\n",
       "      <td>71</td>\n",
       "      <td>0.305</td>\n",
       "      <td>0.349</td>\n",
       "      <td>0.653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>Seattle Mariners</td>\n",
       "      <td>556</td>\n",
       "      <td>5421</td>\n",
       "      <td>1263</td>\n",
       "      <td>109</td>\n",
       "      <td>0.233</td>\n",
       "      <td>1280</td>\n",
       "      <td>125</td>\n",
       "      <td>67</td>\n",
       "      <td>0.292</td>\n",
       "      <td>0.348</td>\n",
       "      <td>0.640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     team  runs  at_bats  hits  homeruns  bat_avg  strikeouts  \\\n",
       "0           Texas Rangers   855     5659  1599       210    0.283         930   \n",
       "1          Boston Red Sox   875     5710  1600       203    0.280        1108   \n",
       "2          Detroit Tigers   787     5563  1540       169    0.277        1143   \n",
       "3      Kansas City Royals   730     5672  1560       129    0.275        1006   \n",
       "4     St. Louis Cardinals   762     5532  1513       162    0.273         978   \n",
       "5           New York Mets   718     5600  1477       108    0.264        1085   \n",
       "6        New York Yankees   867     5518  1452       222    0.263        1138   \n",
       "7       Milwaukee Brewers   721     5447  1422       185    0.261        1083   \n",
       "8        Colorado Rockies   735     5544  1429       163    0.258        1201   \n",
       "9          Houston Astros   615     5598  1442        95    0.258        1164   \n",
       "10      Baltimore Orioles   708     5585  1434       191    0.257        1120   \n",
       "11    Los Angeles Dodgers   644     5436  1395       117    0.257        1087   \n",
       "12           Chicago Cubs   654     5549  1423       148    0.256        1202   \n",
       "13        Cincinnati Reds   735     5612  1438       183    0.256        1250   \n",
       "14     Los Angeles Angels   667     5513  1394       155    0.253        1086   \n",
       "15  Philadelphia Phillies   713     5579  1409       153    0.253        1024   \n",
       "16      Chicago White Sox   654     5502  1387       154    0.252         989   \n",
       "17      Cleveland Indians   704     5509  1380       154    0.250        1269   \n",
       "18   Arizona Diamondbacks   731     5421  1357       172    0.250        1249   \n",
       "19      Toronto Blue Jays   743     5559  1384       186    0.249        1184   \n",
       "20        Minnesota Twins   619     5487  1357       103    0.247        1048   \n",
       "21        Florida Marlins   625     5508  1358       149    0.247        1244   \n",
       "22     Pittsburgh Pirates   610     5421  1325       107    0.244        1308   \n",
       "23      Oakland Athletics   645     5452  1330       114    0.244        1094   \n",
       "24         Tampa Bay Rays   707     5436  1324       172    0.244        1193   \n",
       "25         Atlanta Braves   641     5528  1345       173    0.243        1260   \n",
       "26   Washington Nationals   624     5441  1319       154    0.242        1323   \n",
       "27   San Francisco Giants   570     5486  1327       121    0.242        1122   \n",
       "28       San Diego Padres   593     5417  1284        91    0.237        1320   \n",
       "29       Seattle Mariners   556     5421  1263       109    0.233        1280   \n",
       "\n",
       "    stolen_bases  wins  new_onbase  new_slug  new_obs  \n",
       "0            143    96       0.340     0.460    0.800  \n",
       "1            102    90       0.349     0.461    0.810  \n",
       "2             49    95       0.340     0.434    0.773  \n",
       "3            153    71       0.329     0.415    0.744  \n",
       "4             57    90       0.341     0.425    0.766  \n",
       "5            130    77       0.335     0.391    0.725  \n",
       "6            147    97       0.343     0.444    0.788  \n",
       "7             94    96       0.325     0.425    0.750  \n",
       "8            118    73       0.329     0.410    0.739  \n",
       "9            118    56       0.311     0.374    0.684  \n",
       "10            81    69       0.316     0.413    0.729  \n",
