{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "\n",
    "Linear regression allows to model relationships between **continuos independent and dependent variables** and **between qualitative independent variables and continuous variables**. However, it does not allow to model relationships between continuous or qualitative independent variables and **qualitative dependent variables**.\n",
    "\n",
    "## Example Data\n",
    "Establishing such relationships is useful in different contexts. For instance, let us consider the [Breast Cancer Wisconsin](https://archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic) dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "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>radius1</th>\n",
       "      <th>texture1</th>\n",
       "      <th>perimeter1</th>\n",
       "      <th>area1</th>\n",
       "      <th>smoothness1</th>\n",
       "      <th>compactness1</th>\n",
       "      <th>concavity1</th>\n",
       "      <th>concave_points1</th>\n",
       "      <th>symmetry1</th>\n",
       "      <th>fractal_dimension1</th>\n",
       "      <th>...</th>\n",
       "      <th>texture3</th>\n",
       "      <th>perimeter3</th>\n",
       "      <th>area3</th>\n",
       "      <th>smoothness3</th>\n",
       "      <th>compactness3</th>\n",
       "      <th>concavity3</th>\n",
       "      <th>concave_points3</th>\n",
       "      <th>symmetry3</th>\n",
       "      <th>fractal_dimension3</th>\n",
       "      <th>Diagnosis</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.30010</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.16220</td>\n",
       "      <td>0.66560</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.08690</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.12380</td>\n",
       "      <td>0.18660</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.19740</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.14440</td>\n",
       "      <td>0.42450</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.24140</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.20980</td>\n",
       "      <td>0.86630</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.19800</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.13740</td>\n",
       "      <td>0.20500</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>21.56</td>\n",
       "      <td>22.39</td>\n",
       "      <td>142.00</td>\n",
       "      <td>1479.0</td>\n",
       "      <td>0.11100</td>\n",
       "      <td>0.11590</td>\n",
       "      <td>0.24390</td>\n",
       "      <td>0.13890</td>\n",
       "      <td>0.1726</td>\n",
       "      <td>0.05623</td>\n",
       "      <td>...</td>\n",
       "      <td>26.40</td>\n",
       "      <td>166.10</td>\n",
       "      <td>2027.0</td>\n",
       "      <td>0.14100</td>\n",
       "      <td>0.21130</td>\n",
       "      <td>0.4107</td>\n",
       "      <td>0.2216</td>\n",
       "      <td>0.2060</td>\n",
       "      <td>0.07115</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>565</th>\n",