       "11           126    82       0.322     0.375    0.697  \n",
       "12            69    71       0.314     0.401    0.715  \n",
       "13            97    79       0.326     0.408    0.734  \n",
       "14           135    86       0.313     0.402    0.714  \n",
       "15            96   102       0.323     0.395    0.717  \n",
       "16            81    79       0.319     0.388    0.706  \n",
       "17            89    80       0.317     0.396    0.714  \n",
       "18           133    94       0.322     0.413    0.736  \n",
       "19           131    81       0.317     0.413    0.730  \n",
       "20            92    63       0.306     0.360    0.666  \n",
       "21            95    72       0.318     0.388    0.706  \n",
       "22           108    72       0.309     0.368    0.676  \n",
       "23           117    74       0.311     0.369    0.680  \n",
       "24           155    91       0.322     0.402    0.724  \n",
       "25            77    89       0.308     0.387    0.695  \n",
       "26           106    80       0.309     0.383    0.691  \n",
       "27            85    86       0.303     0.368    0.671  \n",
       "28           170    71       0.305     0.349    0.653  \n",
       "29           125    67       0.292     0.348    0.640  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlb11"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's plot runs and at_bats as points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1919e2b7550>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "\n",
    "plt.scatter(mlb11['runs'],mlb11['at_bats'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6106270467206687"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlb11['runs'].corr(mlb11['at_bats'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 319,
       "width": 622
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams['figure.figsize'] = (10,5)\n",
    "\n",
    "sns.residplot(mlb11['at_bats'], mlb11['runs'], color = 'red')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "runs_bar = np.mean(mlb11['runs'])\n",
    "bats_bar = np.mean(mlb11['at_bats'])\n",
    "\n",
    "SSxy_L = [(mlb11['runs'][i]-runs_bar)*(mlb11['at_bats'][i]-bats_bar) for i in range(len(mlb11['runs']))]\n",
    "SSxy = sum(SSxy_L)/len(SSxy_L)\n",
    "\n",
    "SSxx_L = [(mlb11['at_bats'][i]-bats_bar)**2 for i in range(len(mlb11['at_bats']))]\n",
    "SSxx = sum(SSxx_L)/len(SSxx_L)\n",
    "\n",
    "b=SSxy/SSxx\n",
    "a=runs_bar - b*bats_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   runs   R-squared:                       0.373\n",
      "Model:                            OLS   Adj. R-squared:                  0.350\n",
      "Method:                 Least Squares   F-statistic:                     16.65\n",
      "Date:                Mon, 24 Apr 2023   Prob (F-statistic):           0.000339\n",
      "Time:                        09:26:59   Log-Likelihood:                -167.44\n",
      "No. Observations:                  30   AIC:                             338.9\n",
      "Df Residuals:                      28   BIC:                             341.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept  -2789.2429    853.696     -3.267      0.003   -4537.959   -1040.526\n",
      "at_bats        0.6305      0.155      4.080      0.000       0.314       0.947\n",
      "==============================================================================\n",
      "Omnibus:                        2.579   Durbin-Watson:                   1.524\n",
      "Prob(Omnibus):                  0.275   Jarque-Bera (JB):                1.559\n",
      "Skew:                           0.544   Prob(JB):                        0.459\n",
      "Kurtosis:                       3.252   Cond. No.                     3.89e+05\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 3.89e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "formula_string = \"runs ~ at_bats\"\n",
    "\n",
    "model = sm.formula.ols(formula = formula_string, data = mlb11)\n",
    "model_fitted = model.fit()\n",
    "\n",
    "print(model_fitted.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept = -2789.242885442255\n",
      "Slope = 0.6305499928382827\n"
     ]
    }
   ],
   "source": [
    "print('Intercept =', model_fitted.params[0])\n",
    "print('Slope =', model_fitted.params[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared = 0.37286539018680676\n"
     ]
    }
   ],
   "source": [
    "print('R-squared =', model_fitted.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction and prediction errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 302,
       "width": 598
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = mlb11['at_bats']\n",
    "y = mlb11['runs']\n",
    "\n",
    "y_pred = a+b*x\n",
    "\n",
    "plt.scatter(mlb11['at_bats'], mlb11['runs'])\n",
    "plt.plot(x, y_pred, color = 'orange')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAIBui619WwMOfNbvugsTf6umlDkWdAQg3BFaAQAAAAD8Zrjr1f/gY4qr/bNfdQ1pD+jSmH+RHLEWdQagtyC0AgAAAAD4JK76NaUc/Ae/685PyVdz0mQLOgLQmxFaAQAAAAA65XBdUErp38t5ucSvuvphj8g5498kI0o1NTUWdQegtyO0AgAAAAC0iT+9Xv0q/tGvGk9Uomqm/FHuvqPbrg00ooLdGoAIQ2gFAAAAABEsqvG0Brz3KUU3nvSrri7zadUP/4ZkGBZ1BiDSEVoBAAAAQCQxTSWc/ImSjv3IrzJ33HBdmPQHtcQNtagxAGiP0AoAAAAAernoKxUaWLxIjpZ6v+oujf6hGoZ+0aKuAODmCK0AAAAAoLcxW5R0dLUSKv/TrzJX4iTVZq+XxznAosYAwHeEVgAAAADQC8TU7deg4kV+19WO+7kaUxdb0BEAdA+hFQAAAACEI0+T+h1eofhzG/0qa0y5UxfH/UJmdIJFjQFAcBBaAQAAAECYcNZu18ADn/G77sLE/1ZTyh0WdAQA1iG0AgAAAACbMtz16n/wHxRX+5ZfdQ1p9+vSmB9LjliLOgMA6xFaAQAQgUzTlI6Vy7N1s1S6T3K5JKdTyp4mx4KlUsZoGYYR6jYBICLFVf9RKQcf87vu/JQ/qjlpigUdAUBoEFoBABBhTLdbnnVrpZLdUrNLMk3vA64mqbhIntK9Us50OfKWyYjmVwUAsJrDVauU0i/IeXm/X3X1Q7+iulHflYwoizoDgNDiN1EAACKIaZrXAitXU2cDvNdLdsmzbq0cjyxnxRUAWCC+6jfqV77SrxpPVF/VTMmXu2+WRV0BgL0QWgEAEEmOld84sLqey+Udd7xCyuSPIwDoLkfjaQ1870FFNx73q64uY4XqRzwh8QUCgAhEaAUAQATxbN3ivSXQF80uebZuUdSjT1vaEwD0SqaphJP/V0nH1vhV5o4brguTXlFL3DCLGgOA8EFoBQBAJCnde20Pq66YpnRgj7X9AEAvEn3liAYW3ydHS51fdZdG/0ANQ79kTVMAEMYIrQAAiCQuH1dZtfJ1VRYARCKzRUlHv6+Eyl/6VeZKmKjaiS/J4xxoUWMA0DsQWgEAEEmczq73s7pejNO6XgAgDMXUlWhQ8b1+19WO/Zka0/7Ogo4AoPcitAIAIJJkT5OKi3y7RdAwpIm51vcEAHbmaVK/w08r/twf/Cpr7D9XF8f/QmZ0ojV9AUAEILQCACCCOOYvkad0r2+rrWKccsxfYnlPAGA3zovvaGDJw37XXZi4QU0pc4PfEABEKEIrAAAiSWaWlDNdKtl18/2tnE7vuIzRPdcbAISI4b6i/gf/QXG1b/pV15C6VJfG/FiKirOoMwCIbIRWAABEEMMw5MhbJs+6tVLJbu9G69ffKmgY3n2scqbLkbdMhmGErlkAsFDc+deV8v5X/a47P/k1NSdPtaAjAMBHEVoBABBhjOhoOR5ZLh2vkKdgs1S61xtexTiliblyzF8qI5MVVgB6F6O5VgMOfEHOy/v9qqsf+hXVjXxWcvCnEwD0ND55AQCIQIZhSJlZinpsZahbAQDLxFdtUL/yp/2q8UT1Vc2UP8rdd4xFXQEAfEVoBQAAAKBXcDRWaWDJpxV99bhfdXUZy1U/4knvLdIAANsgtAIAAAAQnkxTCSf/XUnHnvOrzB07VBcmbVRLn49Z1BgAIBgIrQAAAACEjaiGIxpU/HdyuC/5VXdp1PfVMOzL1jQFALAEoRUAAAAA+zJblHT0B0qofNGvMlfCRNVOfEke50CLGgMAWK3boVVhYaF+9rOf3XSMYRh6+eWXJUnV1dX6+te/fsOxs2bN0pNPPnnD1yooKFBlZaUcDocyMzN13333aepUjpwFAAAAeouYuhINKr7X77qLY/9dV9OWBL8hAEBIdDu0ysjI0Kc+9alOH/vggw9UVlamyZMnd3hsxIgRys3N7XB9+PDhnT7X+vXrlZ+frwEDBuiuu+6S2+1WUVGR1qxZo7y8PC1cuLB7bwQAAABAaHhc6le+UvFnf+9XWWP/Obo4/pcyoxMtagwAEEpBCa0yMjI6fexb3/qWJOkTn/hEp3UPPvigT69x+PBh5efnKy0tTc8995wSEhIkSYsXL9Yzzzyjl156SVOmTFFqampgbwIAAABAj3JefFcDS3z7e+B6F7JfUtOAeRZ0BACwG8v2tDp58qQqKiqUkpKiKVOmdOu5tm3bJkm6//772wIrSUpNTdWCBQu0ceNGFRYW+hyCAQAAAOhZhvuK+h/6muIuvOFXXUPqEl0a87wUFWdRZwAAu7IstHrjDe9/jObNmyeHw9Hh8YsXL2rbtm26fPmyEhMTlZWVpREjRnT6XGVlZZKkSZMmdXhs8uTJ2rhxo8rKygitAAAAABuJO/8npbz/iN915ye/qubkaRZ0BAAIJ5aEVi6XS++8844Mw9C8eZ0v3T1w4IAOHDjQ7tr48eP1+OOPa+DAayd8NDY2qra2VnFxcerfv3+H5xk8eLAk6cyZMz71tnLlyk6vr1mzRpLavTYQStHR3h9P5iTCBXMW4YY5i3ATFnP2ygnFvDlThqvWr7KWkf+glpwfSw7ve0y2ojf0uLCYs8B1mLP2Y0loVVRUpCtXrmjKlCkd/p8dGxurBx54QLm5uUpLS5MknThxQq+88oref/99rV69Wj/60Y8UF+dd/tvQ0CBJio+P7/S1Wq9fuXLFircCAAAA4Caidn9JUSd/61eNGdVH7nl/kZk8waKuAAC9gSWh1Ztvvimp8w3Yk5OT9dBDD7W7Nm7cOH3729/Ws88+q4qKCr311lu6917/jrg1DMOnca0rqm6kpqbGr9cFrNIa+DInES6Yswg3zFmEG7vM2ej6Q0rd2/H3/K5cHvGULmc8JbX+3t4siZ+/Xs0ucxbwFXPWGunp6QHXBj20qqys1OHDhzVgwAC/NmCPiorSvHnzVFFRoYMHD7aFVq0rqVpXXH1UVyuxAAAAAHSDaWrg/iVy1u31q8wdm64Lkzaqpc9wixoDAPR2QQ+tWk/6u/POOzvdgP1mkpKSJElNTU1t1+Li4pSSkqLa2lpdvHixw75WZ8+elSQNGTKkO20DAAAA+BvnpR0a+N6n/K5rTLlLtRPXW9ARACASBTW0crlc2r59+003YL+ZiooKSWrb66rVhAkTtH37dr333nu688472z22f//+tjEAAAAAAuBxK23ndEW5zvldem76drXEj7SgKQBApAtqaLVz584bbsDeqqKiQpmZmW278rcqKyvT66+/Lkm6/fbb2z129913a/v27dq0aZNyc3OVkJAgSaqurlZBQYFiYmI0d+7cYL4VAACAoDJNUzpWLs/WzVLpPsnlkpxOKXuaHAuWShmjfd6jEwiGuPOvK+X9r/pddyX97/Vh1j9b0BEAAO0FNbR64403JHW+AXurDRs26NSpUxo/frxSUlIkSSdPnlRZWZkk6aGHHtKYMWPa1YwZM0aLFi1Sfn6+VqxYoRkzZsjtdmvHjh