       "      <td>20.13</td>\n",
       "      <td>28.25</td>\n",
       "      <td>131.20</td>\n",
       "      <td>1261.0</td>\n",
       "      <td>0.09780</td>\n",
       "      <td>0.10340</td>\n",
       "      <td>0.14400</td>\n",
       "      <td>0.09791</td>\n",
       "      <td>0.1752</td>\n",
       "      <td>0.05533</td>\n",
       "      <td>...</td>\n",
       "      <td>38.25</td>\n",
       "      <td>155.00</td>\n",
       "      <td>1731.0</td>\n",
       "      <td>0.11660</td>\n",
       "      <td>0.19220</td>\n",
       "      <td>0.3215</td>\n",
       "      <td>0.1628</td>\n",
       "      <td>0.2572</td>\n",
       "      <td>0.06637</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>566</th>\n",
       "      <td>16.60</td>\n",
       "      <td>28.08</td>\n",
       "      <td>108.30</td>\n",
       "      <td>858.1</td>\n",
       "      <td>0.08455</td>\n",
       "      <td>0.10230</td>\n",
       "      <td>0.09251</td>\n",
       "      <td>0.05302</td>\n",
       "      <td>0.1590</td>\n",
       "      <td>0.05648</td>\n",
       "      <td>...</td>\n",
       "      <td>34.12</td>\n",
       "      <td>126.70</td>\n",
       "      <td>1124.0</td>\n",
       "      <td>0.11390</td>\n",
       "      <td>0.30940</td>\n",
       "      <td>0.3403</td>\n",
       "      <td>0.1418</td>\n",
       "      <td>0.2218</td>\n",
       "      <td>0.07820</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>567</th>\n",
       "      <td>20.60</td>\n",
       "      <td>29.33</td>\n",
       "      <td>140.10</td>\n",
       "      <td>1265.0</td>\n",
       "      <td>0.11780</td>\n",
       "      <td>0.27700</td>\n",
       "      <td>0.35140</td>\n",
       "      <td>0.15200</td>\n",
       "      <td>0.2397</td>\n",
       "      <td>0.07016</td>\n",
       "      <td>...</td>\n",
       "      <td>39.42</td>\n",
       "      <td>184.60</td>\n",
       "      <td>1821.0</td>\n",
       "      <td>0.16500</td>\n",
       "      <td>0.86810</td>\n",
       "      <td>0.9387</td>\n",
       "      <td>0.2650</td>\n",
       "      <td>0.4087</td>\n",
       "      <td>0.12400</td>\n",
       "      <td>M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>568</th>\n",
       "      <td>7.76</td>\n",
       "      <td>24.54</td>\n",
       "      <td>47.92</td>\n",
       "      <td>181.0</td>\n",
       "      <td>0.05263</td>\n",
       "      <td>0.04362</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.1587</td>\n",
       "      <td>0.05884</td>\n",
       "      <td>...</td>\n",
       "      <td>30.37</td>\n",
       "      <td>59.16</td>\n",
       "      <td>268.6</td>\n",
       "      <td>0.08996</td>\n",
       "      <td>0.06444</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.2871</td>\n",
       "      <td>0.07039</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>569 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     radius1  texture1  perimeter1   area1  smoothness1  compactness1  \\\n",