2qr69XXl6eUlNTg/lWAAAAgsZ0u+VZt1Yq2S01uyTT9D7gapKKi+Qp3SvlTJcjb5mMaEvOyQGklqtKf2dUQKVnbyuWJzat64EAAARR0H4rqqys1AcffNDlBuxz5szR7t27dfToUe3fv18tLS1KTk7WbbfdpoULF2rs2LGd1n3hC1/Q8OHDVVBQoDfffFOGYSgzM1OLFy/W1KlTg/U2AAAAgso0zWuBlaupswHe6yW75Fm3Vo5HlrPiCkETf/r/qV/Ft/yuq8t8WvUjnrCgIwAAfGeYZutXfZCkqqqqULcASOK4VYQf5izCTU/NWfOvh+V5/tudB1Yf5YyVY/kPZGRmWdoTwpMvc9Zovqgh7wa21+uZjx+SGZ0UUC3QGX43QLhhzlojPT094FrWnwMAAFjIs3WL95ZAXzS75Nm6RVGPPm1pT+hdEv/6z0o8+X/9rrs45nldHfKwBR0BABAchFYAAABWKt17bQ+rrpimdGCPtf0g7EU1nlbazul+15lGrM7cfkhyxFrQFQAAwUdoBQAAYCWXj6usWvm6KgsRJa1oqqJcZ73/ux91F7J/raYBNz4kCQAAOyO0AgAAsJLT6dt+Vq1inNb1grDhvLRTA997wO+65vhROp/7Z8lwWNAVAAA9i9AKAADAStnTpOIi324RNAxpYq71PcF+TFPpbw8LqPT85NfUnMxp2gCA3ofQCgAAwEKO+UvkKd3r22qrGKcc85dY3hPsoe+p/1Dy0VV+1zX2n6vaib/xhpwAAPRihFYAAABWysyScqZLJbtuvr+V0+kdlzG653pDz/K4lL49M6DS81PylXzL3ZKkWo5iBwBECEIrAAAACxmGIUfeMnnWrZVKdns3Wr/+VkHD8O5jlTNdjrxlMlg906skl/8f9a36td91zfFZOj/9zxZ0BABA+CC0AgAAsJgRHS3HI8ul4xXyFGyWSvd6w6sYpzQxV475S2VkssKqNzCaP9SQd8cFVFs9bZvcCYHVAgDQGxFaAQAAWzJNUzpWLs/WzVLpPu+tdU6nlD1NjgVLpYzRYbUqyTAMKTNLUY+tDHUrCLIB731asZeK/K5zxw5T9W27LOio5/W2n1cAgD0QWgEAANsx3e7Ob6dzNUnFRd6NzVtvp4vm1xn0rKjGSqXtnBFQ7dnb9soTOyTIHYUWP68AAKvwXw0AAGArpmle+wO4sxP3TNN7vWSXPOvWyvHIclZwwHKD/zJeDvclv+saB9yt2uz/F/R+7IKfVwCAlQitAACAvRwrv/EfwNdzubzjjld4T+gDgiim7j0NKv5kQLVnPn5YZnRCkDuyKX5eAQAWIrQCAAC24tm6xXuLkS+aXfJs3aKoR5+2tCdEhvTCoQHV1X/sH1Q38ttB7iY88PMKALASoRUAALCX0r3X9sTpimlKB/ZY2w96rdiarRpQ9uWAaqvmnJAc/CrNzysAwEr8lzaCccoLAMCWXD6u2mjl6yoPwDSV/vawgEovZa1RQ/rng9xQL8DPKwDAQoRWEYpTXgAAtuV0dr0/zvVinNb1grDXt3Kdko98J6DaqjsqJb7Auzl+XoFuYSEBcHOkERGIU14AALaWPU0qLvLtliPDkCbmWt8TwoenWenbMwIqvZD9kpoGzAtuP70dP69AwFhIAHSNmR+JOOUFAGBjjvlLvL+o+7J6I8Ypx/wllvcEe0uqeFYJp/8roNqquaeD3E1k4ecVCAwLCQDfEFpFIE55AQDYWmaWlDNdKtl18/1ynE7vuIzRPdcbbMFw12nIX8YGVFs9bavcCeOD3FEE4+cVCAwLCQCfOELdAEKAU14AADZmGIYcecuknBmSM7bjnkKG4b2eM8N7ywTfPEeEASUPK71wqNILh/oVWLXEDlHV3NNt/xBYBRc/r0BgAllIAEQiVlpFIk55AQDYnBEdLccjy6XjFfIUbPZ+4dLs8m7iPDFXjvlLZWSyYqM3i2o8rbSd0wOqPTtzjzxx6UHuCDfCzysQABYSAD4htIpEnPICAAgDhmFImVmKemxlqFtBD0l7d5Kims/7XdeYMk+1E1+yoCP4ip9XwE8sJAB8QmgViTjlBQAA2IDz0i4NfO/+gGrPfPywzOiEIHcEAD2EhQSATwitIhCnvAAAgFBJLxwaUF39sEdVN+rZIHcDACHCQgLAJ4RWkYhTXgAAQA/pc3aj+n/wjYBqq+ackBz8ugqg92EhAeAbfguIQK2nvHjWrfUen9rsap/wG4Z3+WnOdE55AQAA/jFNpb89LKDSyyOe0uXMbwa5IQCwIRYSAD4htIpQnPICAACCJfHY80o88UJAtVV3VHq/MAOACMJCAsA3hFYRjFNeAABAQDwupW/PDKj04tj/q6tpgW2+DgC9CQsJgK4RWgEAAKBL/cseUZ+aPwVUWzX3dJC7AYDegYUEwM0RWgEWM01TOlYuz9bNUuk+7z3rTqeUPU2OBUuljNEs9wUA2I7RfElD3h0fUG3NpM1y9Zse5I4AAECkIbQCLGS63Z3fp+5qkoqLvCeGtN6nHs2PIwAgtFJ33qboxpMB1bKaCgAABBt/JQMWMU3zWmDV2VG2pum9XrJLnnVr5XhkOSuuAAA9KurqcaXtmh1Q7bkZ76qlT0ZwGwIAALgOoRVglWPlNw6srudyeccdr/AefQsAgIXSC4cGVOeOHarq23YHuRsAAIAbI7QCLOLZusV7S6Avml3ybN2iqEeftrQnAEDkcX64RwP3Lwmo9szsMpkx/YPbEAAAgI8IrQCrlO69todVV0xTOrDH2n4AABEj0NVUVwcs0MXsdUHuBt1x/YEu58qKvSu4YzjQBQAQGQitAKu4fFxl1crXVVkAAHxEn3Nb1P/Q4wHVVs05JjmcQe4IwcCBLgCASMd/3QCrOJ1d72d1vRj+YAAA+Mg0lf72sIBKL494QpczuR3d7jjQBQAAQivAOtnTpOIi324RNAxpYq71PQEAwlb86fXqV/GPAdVW3VHp/W8NwgcHugAAQGgFWMUxf4l32b4vq61inHLMX2J5TwCAMOJxK337iIBKL976r7o6+NNBbgg9iQNdAAAgtAKsk5kl5UyXSnbdfH8rp9M7LmN0z/UGALClpKPfV8KpnwdUWzX3dJC7QUhxoAsAAIRWgFUMw5Ajb1nnG6h6B3j3sWrdQJXbNgAg4hjueg35y5iAamsmbZSr38wgdwTb4EAXAAAIrQArGdHRcjyyXDpeIU/BZu+3ps0ub1g1MVeO+UtlZLLCCgAiSerO2YpuPO53XUtMis7NLg1+Q7AnDnQBAIDQCrCaYRhSZpaiHlsZ6lYAACEQdfWk0nbdFlDtuZm71BIX2CmB4cA0TelYuTxbN0ul+7yri5xOKXuaHAuWShmjI3clMge6AABAaAUAABBs6YVDA6pr6jdbFyb9Psjd2JPpdnd+C72rSSou8h5m0noLfXTk/crKgS4AABBaAQAAdFvMh/s0aP/igGrPzD4oMyY5yB3Zm2ma1wKrzkIZ0/ReL9klz7q1cjyyPPJWXHGgCwAAhFYAAACBCHQ1VeOAT6g2+9dB7ibMHCu/cWB1PZfLO+54hTfEiSAc6AIAAKEVAACAT+KqX1XKwa8FVFs156+SIzbIHYUvz9Ytvp921+ySZ+sWRT36tKU92VGHA13K9nmDPg50AQBECEIrAACAzpim0t8ObBP0yx97XJdH/p8gN9SLlO71bYNxyTvuwB5r+7Gx6w90GThwoCSppqYmxF0BANAzCK0AAAD+JuHEvynp2I8Cqq26o9J7yxa6drM9mjrj66osAADQqxBaAQCAyOVxB7w31cUxL+jqkIeC3FCEcDp9OxWvVYzT56GmaUrHyuXZulkq3ecNyJxOKXuaHAuWShmj2f8JAIAwQWgFAAAiSr+Djyu+ektAtVVzTwe3mUiVPU0qLvLtFkHDkCbm+vS0ptvd+cblriapuEie0r3XNi6P5tdgAADsjv9ao9fgm1UAQGcMd52G/GVsQLU1Ob+Xq//sIHcEx/wl3gDJl9VWMU455i/pcphpmtcCq86e1zS910t2ybNurRyPLOf3AgAAbI7QCr0C36wCAK43aPdcxTRUBFTLaqoekJkl5UyXSnbdfH8rp9M7LsOHE/KOld84sLqey+Udd7zC2wcAALAtR6gbALqrwzerH73V4CPfrJq+nlYEAAgbUVdPKb1waNs//gRW56a/raq5p9v+gfUMw5Ajb5mUM0NyxnbcwN4wvNdzZni/cPJhRZRn6xbfN2xvdnnHAwAAW2PJCcIf36wCQEQKdAP1lpgBOjf7gAYOHOj995qaYLYFHxnR0XI8slw6XiFPwWapdK83dIpxShNz5Zi/VEamDyusWpXu9W2PLMk77sCewBoHAAA9htAKYS+Qb1ajHn3a0p4AAMEXU1esQcX3BVR7dlapPM6UIHeE7jIMQ8rMUtRjK7v/ZDe7zbAzvv7uAAAAQobQCuGPb1aBiMThC5Eh0NVUjf3nqjZnQ3Cbgb05nb5t7N4qxmldLwAAICgIrRD++GYViDgcvtB7xZ1/XSnvfzWg2qrbj0pRcUHuCGEje5pUXOTbF1mGIU3Mtb4nAADQLfwmj/DHN6tAROFY+17GNJX+9rCASi9/7Gu6PPJbQW4I4coxf4k3sPbld4IYpxzzl1jeEwAA6B5CK4Q/vlkFIguHL4S9hBM/VdKx5wKqrbqjsuNJc4Dk/TnPmS6V7Lr5Kmyn0zsuw49N3gEAQEgQWiHs8c0qEFk4fCEMedxK3z4ioNJLWf+ihvTPBrkh9EaGYciRt6zzW4e9A7yrrVtvHSb8BADA9gitEP74ZhWILBy+EBb6HXpC8ef+EFBt1dzTQe4GkcKIjpbjkeXS8Qp5CjZ7Py+aXd6wamKuHPOXysjk9wAAAMJFt0OrwsJC/exnP7vpGMMw9PLLL7e7dvjwYW3atEnl5eVqbm7W4MGDdeedd+qee+6Rw+G44WsVFBSosrJSDodDmZmZuu+++zR16tTuvg2EMb5ZBSIMhy/YkuGu15C/jAmotibnZbn6fzzIHSFSGYYhZWYp6rGVoW4FAAB0U7dDq4yMDH3qU5/q9LEPPvhAZWVlmjx5crvre/bs0fPPP6+YmBjNmjVLCQkJ2rdvn37961/r8OHDeuqppzo81/r165Wfn68BAwborrvuktvtVlFRkdasWaO8vDwtXLiwu28FYYxvVoEIwuELtjFozycUc+VQQLWspgIAAEBXghJaZWRkdPrYt77lPdHnE5/4RNu1hoYGvfjii3I4HFq1apVGjhwpSXrooYe0evVq7dy5U++++65mz57dVnP48GHl5+crLS1Nzz33nBISEiRJixcv1jPPPKOXXnpJU6ZMUWpqanffDsIY36wCEYLDF0ImqvG00nZOD6i2OrdQ7r58eQAAAADfdX4fXhCcPHlSFRUVSklJ0ZQpU9qu79y5U3V1dZo1a1ZbYCVJTqdTDz/8sCRp69at7Z5r27ZtkqT777+/LbCSpNTUVC1YsEDNzc0qLCy06q0AAGzEMX+J76unOHyh29ILh7b9409g5YlKUtXc023/EFgBAADAX5aFVm+88YYkad68ee32qCorK5MkTZo0qUPN2LFjFRsb27bPlS81rbceto4BAPRyrYcvOLsIrjh8ISAxdSXtgip/nJ11oC2kOnt7YLcNAgAAAK0sOT3Q5XLpnXfekWEYmjdvXrvHzpw5I0lKT0/vUBcVFaXU1FSdOnVK586d07Bhw9TY2Kja2lrFxcWpf//+HWoGDx7c7nm7snJl57eOrVmzRpI0cOBAn54HsFp0tPfHkzmJcNGTc9Z8+geq+7fVatzzF+/+Vh89fMEZq7jcjyvpiWdlRHNQblecf4gNqM6Tepfcc/7U9u8pwWqoh/A5i3DDnEW4Yc4i3DBn7ceS3+SLiop05coVTZkypcP/sxsaGiRJ8fHxnda2Xm8d5+v4K1eudL9xAEBYMKKjlfTU9xRfcUhXXv1vNe0r8oZXzljFTputvn/3GcWMHhfqNm3LOPeWYt65J6Ba19IPpai4IHcEAAAAdGRJaPXmm29Kar8Bu69MXzbW7YRhGD6Na11RdSM1NTUBvT4QbK2BL3MS4SIkczYlVfryk4r68pNtl9ySPvQ20nN9hAF/b/VrVT/sEdWNWnXtwsV6SfVB6SnU+JxFuGHOItwwZxFumLPW6OxOO18FPbSqrKzU4cOHNWDAgHYbsLf66Eqqj7p69Wq7cV2N72olFgAAkajP2d+r/wfLAqqtuqPSe5slAAAAEEJBD61aT/q78847223A3mrIkCE6evSoqqqqdMstt7R7rKWlRdXV1YqKilJaWpokKS4uTikpKaqtrdXFixc77Gt19uzZtucFACBimS1Kf3t4QKW143+pxkGfDHJDAAAAQPcE9fRAl8ul7du3d7oBe6sJEyZIkt57770Ojx06dEhNTU3KyspSTEyMTzX79+9vNwYAgEjR74Nl10768zOwaj3lr2ruaQIrAAAA2FJQQ6udO3fqypUrmjx58g132585c6YSExNVVFSko0ePtl13uVz63e9+J0maP39+u5q7775bkrRp0ybV11/bR6O6uloFBQWKiYnR3Llzg/lWAACwHcNdfy2kKhyq+LO/97n2/ORX2wVVAAAAgN0F9fbAN954Q9LNN2CPj4/Xo48+qhdeeEGrVq3S7NmzlZCQoL1796qqqkozZ87UrFmz2tWMGTNGixYtUn5+vlasWKEZM2bI7XZrx44dqq+vV15enlJTU4P5VgAAsIWBexfIWV/md51pxOrMHX+1oCMAAACgZwQttKqsrNQHH3xwww3Yrzd9+nStWrVKmzdv1q5du+RyuTR48GB94Qtf0L333tvpSYBf+MIXNHz4cBUUFOjNN9+UYRjKzMzU4sWLNXXq1GC9DQAAQsrRWKXBO3MDqq3O/bPcfbOC3BEAAAAQGoZpmmaom7CTqqqqULcASOK4VYQf5mzg0guHBlTniUrQ2dsPB7mbyMGcRbhhziLcMGcRbpiz1khPTw+4NuinBwIAgJuLuXxAg/bdE1Dt2VnvyeMcFOSOAAAAAPshtAIAoAcEupqqKfk2XZj8hyB3AwAAANgfoRUAABaIrdmqAWVfDqi26vYjUlSfIHcEAAAAhBdCKwAAgiTQ1VT1Q7+iutGrg9wNAAAAEN4IrQAACFDfUy8q+WhgYVPVHackwxHkjgAAAIDeg9AKAABfmS1Kf3t4QKWXRv9ADUO/FNx+AAAAgF6M0AoAgJtIPvy0+p7ZEFBt1dzTQe4GAAAAiByEVgAAXMdwX9GQv2QFVHsh+zdqGnBnkDsCAAAAIhOhFQAg4g3cd6+cl0sCqmU1FQAAAGANQisAQMRxuGo0uCgnoNrqaW/InTA2yB0BAAAA+ChCKwBARBi05xOKuXLI7zrTcOrMHccs6AgAAADAzRBaAQB6paiGI0rbfUdAtWdv2y9PbGqQOwIAAADgD0IrAECvkV44NKC6puTpujB5c5C7AQAAANAdhFYAgLAVW7NVA8q+HFBt1e1Hpai4IHcEAAAAIFgIrQAAYSXQ1VR1mStVP+IbQe4GAAAAgFUIrQAAtpZ47EdKPPFvAdVW3XFKMhxB7ggAAABATyC0AgDYi9mi9LeHB1R6cey/62rakuD2AwAAACAkCK0AACGXUvpFxV14I6Daqrmng9wNAAAAADsgtAIA9DjDXa8hfxkTUC2rqQAAAIDIQGgFAOgRae9mK6q5NqBaVlMBAAAAkYfQCgBgCUfTWQ3eMTWg2vOTX1NzcmC1AAAAAHoHQisAQNDEbIxXutkSUC2rqQAAAABcj9AKABCw6Pr3lbp3fkC152buUkvcsCB3BAAAAKC3ILQCAPglvXBoQHUtMQN1bnZJkLsBAAAA0FsRWgEAbir2wpsaUPqFgGrP3F4hMyo+yB0BAAAAiASEVgCADgJeTZX5FZ0bsTrI3QAAAACIRIRWAADFV/5K/Y58O6DaqjtOSkaUBg4c6L1QUxPEzgAAAABEKkIrAIhEpkfpb38soNIPR67SlY89EuSGAAAAAKA9QisAiBDJ5d9S36r/F1Bt1dzTwW0GAAAAALpAaAUAvZTRclVD3hkVUO2FCb9S08D5Qe4IAAAAAHxHaAUAvciA/fcr9sNdAdWymgoAAACAnRBaAUAYczRVa/COyQHVVk8tkDtxQpA7AgAAAIDgILQCgDAzZPtIGZ7GgGpZTQUAAAAgXBBaAYDNRdd/oNS9dwVUe3bmHnni0oPcEQAAAABYj9AKAGwovXBoQHWuhGzVTPufIHcDAAAAAD2P0AoAbMBZu10DD3wmoNozHy+XGd03yB0BAAAAQGgRWgFAiAS6murK4If14a3PB7mbyGGapnSsXJ6tm6XSfZLLJTmdUvY0ORYslTJGyzCMULcJAAAARDxCKwDoIfGn16tfxT8GVFt1x0nJiApyR5HHdLvlWbdWKtktNbsk0/Q+4GqSiovkKd0r5UyXI2+ZjGj+EwkAAACEEr+RA4BVTI/S3/5YQKUXb/1XXR386SA3FNlM07wWWLmaOhvgvV6yS551a+V4