       "0      17.99     10.38      122.80  1001.0      0.11840       0.27760   \n",
       "1      20.57     17.77      132.90  1326.0      0.08474       0.07864   \n",
       "2      19.69     21.25      130.00  1203.0      0.10960       0.15990   \n",
       "3      11.42     20.38       77.58   386.1      0.14250       0.28390   \n",
       "4      20.29     14.34      135.10  1297.0      0.10030       0.13280   \n",
       "..       ...       ...         ...     ...          ...           ...   \n",
       "564    21.56     22.39      142.00  1479.0      0.11100       0.11590   \n",
       "565    20.13     28.25      131.20  1261.0      0.09780       0.10340   \n",
       "566    16.60     28.08      108.30   858.1      0.08455       0.10230   \n",
       "567    20.60     29.33      140.10  1265.0      0.11780       0.27700   \n",
       "568     7.76     24.54       47.92   181.0      0.05263       0.04362   \n",
       "\n",
       "     concavity1  concave_points1  symmetry1  fractal_dimension1  ...  \\\n",
       "0       0.30010          0.14710     0.2419             0.07871  ...   \n",
       "1       0.08690          0.07017     0.1812             0.05667  ...   \n",
       "2       0.19740          0.12790     0.2069             0.05999  ...   \n",
       "3       0.24140          0.10520     0.2597             0.09744  ...   \n",
       "4       0.19800          0.10430     0.1809             0.05883  ...   \n",
       "..          ...              ...        ...                 ...  ...   \n",
       "564     0.24390          0.13890     0.1726             0.05623  ...   \n",
       "565     0.14400          0.09791     0.1752             0.05533  ...   \n",
       "566     0.09251          0.05302     0.1590             0.05648  ...   \n",
       "567     0.35140          0.15200     0.2397             0.07016  ...   \n",
       "568     0.00000          0.00000     0.1587             0.05884  ...   \n",
       "\n",
       "     texture3  perimeter3   area3  smoothness3  compactness3  concavity3  \\\n",
       "0       17.33      184.60  2019.0      0.16220       0.66560      0.7119   \n",
       "1       23.41      158.80  1956.0      0.12380       0.18660      0.2416   \n",
       "2       25.53      152.50  1709.0      0.14440       0.42450      0.4504   \n",
       "3       26.50       98.87   567.7      0.20980       0.86630      0.6869   \n",
       "4       16.67      152.20  1575.0      0.13740       0.20500      0.4000   \n",
       "..        ...         ...     ...          ...           ...         ...   \n",
       "564     26.40      166.10  2027.0      0.14100       0.21130      0.4107   \n",
       "565     38.25      155.00  1731.0      0.11660       0.19220      0.3215   \n",
       "566     34.12      126.70  1124.0      0.11390       0.30940      0.3403   \n",
       "567     39.42      184.60  1821.0      0.16500       0.86810      0.9387   \n",
       "568     30.37       59.16   268.6      0.08996       0.06444      0.0000   \n",
       "\n",