ZDkrrgAAAIAQIrQCgCBKqnhWCaf/K6Daqrmng9wN2jlWfuPA6noul3fc8QopM6tnegMAAADQAaEVAHRHy1WlvzMqoNLa8f+lxkELg9wQbsSzdYv3lkBfNLvk2bpFUY8+bWlPAAAAAG6M0AoA/DTgvQcVe+ndgGpZTRVCpXuv7WHVFdOUDuyxth8AAAAAN0VoBQBdcLhqNLgoJ6Da81P/PzUnTgxyRwiIy8dVVq18XZUFAAAAwBKEVgDQicHvjJGjpT6gWlZT2ZTT2fV+VteLcVrXCwAAAIAuEVoBgKToK+VK3XNnQLXnZu5WS9zQIHeEoMueJhUX+XaLoGFIE3Ot7wkAAADADRFaAYhY6YWBBU3NfcfpfO62IHcDqznmL5GndK9vq61inHLMX2J5TwAAAABujNAKQMRw1m7XwAOfCaj2zMcPy4xOCHJH6FGZWVLOdKlk1833t3I6veMyRvdcbwAAAAA6ILQC0KsFupqqIe3TujT2X4PbDELKMAw58pbJs26tVLLbu9H69bcKGoZ3H6uc6XLkLZNhGKFrFgAAAAChFYDeJb5qg/qVPx1QbdWcE5KDj8XezIiOluOR5dLxCnkKNkule73hVYxTmpgrx/ylMjJZYQUAAADYAX+dAQhvpqn0t4cFVFp3y/9R/fDHg9wQ7M4wDCkzS1GPrQx1KwAAAABugtAKQNhJOrJaCZUvBlRbNfd0kLsBAAAAAFiB0AqA/bU0Kv2dkQGV1o7/pRoHfTLIDQEAAAAArEZoBcCWUko+o7iL2wOqZTUVAAAAAIQ/QisAtuBwXdDgookB1Z6fkq/mpMlB7ggAAAAAEEqEVgBCZvBfxsvhvhRQLaupAAAAAKB3I7QC0GOirxxR6p47Aqo9N3OXWuICOyUQAAAAABB+CK0AWCq9cGhAdc3xo3V+emFwm0GPMk1TOlYuz9bNUuk+yeWSnE4pe5ocC5ZKGaNlGEao20Qvd7N52PzglxU9emyoWwQAAMANEFoBCCrnxb9oYMlDAdWe+fgHMqMTg9wRQsF0u+VZt1Yq2S01uyTT9D7gapKKi+Qp3SvlTJcjb5mMaP5TBGt0NQ9ry/YpLvfjMj/3NeYhAACADfEbGoBuC3Q1VUPqUl0a99Mgd4NQM03zWlDgaupsgPd6yS551q2V45HlrLhC0Pk0D5sa1bj7HampiXkIAABgQ4RWAPzW58zv1P/wNwOqrZpzQnLw0dOrHSu/cVBwPZfLO+54hZSZ1TO9IXL4PA+bmIcAAAA2xV+OALpmmkp/O7BN0OsyV6p+xDeC3BDszLN1i/dWLF80u+TZukVRjz5taU+IPMxDAACA8EdoBaBTiUd/oMRTPwuotuqOSonbbCJX6d5rewd1xTSlA3us7QeRiXkIAAAQ9oIaWh06dEivv/66ysvLVV9fr4SEBA0fPlz33nuvpkyZIkmqrq7W17/+9Rs+x6xZs/Tkk092+lhhYaEKCgpUWVkph8OhzMxM3XfffZo6dWow3wYQmTxNSt9+S0ClteN+rsbUxUFuCGHL5ePqlla+roYB/ME8BAAACHtBC602btyol19+WYmJiZo6dar69euny5cv6/jx4zp48GBbaNVqxIgRys3N7fA8w4cP7/T5169fr/z8fA0YMEB33XWX3G63ioqKtGbNGuXl5WnhwoXBeitAxEg58PeKq30roNqquaeD3A16Daez632ErhfjtK4XRC7mIQAAQNgLSmi1Y8cOvfzyy8rOztby5cvVp0+fdo+73e4ONRkZGXrwwQd9ev7Dhw8rPz9faWlpeu6555SQkCBJWrx4sZ555hm99NJLmjJlilJTU7v/ZoBezOGq1eCi7IBqz09+Tc3JrGqED7KnScVFvt2aZRjSxI5fYADdxjwEAAAIe47uPoHH49GGDRsUGxurJ554okNgJUnR0d3LxrZt2yZJuv/++9sCK0lKTU3VggUL1NzcrMLCwm69BtBbpb2bo/TCoUovHOp3YFU193TbPwRW8JVj/hLfV63EOL3jgSBjHgIAAIS/bq+0Ki8vV3V1tWbOnKm+ffuquLhYJ0+elNPp1KhRo5SV1fnx0RcvXtS2bdt0+fJlJSYmKisrSyNGjOh0bFlZmSRp0qRJHR6bPHmyNm7cqLKyMp9XbgG9WVTDUaXtnhNQ7bkZO9XS52NB7ggRJzNLypkuley6+b5CTqd3XMbonusNkcPneRjLPAQAALCpbodWR44ckSQlJydr5cqVOnnyZLvHx44dq29+85tKSkpqd/3AgQM6cOBAu2vjx4/X448/roEDB7Zda2xsVG1treLi4tS/f/8Orz948GBJ0pkzZ3zqd+XKlZ1eX7NmjSS1e20glFpXKPoyJ51/iA3oNcyEUWpe+H7bv3f8CQN81zpnBw0aJPPpH6ju31arcc9fvPsKXX+LlmFIzljF5X5cSU88K6Obq3GBG+lqHhrOWMXNmKPE//1t5iHCgj+/GwB2wJxFuGHO2k+3f0Orq6uT5L2FLzU1Vd/5znc0evRonT9/XuvXr1dJSYleeOEFrVq1SpIUGxurBx54QLm5uUpLS5MknThxQq+88oref/99rV69Wj/60Y8UFxcnSWpoaJAkxcfHd/r6rdevXLnS3bcChA2j+m3FbJ8fUK1r8TnJ2S+4DQEfYURHK+mp7ym+4pCuvPrfatpX5A0NnLGKnTZbff/uM4oZPS7UbaKX62oeJt3/93Jmjet0700AAACEnmGavuxQemO/+c1v9Nprr8kwDK1Zs0YZGRltj7lcLj3xxBO6cOGCvv/979/wVkFJamlp0bPPPquKigp96Utf0r333itJqq2t1WOPPaaUlBT94he/6FDndrv12c9+VjExMdqwYUN33ookqaqqqtvPAQRDa7pfU1MjSUovHBrQ81wdtFgXx/88aH0BN/LROQvYHXMW4YY5i3DDnEW4Yc5aIz09PeDabm/E3rdvX0lSWlpau8BKkpxOp3JyciRdu43wRqKiojRv3jxJ0sGDB9uut66kal1x9VFdrcQCwpWj/N/k/ENs2ybq/qiac7xtA3UCKwAAAABAOOr27YGtiVlrePVRrdddN9sE9W9a971qampquxYXF6eUlBTV1tbq4sWLHfa1Onv2rCRpyJAh/jcP2IlpKv3tYQGVflj2MdU5H5Ajbxn7sgAAAAAAeoVu/3U7duxYRUVF6cyZM3K73W0bl7U6deqUJO/GvF2pqKiQpLa9rlpNmDBB27dv13vvvac777yz3WP79+9vG4PIZpqmdKxcnq2bpdJ93tOinE4pe5ocC5ZKGaNlGEao22wn+YNvqu/Z3wVUe2rDFEnXvR/nLnnWrZXjkeW2e58AAAAAAPir26FVUlKSbrvtNv3lL3/RH/7wBz388MNtjx04cEAlJSWKj4/XpEmTJHmDqczMzA7hVllZmV5//XVJ0u23397usbvvvlvbt2/Xpk2blJubq4SEBElSdXW1CgoKFBMTo7lz53b3rSCMmW63POvWSiW7pWbXtROiXE1ScZE8pXulnOmhX4nU0qj0d0YGVFq7e7iuVNwk/HW5vO//eIX3qHcAAAAAAMJYUP56/+IXv6gjR45o06ZNOnTokEaOHKmamhrt3r1bDodDjz76aNttghs2bNCpU6c0fvx4paSkSJJOnjypsrIySdJDDz2kMWPGtHv+MWPGaNGiRcrPz9eKFSs0Y8YMud1u7dixQ/X19crLy1Nqamow3grCkGma1wIrV1NnA7zXS0KzEiml9IuKu/BGQLWuTzXp3PdXSMVF7Y9qv5Fmlzxbtyjq0acDej0AAAAAAOwiKKFVcnKyfvjDH2rjxo3avXu3ysvL1adPH02ZMkVLlixpd2rgnDlztHv3bh09elT79+9XS0uLkpOTddttt2nhwoUaO3Zsp6/xhS98QcOHD1dBQYHefPNNGYahzMxMLV68WFOnTg3G20C4OlZ+48Dqej20EslortWQd7MDqq2Z+Fu5UuZIunZyhUr3+hZYSd5xB/YE9NoAAAAAANiJYZq+/jUcGaqqqkLdAvzU8os1vq9EMgxp6uygr0RKK5qqKNfZgGqr5p7u9HpraHVu6WxJfvyYGoaifvlqQL0A3cERwaERjvv52QVzFuGGOYtww5xFuGHOWqP1AL9AcMwYwl8IViJFNfxVabtv73pgJ87NKFJLnxG+FzidXa8iu16M0/+mAISlsNnPDwAAAAgAv8Ei/Llc/o1v9nP836QXDg2ozh03QtUziwKqlSRlT/NvJdnE3MBfC0DYsPt+fgAAAEB3