       "     concave_points3  symmetry3  fractal_dimension3  Diagnosis  \n",
       "0             0.2654     0.4601             0.11890          M  \n",
       "1             0.1860     0.2750             0.08902          M  \n",
       "2             0.2430     0.3613             0.08758          M  \n",
       "3             0.2575     0.6638             0.17300          M  \n",
       "4             0.1625     0.2364             0.07678          M  \n",
       "..               ...        ...                 ...        ...  \n",
       "564           0.2216     0.2060             0.07115          M  \n",
       "565           0.1628     0.2572             0.06637          M  \n",
       "566           0.1418     0.2218             0.07820          M  \n",
       "567           0.2650     0.4087             0.12400          M  \n",
       "568           0.0000     0.2871             0.07039          B  \n",
       "\n",
       "[569 rows x 31 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from ucimlrepo import fetch_ucirepo \n",
    "from matplotlib import pyplot as plt\n",
    "  \n",
    "# fetch dataset \n",
    "breast_cancer_wisconsin_diagnostic = fetch_ucirepo(id=17) \n",
    "  \n",
    "# data (as pandas dataframes) \n",
    "X = breast_cancer_wisconsin_diagnostic.data.features \n",
    "y = breast_cancer_wisconsin_diagnostic.data.targets \n",
    "\n",
    "data = X.join(y)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset contains several measurements of given quantities measured from digitized image of a fine needle aspirate (FNA) of a breast mass, together with a categorical variable `Diagnosis` with two levels: `M` (malignant) and `B` (benign).\n",
    "\n",
    "In this case, it would be good to be able to study whether a relationship exists between some of the considered independent variables and the dependent variable. \n",
    "\n",
    "We will consider the `radius1` variable for the moment. Let us plot this variable with respect to `Diagnosis`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot.scatter(x='radius1',y='Diagnosis', figsize=(8,6))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot above, we can note that there is some form of relationship between the two variables. Indeed:\n",
    "* For low values of `radius1`, we tend to have more benign cases;\n",
    "* For large values of `radius1`, we tend to have more malignant cases.\n",
    "\n",
    "## Limits of Linear Regression\n",
    "Of course, we would like to quantify this relationship in a more formal way.\n",
    "**As in the case of a linear regressor, we want to define a model which can predict the independent variable $y$ from the dependent variables $x_i$. If such model gives good predictions, than we can trust its interpretation as a means of studying the relationship between the variables.**\n",
    "\n",
    "We can think of converting `B => 1` and `M => 0`, and then compute a linear regressor:\n",
    "\n",
    "$$Diagnosis = \\beta_0 + \\beta_1 radius1$$\n",
    "\n",