EVoh/Fm0EimmrkSDiu8NqKUzsw/KjEkOqPajHPOXeFdL+PIeY5xyzF8SlNcFYHM2288PAAAACDZCK4S/IK5ECnQ11dVBn9TF8b8MqLZLmVlSznSpZNfNV5U5nd5xGaOt6QOArXi2bvF95SgniwIAACAMEVoh7HVnJVJszTYNKPtSQK9bNeeY5LB+/yjDMOTIW9b5vjXeAd7VY6371nD7DxAZOFkUAAAAvRyhFcKfXyuRcjX0xJ3SCf9f5vKIp3Q585uB99kNRnS0HI8sl45XyFOw2fvHarPLG1ZNzJVj/lIZmaywAiJKD+3nBwAAAIQKoRXCXlcrkRLGnFf/aSf/9m87/HruqjsqvSuZbMAwDCkzS1GPrQx1KwDsgJNFAQAA0MsRWqFXaL8SaaM+dutPA3qeC9nr1TTgriB3BwAW4GRRAAAA9HKEVugV4s7/j1Le/4r3X271r7Zq7ungNwQAFuNkUQAAAPR2hFYITy2NSn9nZECl1VML5E6cEOSGAKCHcbIoAAAAejlCK4SN+KqX1K/8Gb/rWpxpOjer2IKOACB0OFkUAAAAvR2hFWzLaP5QQ94dF1Dtmdnvy4zpF9yGAMBmOFkUAAAAvRmhFWwl8djzSjzxgt91l7L+WQ3pf29BRwBgb5wsCgAAgN6K0Aoh5Wg6o8E7pgVUW3X7USkqLsgdAQAAAAAAOyC0Qo/r98FTij/7st91teP/S42DFlrQEQAAAAAAsBtCK1gu+kqFUvfM9bvOHfcxVc94VzKigt8UAAAAAACwNUIrBJ9pakDJQ4q99K7fpTWTNsvVb7oFTQEAAAAAgHBCaIWgiPlwjwbtX+J3XVO/23Qh5xXv0ewAAAAAAAB/Q2iFwJgtSt11u6IbT/hdWp37ltx9x1jQFAAAAAAA6C0IreCz2JqtGlD2Zb/rGtI+pUtj/82CjgAAAAAAQG9FaIUba2nUkHdGyZDpd+nZmbvliRtqQVMAAAAAACASEFqhnfiq/1a/8hV+110e8YQuZz5tQUcAAAAAACASEVpFOo9LfU//SslHV/tdemZ2mcyY/hY0BQAAAAAAIh2hVQSKuVyqpCPfU+yHO/yquzT6h2oY+kWLugIAAAAAALiG0CoCGC1X1ffUL5R0/Md+11bdfkSK6mNBVwDgH9M0pWPl8mzdLJXuk1wuyemUsqfJsWCplDFahmGEuk0AAAAAQUJo1Us5L+1S0pHvyllf6lfdxTHP6+qQhy3qCgACY7rd8qxbK5Xslppdkvm3AyJcTVJxkTyle6Wc6XLkLZMRzX/aAAAAgN6A3+x7mbjzryvl/a/6NLYlur/qRq/W1dQlkuGwtrEwwUoOwH5M07wWWLmaOhvgvV6yS551a+V4ZDk/pwAAAEAvQGjVm5gt6n/wazcdcmXww7qc+bQ8sWk91FT4YCUHYFPHym8cWF3P5fKOO14hZWb1TG8AAAAALMPymt7ENNWckN3ukjtuuC5M+JWq7qhU1dzT+vDW5wmsOtFhJUdrYHVtQLuVHOZHHwdgGc/WLd4g2RfNLu94AAAAAGGP5SK9iSNaNZNeUcyVcrn7fExmTEqoOwofrOQA7Kt0b8cg+UZMUzqwx9p+AAAAAPQIVlr1NlF91JyUQ2DlJ1ZyADbm8vFns5WvP8sAAAAAbI3QCpBYyQHYmdPp3/gYP8cDAAAAsCVCK0BiJQdgZ9nTJF9PAzQMaWKutf0AAAAA6BHsaQVI3pUcXe1ndT1WcsACpmlKx8rl2bpZKt3nDVOdTil7mhwLlkoZo2X4Gt70Io75S7ynd/ryMxrjlGP+Est7AgAAAGA9QitA8q7kKC7y7RZBVnLAAqbbfe0Ey2bXtbnoapKKi7yhTc50OfKWyYiOsI/uzCwpZ7pUsuvmqyKdTu+4jNE91xsAAAAAy3B7ICDvSg6fV0+xkgNBZprmtcDK1dQxPDVN7/WSXfKsW+tdkRVBDMOQI2+ZlDNDcsZ2vFXQMLzXc2Z4Q70IXI0GAAAA9EYR9nU9cAOs5EAoHSu/FljdjMvlHXe8wjtnI4gRHS3HI8ul4xXyFGz2Hp7Q7PKGzRNz5Zi/VEYmP5cAAABAb0JoBejaSo5Ob8/yDvD+cdx6exYrORBEnq1bfN/cv9klz9Ytinr0aUt7siPDMKTMLEU9tjLUrQAAAADoAYRWwN+wkgMhU7rXt/3UJO+4A3us7QcAAAAAbIDQCrgOKzkQEje7JbUzvq7KAgCEBU6PBQCgc4RWABBqTmfX+1ldz9dDAwAAtufP6bEAAEQaTg8EgFDLntbxRLwbMQxpYq61/QAAegSnxwIAcHOEVgAQYo75S3xfPRXj9I4HAIQ/P0+PdVcc6pm+AACwCUIrAAi1zCwpZ7r3NsGbcXpPsFQGBwIAQG/g7+mxV177raX9AABgN4RWABBihmF49yrJmSE5YzveKmgY3us5M+TIW8ZmvADQW/h5emzT3net7QcAAJthI3YAsAEjOlqOR5ZLxyvkKdjs/UOm2eW9bXBirhzzl8rIZIUVAPQq/p4e68+hHQAA9AKEVgBgE4ZhSJlZinpsZahbAQD0BH9Pj3XGWtcLAAA2RGgVwUzTlI6Vy7N1s1S6z/ttn9MpZU+TY8FSKWM0tyEBAABYJXuaVFzk2y2ChqHYabOt7wkAABshtIpQptt97YjlZte1X5ZcTVJxkTyle6Wc6d79c6KZJgAAAMHmmL/E+zuXL6utYpzqu/gz1jcFAICNsBF7BDJN81pg5Wrq+O2eaXqvl+ySZ91a74osAAAABJefp8dGjx7bM30BAGAThFaR6Fj5tcDqZlwu77jjFT3TFwAAQATh9FgAAG6O+74ikGfrFu8tgb5odsmzdYuiHn3a0p4AAAAiEafHAgBwY4RWkah0r28bfkrecQf2WNsPAABABOP0WAAAOsftgZHI5eMqq1a+rsoCAAAAAAAIEkKrSNTVZp8fFePneAAAAAAAgG4itIpE2dM6bvR5I4YhTcy1th8AAAAAAICPILSKQI75S3xfPRXj9I4HAAAAAADoQYRWkSgzS8qZ3vVtgk6nd1wGJ9YAAAAAAICeRWgVgQzDkCNvmZQzQ3LGdrxV0DC813NmyJG3zHuiDQAAAAAAQA+KDnUDCA0jOlqOR5ZLxyvkKdgsle71nhIY45Qm5soxf6mMTFZYAQAAAACA0CC0imCGYUiZWYp6bGWoWwEAAAAAAGiH2wMBAAAAAABgO4RWAAAAAAAAsJ2g3h546NAhvf766yovL1d9fb0SEhI0fPhw3XvvvZoyZUq7sYcPH9amTZtUXl6u5uZmDR48WHfeeafuueceORydZ2mFhYUqKChQZWWlHA6HMjMzdd9992nq1KnBfBsAAAAAAAAIsaCFVhs3btTLL7+sxMRETZ06Vf369dPly5d1/PhxHTx4sF1otWfPHj3//POKiYnRrFmzlJCQoH379unXv/61Dh8+rKeeeqrD869fv175+fkaMGCA7rrrLrndbhUVFWnNmjXKy8vTwoULg/VWAAAAAAAAEGJBCa127Nihl19+WdnZ2Vq+fLn69OnT7nG32932vzc0NOjFF1+Uw+HQqlWrNHLkSEnSQw89pNWrV2vnzp169913NXv27Laaw4cPKz8/X2lpaXruueeUkJAgSVq8eLGeeeYZvfTSS5oyZYpSU1OD8XYAAAAAAAAQYt3e08rj8WjDhg2KjY3VE0880SGwkqTo6GvZ2M6dO1VXV6dZs2a1BVaS5HQ69fD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      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 302,
       "width": 598
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = mlb11['at_bats']\n",
    "y = mlb11['runs']\n",
    "\n",
    "y_pred = model_fitted.predict(x)\n",
    "\n",
    "plt.scatter(mlb11['at_bats'], mlb11['runs'])\n",
    "plt.plot(x, y_pred, color = 'orange')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1: If a team manager saw the least squares regression line and not the actual data, how many runs would he or she predict for a team with 5,578 at-bats? Is this an overestimate or an underestimate, and by how much? In other words, what is the residual for this prediction?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 322,
       "width": 626
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.residplot(x, y, color = 'red')\n",
    "plt.xlabel('at_bats', fontsize = 16)\n",
    "plt.ylabel('residuals', fontsize = 16)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gwIExc+bMqKqqihdffDEefPDB2LBhQ9x2221nYsj0IY899lhs27YtBg8eHBdddFG8/vrrp9y+N3PQ6zq90dO5GeE9J6UjJlG2Kisr44477ogxY8bE8OHDo6mpKRYvXnzKfTZs2BBLly6NUaNGxd/+7d92fso+d+7c+Ou//uv4t3/7t7jiiiti5MiRnfssXbo0NmzYEDNmzIgvfvGLnZ8uzZw5M/7+7/8+7r333vja177mk096ZMyYMdHY2JjatjfzFnrjW9/6Vhw4cCA+/elPx5w5czqXP/jgg7Fs2bJ45JFH4pZbbinhCDlXnH/++alr5Ntvvx333Xdf9O/fP+6666647LLLIiLi5ptvjrvvvjtWrlwZP/7xj+NDH/rQ6R4yfci8efPioosuitra2mhpaYm/+Zu/Oem2vZmDXtfprZ7MzQ7ec1Iq/jqmbFVUVMS0adNi+PDh6X2efvrpiIj4vd/7vS5f1xg5cmRce+21ceTIkXj22Wc7l7e3t3fu86lPfapLMGpoaIgJEybEjh07oqWlpcD/DZxcT+ct9MaePXuiubk5RowYEddee22XdY2NjVFZWRk/+tGP4p133inRCOFEK1eujLfeeitmzpzZ+Ud8RMSgQYPi93//9yMi4qmnnirV8DhLTZ48Oerq6qJfv37vuW1v5qDXdXqrJ3OzN8xNiklMok9Zt25dRERcfvnlJ6ybNm1al20i3v3jqrW1Nerq6rot8B3H+b/7QMbPf/7zePrpp2PJkiXx9NNPx7Zt2066bU/nLfRGxxyaOnXqCXdaDhkyJMaPHx9tbW2xadOmUgyPc8yRI0fihz/8YSxZsiSWL18e69ati+PHj5+w3amujxMmTIjKysrOZ9jA6dCbOeh1nTPJe05Kxdfc6DPeeeedePPNN2Pw4MHd3s1UW1sbERG7du3qXLZz586IiKirq+v2mB3L/+8+kPHyyy/Hyy+/3GXZpEmT4tZbb42amprOZb2Zt9Ab73W9q62tjebm5ti1a1dMmTLlTA6Nc9D+/fvjG9/4RpdlI0eOjD/7sz+LiRMndi7ruPbV19efcIwBAwbEyJEjY/v27bFnzx4/mMFp0dM56HWdM817TkpFTKLPePvttyPi3Yd6dqdj+S9/+cse79OxHbyXysrK+NjHPhYNDQ0xatSoiIjYtm1bfOc734lXXnkl7r777vi7v/u7zofM9mbeQm+Ya5SL2bNnx4QJE2L06NExZMiQ2LNnT3z/+9+PZ555Jr761a/GV77ylRgzZkxEeJ2m9Ho6B11rOVO856TUxCROq1P9/G933utnWYuhJ99Bbm9vP40joVwVMm+HDh0aN998c5f1EydOjDvvvDMWLlwYmzZtih/84Afd/orRqZyu785Dh47rnbnG6XbTTTd1+fcll1wSt9xySwwePDiWLl0a3/nOd+L2229PHcvrNKXW2znoWkuhvOek1MQkTqtRo0bFwIED09tfeOGFvT7Xe3062V2Nf699Dh06dMI+9H2nY94OGDAgPvKRj8SmTZuipaWl84W9N/MWesP1jnL30Y9+NJYuXRrr16/vXGbeUmo9nYNe1yk17zk5U8QkTquFCxeesXMNHjw4LrzwwnjzzTfj5z//+QnfBd69e3dEdH1eSMf330/23eCO5Sd7xgh90+matxdccEFERLS1tXUu6828hd54r+uduUapdXeNrKuri5/97Gexc+fOuPTSS7tsf+zYsdi7d28MGDCg8yseUGw9nYNe1ykH3nNyJvg1N/qUyZMnR0TE2rVrT1j30ksvddkm4t07UGpqamLXrl2xd+/eE/bpOM7/3Qd6q+NXsn71j56ezlvojUmTJkVERHNz8wm/mnXo0KF49dVXY9CgQTF27NhSDA9i48aNERFdfl31VNfH9evXR1tbW4wbN65Hd5NCT/RmDnpdp9S85+RMEJPoU6655pqIiFiyZEn84he/6Fy+d+/eWLFiRQwcODBmz57dubxfv36d+3z729/u8gfW6tWrY/369TF69OguvywDp7Jp06Y4evToCcvXrVsXy5Yti4iI3/qt3+qyrqfzFnqjtrY2pk6dGvv27YsVK1Z0WdfU1BRtbW0xa9aszgd1wumwffv2Lte5Dvv27YsHHnggIrpeI2fMmBHV1dXx3HPPxc9+9rPO5YcPH47/+I//iIh3vx4Hp0tv5qDXdc4E7zkptX7tnlxIGXviiSfi9ddfj4iIrVu3xrZt2+KDH/xg509Xjh8/Pq6++uou+zz00EOxdOnSuOiii+LXf/3X4+jRo/H888/HwYMH4zOf+Uxcd911XbY/cuRI3H333bFhw4a47LLLYvLkydHa2horV66MioqKWLhwoU/qSbvrrrti+/btMWnSpM5nKb322muxbt26iIi4+eab42Mf+9gJ+/V03kJv7N69OxYsWBAHDhyI6dOnx+jRo2PTpk3xyiuvRF1dXXzlK1+J6urqUg+TPqypqSm++93vxqRJk2LkyJExePDg2LNnT6xZsyaOHDkS06ZNi9tvvz0qKv73SQyrVq2Kr3/96zFw4MD40Ic+FFVVVfGTn/wkdu7cGTNmzIgvfelLHhhLj6xatSpWr14dERH79++P5ubmGDVqVIwfPz4iIqqrq+MP//APu2zf0znodZ3e6Mnc9J6TUhOTKGt33XVXtLS0nHT9hz/84bj11ltPWP7ss8/GihUrYseOHdGvX794//vfH3Pnzo0rr7yy2+McPnw4nnjiifif//mfaG1tjSFDhsSkSZOisbExRo8eXbT/D33fD37wg1i1alVs37493nrrrTh27FgMHTo0xo0bF9ddd11MmDDhpPv2dN5Cb7S2tkZTU1OsXbs2Dh48GMOHD4+Ghoa46aaboqqqqtTDo49raWmJp556KrZu3Rr79++Ptra2OO+882LMmDExa9asmDVrVrdh6NVXX43HH388Nm7cGIcPH47a2tq46qqr4vrrr4/+/d1oT880NTXF4sWLT7p+xIgR8U//9E9dlvVmDnpdp6d6Mje956TUxCQAAAAA0nyUAwAAAECamAQAAABAmpgEAAAAQJqYBAAAAECamAQAAABAmpgEAAAAQJqYBAAAAECamAQAAABAmpgEAAAAQJqYBAAAAECamAQAAABAmpgEAAAAQJqYBAAAAECamAQAAABAmpgEAAAAQJqYBAAAAECamAQAAABA2v8H1HdMgEF3ABoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 302,
       "width": 585
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals = (y - y_pred)\n",
    "plt.hist(residuals, bins = 8)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 335,
       "width": 622
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import probplot\n",
    "probplot(residuals, plot = plt)\n",
    "plt.show(); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2: Fit a new model that uses homeruns to predict runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}