    "This would be the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "data['Diagnosis']=data['Diagnosis'].replace({'B':0,'M':1})\n",
    "plt.figure(figsize=(8,6))\n",
    "sns.regplot(x=data['radius1'],y=data['Diagnosis'], ci=None, line_kws={'color':'red'})\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can immediately see that this function does not model the relationship between the two variables very well. While we obtain a statistically relevant regressor with $R^2=0.533$ and statistically relevant coefficients, the residual plot will look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0jDHUNEUu2gDKDzbyld+vZf4zG2LeXhGRnnBpj9tE+60LruHMDa+QlpHO2Xd9DWbNguzseDdNRGIotCfcjv11AIwbnMOdMwr4zvPvUF5V36XX0opUEekrKb8B78DRBfbUbzxGsz/IQ2ObOHXdCli3Di6+GK64AsaPj3cTRaQPXfP467yxY3+H+8O1p2BoP+6aeawKOBGJmZTfgDcQtOTnZjJ3+jhOLciHq2ZARQUsWQI33QSjRzsF3Hnngc8X7+aKSIzNnT6OzR8eaHeOW0dKP6rh+ifX4gEmDcvlzhkFKuJEJG5c2ePW4Qa8fj+UlMCiRbBzJ1x6KVx+OQwd2octFJG+FmlVaXeNysvi+5ecoAJORHpFyg+VRp2csH07LF4ML78Mp5wCV14JZ5xBSVklD7xcyvZKZ2HD2EHZGioRcZn5z2xgycY93X6+x8DEfA2jikjPqXDrauRVXZ1TvC1axL59B1mQN5kXRp9GdXoWQets4unzGm457xjt9yTiIguKy/jVq+9R39xB/EIHPMaJ35qY309DqCLSbSrcuptVai133vtHxrzyIlN2bWb16JNYNmkq2waPBpzNOhdee6ouziIuU1JawT0tK0+7ekVM9xo8xpDfP5P75hyv64OIdJkKtx6EzE97YAV7D9aTW1fNBVvfYOaW1RzM7MeygmmsHjeFk48Zpg19RVyuo019w3kMpKd5CAQtg/ul83FtM41h4akZXsNN6qkXkU6ocOtB4XbN46/z5gdVNLRcfD0EOW3Xf5i1ZTUF+z/g3ydMZd4v74JRo3qzySKSYEpKK3jg5VLKPqqmvfrN5zF4PAYDNPmDdDTgeqxWpIpIO1S49aBwKymt4I7Fm6isacLi7MBucfJPjwse5PKda7m+8i049lhnMcO0aeDxtD534crt7KqqY1RetkLuRVwitLHve/tqaQ5aDE5vW5rXg7XO7w3+zufJDemXzv9ccZKuCyLShgq3HhRucOS2ARlew1H90vF5vc4clrEDoLjY2VKkshIuv5xVx03l1uIPqGn0EwhavB5Dv4w0fqqLtIirhIq4rftq8Hk8DO2fQfmBegJdWN9gDIzor3xUEXGocOth4RYS6kErr6pjZHs9aKWlsHgxbz25mNX5k/j7sZ+mdNg4LIaAtRwzJIeX55/b47aISGIJvz4crG/mUIO/W6+Tne7la9PHaR6cSApT4dZLhVtXTLnjL5y79Q1mla7G703j5WOn8cq4U2lMz2LLD2b2aVtEpG+VlFbwjT+/ycH67hVvAP0yPJw4Ik9TLERSkAq3OBRuk77zEtZavMZw4u4yLi5dxXG7y1g97lRu//W32+Sjai6ciPuEthTZ1cUw+0iUzCCSWlS4xaFwm/nwSrZW1OD1GIwBa2FAdRXX7tnAvEPvtOajvnr08cz76zscqve37hflNfCNCyZoqETEJRYUl/HYyu3UNXU9GzWcAXIz07hh2lhdH0RcTIVbHAq30GrU6gY//mCQNI+H3Mw0ZwXZMUe15qP++5UNLB17Bi9PPJvKnLw2r6GLtIg7LSgu4+F/biXYyeU29KUvkrPH5vH03HN6v3EiEncq3OJQuEF0ixmmf+03zNyyinO3b2Dz0HEsmzSNjcMnYo2zpYjXAMbwjfO1aaeIm0TTC9dR4RYu2+fla+dqQYOIW6hwi1PhFo0xd70IQGZzA+du38DsLavI8DexbNJU/nnMmdRlZgMQtOD1GHLSveqBE3GZBcVlPLFqBzWN/ja9cKF9I6PhMXCrpliIuIIKtwQu3I6956W2gdbWUrBvJ7NKV3FG+WbWfOqTfFSfB8IPTfMYjhmSw10zj9WkZRGXWFBcxoIVW/EHoyvcwnvlQtMr0tM8TMjP1UInkSSlwi2BC7cFxWX8rHhrxMcG1FfzmW1vMCMsH/VfY6bQlOZrc1xuhpefXzNFF2gRlwht6rtjfx3+oCXQwWS4w4s7r6FNJNfIAdrYVyTZqHBL4MINnOLtFyXvtQmjDmdskNPKnXzUiZXv88/xZ/LSpHPY039I6zFpHjh9zCB9wxZxoWsWruG1HVU9fp2RAzP5waUn6hohkuBUuCV44RYSWszwzocHqGsOYq0laJ1v1OB8qx52qJIZZWu4cNsbvDdoJMsmTWPtyOOwHi9D+2dQWdOIMQaPMYwbnKMQaxGXCM2Dq27wRz3vrT3qhRNJbCrckqRwi2RBcRmPrNh2xFCJL9DM1J0bmV26mkF1B3hp0jkUTzybqsxcoO3wiS7SIu4Syk/+8GADtuXLndeAvwuX78H90pWdLJKgVLglceEGLdsGvLqduubI2waM37+LWVtWM3XnRtaPOJZlBdPYnD/OmbUcpl+6h0e/eKou1CIuUlJawb1LN9PkD/DRocboV6EC4ZMzMtI83FQ4XqtSRRKACrckL9xCSkor+M6Styg/2Njmfq/HKdCy6ms5/721zNqyCr8njRcnTeWV8afR4Mtsc3z/zDSOHz5A8+FEXOKTaRZV1DQGezyUqiJOJL5UuLmkcAsJXaS3VlRT3eAnL9tHdYOfuqaAc8G2lpP2lDFzy2om793GyrFTWDZpKh/kHX3EaymdQcRdejMjVekMIvGhws1lhVu41iLuo0McqG/m8IWpg2oPcPHW17i47DV25w5mWcE0Xhs9Gb837YjX8gK/uf509cKJuEBJaQXffHYj++uae/xaWo0q0rdUuLm4cAvX3lAqgDcY4MwP3mb2llWMOvARyyecxd8nnsO+fnlHHDsqL4vvX3KCLtIiLlBSWsEDL5eyraIGv7V4jZPE0llOaiQGuPTko3no6im93k4R+YQKtxQp3EJKSiu45ekNVDdGXsww6sBeZm5ZTeH29RHzUUMGZft48KqTVcCJuExHG39HQytSRWJLhVuKFW4h85/ZwHOb9rQbUt1ePmpNRnbrMV4DeTnpis8RcZkFxWU8umIbTd3pegNGH5XNfXOO1zVBJAZUuKVo4RbS6YqzDvJRw2mYRMSdFhSX8XDxViJnt0Q2fkgO+bmZzJ0+joUrt7Orqo5Redn6gifSC1S4pXjhFq6jeXBwZD7qS5OmsXLsFJrTfEcUfBpKFXGXzuL3wp0wvD97DzWQnZ5Gkz/AvurGNhmpl+lLnki3qXBT4XaEBcVlPFS8td39ng7PR10x/gxemnQOu/sfWaRl+zz88kva2FfELTrb9Htglo9B/dLZV91Idrq33Y1/tem3SPckTeFmjJkBPIKzM8UT1tr7D3vctDw+C6gDrrfWbujsdVW4tS+04uzdvdXtHjOsupIZW47MRw16vK3HGGD+hRO0F5yIy8x/ZgPPbdzTWpgNyExjcG4GzQFLbWMzDc1BapsiF3gh2tBXpGuSonAzxniBMuAzQDmwFrjGWvufsGNmAbfgFG5nAo9Ya8/s7LVVuEWns2/ZkfJRl084m4NZuRGP1+adIu4RmitbXlXHyJa5bAtXbmftzo/xR7nAwesxpHkM4wbncOeMAvXEibQjWQq3s4HvWmsvbrl9N4C19sdhxywESqy1T7fc3gIUWmv3dPTaKty6Z/4zG1iyMfKpHb9/FzO3rGZaJ/mo6okTca+S0grm/nF9VHPiItGekSKRdaVw83R+SMyMAHaF3S5vua+rxxzh/fff54UXXgDA7/dTVFTEsmXLAGhoaKCoqIjly5cDUFNTQ1FREStWrADgwIEDFBUVsXLlSgAqKyspKipizZo1AOzdu5eioiLeeOMNp0Hl5RQVFbF+/XoAdu7cSVFREZs2bQJg27ZtFBUVsXnzZgC2bNlCUVERW7ZsAWDz5s0UFRWxbds2ADZt2kRRURE7d+4EYP369RQVFVFeXg7AG2+8QVFREXv37gVgzZo1FBUVUVlZCcDKlSspKiriwIEDAKxYsYKioiJqamoAWL58OUVFRTQ0NACwbNkyioqK8Pv9PHT1FOYM3M1RG55sPZcZH66j/4bf896gUTx6ztXcdNZsPqjdxS1rnuHRpT/hklW/Zcj6P7Qen/n+an794PcZc9eLzHjoVe79yaPcfffdrY8/8cQT3HPPPa23H3vsMb73ve+13n700Uf54Q9/2Hr74Ycf5oEHHmi9/eCDD/Lggw+23n7ggQd4+OGHW2//8Ic/5NFHH229/b3vfY/HHnus9fY999zDE0880Xr77rvv5sknP3m/d9xxB0899VTr7fnz5/P000+33p43bx6LFi1qvX3jjTeyZMmS1ttFRUX67HXjswfwwgsvUFRU1HoulyxZwo033th6e9GiRcybN6/19tNPP838+fNbbz/11FPccccdrbeffPJJffZ6+bOXdXAHNxWOJ63+Ywas+x1pVTsB8NZWOrcPfODcrvnIuX3wQ+d29R4GrPsduz/YzvVPruXEeb/mqmu/os9eC332dN3riiNzkPqOiXDf4d1/0RzjHGhMEVAEMGDAgJ61LIV95vhhNGzP4/H7ZzP/mQ0s+7Dt47W+DF46+lP8+eRrOWlPGZ9bu4gvVuzgleZslk2ayr6wY0s/quH9neXkNlRQUlqhb9kiLjDvwomMSK/nh+8u7fZr1Ddbtuyt5gsL1zBxQiUXD2voxRaKuJuGSqVT1yxcw2s7qtp9fFDtAS7a+jozytZ0mI/qMTBpaK7muoi4RE8D7nPSvQwbkElzwGpzX0lpyTLHLQ1nccIFwIc4ixO+aK3dHHbMbOBmPlmcsMBae0Znr63CLTZaA+4rqtlf03RE12dX8lFzMzz8/BptGyDiBqH9Ij881NhuckskPq+hYFh/6pr8+DyGvJwMbewrKSkpCjdoXTX6MM52IL+11v7QGPM1AGvtYy3bgTwKzMDZDuQr1tpOKzIVbrFXUlrBf/1hLc3tzFGONh8VoH9mGjdMG6sFDSIusaC4jIf/ubXTYPucdC/jhvTjUH0Tu6rqSfd68AeDpHk85Gam8T/KR5UUkTSFW6yocOs7C4rLeKR4K+3t6hRNPmqIz2u45bxjVMCJuEA0w6ifOiqb/lk+tuw9RFPAkpHmwRiwFpr8QYwBYww56V59uRNXU+Gmwq3PhTb23bK3OnL+4WH5qK+NnsyLBdOOyEcNyfJ5+Pq52sBTJNmVlFbwzWffZH+dv839w/pnMLhfBvXNAd7bV4vXQHqas8l3cyDYulecz0Nrz/7IARn84LLJ6oUT11HhpsItrkpKK7h90UYqa5sjPt6/oYbPbH2DmVtWtclHbUrzRTz+Nu0LJ+Iqh2/uu3bnx3gMeD3OVIr6sE3BQ1sLWJwFTiPzsrWQQVxHhZsKt4SwoLiMX736HvXtTIQzNsipH77L7NJVneajgubCibjVjIdeZdu+WrzGYAw0hG3wa1r+J/R/VeOH5JCfm9ma5KDFDOIGKtxUuCWcjlIZAIZWVzKzk3zUEI+BWy9QL5yIW5SUVnD74k3UNPoJBC3NgU/+fykUzmKt82//uKP7s/dgPdkZPnxeQ5bPS31zQFuKSFJT4abCLWEtKC7j5yu20dzOcrNI+aj/mHAWB7L6H3GsthQRcY/w4VNrLbsPNhyxKnVIv3T6Z/nYV93IkNwMstM/2StSW4pIMlPhpsIt4c1/ZgPPbdrT4Z5P0eajAgzO8fHTK0/WRVrEJRYUl/HYyu3UNQXwGBiU46N/VjrNAUtdk59h/TMxYdeCQ/VNlB+oJz83g4N1zTQGnG1FbirUIidJfCrcVLgljZLSCr7z3NuUH2g/8iansY7z31vLrC2rCXi8LJs0lVfGnUZ9embE4y87+WgeunpKrJosIn3o8IUMobltFdUNbXrctlZUEwxawLRsI+KsTg0GwetxFj6MHZTNXTOP1Rc8STgq3FS4JaWS0gq+8uTayGG0ANYyee9WZpWu4qS9W1k5dgrLJk3l/bzhEQ/XalQRdyopreDepZvbzHHbub+ONAMYg8cYAkFLU8BZ5GBw9okMWhiY7eOn2thXEowKNxVuSW1BcRkPFW9tv4Aj+nzUEPXCibjL4T1xB+qaKKuoxuf1YDA0+gOtc+QMkOnzEgxajAdOGZXH00VnxbX9IuFUuKlwc40FxWX8rHhru493JR8V4OyxeTw995xYNVdE4qSktIK5f1xP0Fq8xrTZUsRjICPNi7WWgLUM65/J9y85QduJSMJQ4abCzXXmP7OB5zbu6bAXbuSBvcyKIh/VC/zm+tN1kRZxmQXFZfyi5D0CQUvQ2tYeN5/HkOb1tPa4jTkqm7rmoLYTkYShwk2Fm6tN+3Ex5Qcb2308lI86a8tqsvyNLJs0leJ28lFBvXAibhIaQt1aUc3B+mYCAUua11l9GprjNqRfBk2B4BHbieTnZmoIVeJChZsKt5Qw46ESSj+qbf+AlnzUmVtWc+audzrNRx2U7ePBq7SliIhbhDKUt1c614nQqtLvPP8OA7N8bbYTsdZysL6Zf915fmvxp2FU6Ssq3FS4pZzO5sKF8lFnlK3mUEYOL02axr/GnkJjWvqRx2amseDqU3ShFnGpax5//YjtREI9bnOnjztixaqGUSXWVLipcEtZnfXCdTUfVatRRdwn0nYioeIs0h5xGkaVWFPhpsJNiD4f9YJt/2b7oBEd5qNqTzgRd4m0sW9hQT7THljR4TCqSCyocFPhJmE6W5EaykedtWU1g2s7zkcdOTCTH1x6ooZMRFyqo2FU9bhJrKhwU+EmEZSUVnDj/66nrjnY7jHj9pc7+ajvb2TD8AKWTZrK5qHjI+ajZnhh4XXaVkTETToaRtW/dYmVXi/cjDE5QL21NmiMmQgUAC9Za5t71tTYUOEmnblm4Rpe21HV7uNt8lGNh2UF0zrMRy0YmsPL8wtj01gR6VPtDaOKxEosCrf1wKeBPOB1YB1QZ639Uk8aGisq3CRanc2D62o+qhYziIhIV8WicNtgrZ1ijLkFyLLW/sQY86a19pSeNjYWVLhJVy0oLuOR4q0EOjhG+agiIhILsSjc3gRuBB4Cvmqt3WyMedtae2LPmhobKtykJxYUl/HIP7cSaOefRlfyUbN9Hn75pVM1zCIi2thX2hWLwu1c4JvAamvtA8aYccCt1tp5PWtqbKhwk96woLiMR1/ZRlN7FRxt81H/kz+WZQXTeHP4pCPyUQFyM7z8/JopulCLpKDDFz3sr23k49pm+mV4mTi0v4q4FKdVpSrcpJd1Nhcus7mBc3dsYFZp5/moWsggknrCtxmpbmhm94EGbMsmRf6A81uWz8PXzx2vPSNTUK8VbsaYh621txpjXoAjt8Gy1s7pfjNjR4WbxEpJaQU3/2k9NU3tbCnShXzUjDQPNxXqIi2SCsI39t2+rwZ/0OIPBAlYMDj/B2sAj8fwjfOP0XUhxfRm4XaqtXZ9y1DpEay1r3azjTGlwk1ibUFxGQ//cyvBDjqsu5KP6gFuVTqDiGuF97iV7j2E12NoaNlT0hiwLQVcWstQ6lvfvTi+DZY+FdOhUmNMHjDKWvtWdxrXF1S4SV/qrIjraj6q4rVE3Cd8jtueA/U0By3NLfNnQ4Wbx4DPa/AH4TdfPk0LGVJILBYnlABzgDRgI7APeNVae1v3mxk7KtwkXjqbC5dfvZ+ZZWu4cOsbbB80gpcmTeXfI4+PmI/aL93Do1/UilQRtwitKt1aUU11g59Gf9spFz6PAQNpHsOQ3EylN6SQmGwHYq09xRhzA05v238bY96y1k7uaWNjQYWbxFNJaQXfWfIW5Qcb2z0mPB91SG0VL02cyvKJkfNRfR7DLZrzIuIqJaUV3PP8O+yqqscAXg8YYwhaGD4gk/Q0j/JSU0gsCre3gYuA3wPfttauVeEmEp3O4rW6ko9qgEu1sa+IaywoLuOJVTuobQqQk+7lhmljeXZ9eetChhBrLQfrm/nXnefHsbUSK7Eo3K4E7sHZx+3rLfu4/Y+19vM9a2psqHCTRNRZOkNX8lHPHpvH03PPiW2DRSQuwhcyhKjHzd20j5sKN0lg0WwpEspHnbx3G/8ae0qH+aiDsn08eNXJmvsi4hKHb9arOW7uF4set5HAz4GpONvNrAK+Ya0t70lDY0WFmySLzhYzhOej7skdzLJJU1nzqZMi5qNqNaqIe4QWMpRX1TFSq0pdLxaF2z+APwFPtdx1LfAla+1nut3KGFLhJsmmswIulI86a8tqRh/Y224+aprHcMyQHO6aeawu8iIiSSIWhdtGa+3Jnd2XKFS4SbJaUFzGL0reO2KbgHAjD+xl5pY1nLd9XYf5qINzfPz0Sg2hiogC7hNdLAq3YuBJ4OmWu64BvmKtvaC7jYwlFW7iFjMeKqH0o9qIj2U0N1K4Y32bfNR/HnMG1Rk5Rxzr9RjmTB6m1agiKUhz5hJfLAq30cCjwNk4c9zW4Mxxe78nDY0VFW7iJguKy/jVq+9R39wL+aheWHjd6bpYi6QQrVJNfFpVqsJNXKqktILbF22ksrY54uNdyUfN9nn52rnjtKBBxOXCA+5DtC9cYolFj9sQ4L+AMTixVwBYa/9vN9sYUyrcJBWUlFZw/0vvUlZRc0ROqrFBpnxYyuzSVUyq3MmKcafzUsHUiPmouRkefn6NorVE3KorPW6aCxcfsSjc1gD/AtbDJ/uHWmv/0t1GxpIKN0klJaUV3L54E5U1TREfD89H3XHUCJYVRM5HHTkggx9cNlkXaRGXiXaOm+bCxU+frCpNZCrcJBUtKC7jF69sozEQ+d90V/JR+2emccO0sRpGFXGJaPaF01y4+IlF4fYDYI21dllPG9cXVLhJKgtdoN/Yvp/2NhXpSj5qutdw83kKuRdxO82Fi59YFG7VQA7QCDTjZF1ba+2RX9UTgAo3EceC4jIWrNiG//BJcC1C+agzt6wm2Ek+6mUKtxdxNfW4xY9WlapwE2ljQXEZj76yjaZ2hlGxlhP3bmP2llWctKeMlWOnRMxHLRjaT6kMIi6lOW7xE4set0hfsw8C71tr/V1sX8ypcBOJrKS0gu889zblBxraPSaUj3px2WvszR3UJh/VY8AYw8T8ftw5o0AXcxGX6UlGqlakdl8sCrfXgSnA2y13nQhsAgYBX7PWLu9mW2NChZtI5zpbjeoNBjhj1zvMLl3VJh/149w8ghY8HpgwRD1wIqLeup6KReH2DPB9a+3mltvHAXcA3wf+2tUVp8aYo4A/4+wLtxO4ylpbFeG4nUA1zhYk/mjflAo3kegtKC7jiVU7ONTQfud5pHzUzaMKMF4v+bmZujiLpDjNj+uZPg2Z785WIcaYnwAfW2vvN8bcBeRZa++McNxO4DRrbWVXXl+Fm0j3lJRWMO+ZN9st4kL5qLO3rCbb38hLBVPZenohOfmDdXEWSWFakdozXSnc0jo/BIAtxphfAc+03P4CUGaMycBZZdpVlwCFLb//HigBjijcRKRvFRbk89Z3L46Yj+o10OjLYPnEc3ilYGpLPuoqrv/9Pfx7zEkwrT8cd1wcWy8i8TIqL/uIHrf65gAj87Lj2Cp3irbHLQu4EZiGsxXIKuCXQAOQba2t6dJfaswBa+3AsNtV1tq8CMftAKpwgu0XWmsf7+A1i4AigNGjR5/6/vvvd6VJItKOULTW1n01BIPg9YDXeAhiGT4gi4GNNVy8fS037t8IAwbAlVfCRRdBZmbr8zVhWcTdNMetZxJiOxBjTDEwLMJD3wZ+H2XhNtxau9sYkw/8A7jFWruys79bQ6Uiva+ktIIHXi6lrKIGn9cwNDeDNK/nk4vzxMHw2muwaBG8/TbMns1rJxdy57qDNPkDVDf4afQH8XoMNxWO14a+Ii7T3RWp+nIXmzluE4AfA8cBrTtzWmvHdbOBW4BCa+0eY8zRQIm1dlInz/kuUGOt/Wlnr6/CTSR2oro4794Nf/kLb//qKbb0H8aSY85hw6gTsF4vAWvxGMPCaxVsL5Lq1FPniMUct98B/w08BJwHfAVnyLS7lgL/B7i/5c/nDz/AGJMDeKy11S2/XwTc14O/U0R6QWFBfucX1OHD4ZZbuOXQRAreeYPL317B3Nf/wvKCaRRPOot9Gf1YuHJ7Sl2YReRIC1dux+c1rXPjstPTqGvy6/rQgWgLtyxr7T+NMcZa+z7wXWPMv3CKue64H3jWGPNV4APgSnCGRoEnrLWzgKHAkpYVKmnAn6y1L3fz7xORODh6yACKx55GyfjTGfvxh1z07ioe+cuP2DSigDdqzgN7ZsR8VBFJDbuq6hiY5WtzX5bPS3lVXZxalPiiLdwajDEeYKsx5mbgQ6DbpbC1dj9wQYT7dwOzWn7fDpzU3b9DROJv7vRxbPigioC17Bg0gsemfoHfnzaHz5ZvoGj1s/CFFXDFFTB7NuTkaK6LSIrRatSu80R53K1ANjAPOBW4DmeIU0SkXYUF+dxUOB6PMTQHgngNZB3Vn5WnXED9H5+G//f/YP16+Oxn2X7bt1n42+Xs3F/DxzWN/Hvnfub+cT0Lisvi/TZEJEbmTh9Hc8BS1+THWufP5oBl7vRuTaFPCQqZF5GY63RBQ0UFv77tZ5ywdgXlWXm8fOyn+ffYyTSYNKy1TMjPpbrRr144ERfqST6qW/TaqlJjzMPW2luNMS/g7KXWhrV2TvebGTsq3ESSz7QHVnDwUB1T3n+bme+uYlTVHpZPOItlE86heuAgjsnvl7IrzkTE3XqzcDvVWrveGHNupMetta92s40xpcJNJPlc8/jr/HvnfnxeDwbDiKq9nL/5XxRuX0fpsHH8Z+rFlH3qOGr9QdK9HgZmp2sunIi4Qkw24DXGDAGw1u7rQdv6hAo3keRTUlrB3D+uJ2gtXmOwFhoDQbL9jVzwwUau2P4aGU0N/PO4aTw7fAqDRwxJ6X2fRMQ9ulK4dbg4wTi+a4ypBEpx8kn3GWPu7Y2GioiEhC9k8ActaV5DutfQlJ7J26efx0+/fC9/nH0DAz98n1//5ft8tfgPfGrvTrJ9Xnxew8KV2+P9FkREYq6z7UBuBaYCp1trdwAYY8YBvzLGzLfWPhTj9olICpl34UQmjxzYOlE5J93L/tomvB6DBd4d/Cle+vSXKEj3c8F7a/nyCwupy8zhXycX8uqnTol380VEYq6zOW5vAp+x1lYedv8QYLm1NiGvlBoqFXGPw1ecVdU20hy0ZKenYYJBCna+w5nrVzCpYicnFH3R2Rdu9GjtCSciSaM3Fye8Y609oauPxZsKNxH3ai/b8P6zBnHOpldh6VI+HDKKB3JP5N1jJpORka55cCKS0HptjhvQ1M3HRERiorAgn/vmHE9+biYH65vJz83kvjnHc870yXDLLfDiizw1+ERmvrmcHz/5HS56/UWGNtdqHpyIuEJnc9xOMsYcinC/ATJj0B4RkU51GHSfns7fRpzEqmtPY8S+XUzdWMJdv7mH0jHH8/djpyofVUSSmpITRMR1rnn89Tb5h5mNdUzetIqL/rOKM8cPbpOPKiLSnr6aK9ubQ6UiIknn8PzDj006/zjxvCPyUfnxj2Hr1ng3V0QSUGg+bUV1AwOzfFRUN3Dv0s2UlFbEtV3qcRMRV+o0/3DfPliyxPkZMQKuvBLOOw/S0+PXaBFJGIf33APUNfnxeQx5ORm92gsXk+SEZKLCTUSi5vfDypWwaBG89x5ceilcdhkcfXS8WyYicTTtgRUMzPJhwubEHqpvovxAPWMG5fRqcouGSkVEopWWBuefD7/6FTz+ONTXw5e+BLfdBmvWQDAY7xaKSByMysumvjnQ5r6PqhvxeTzOPpLGkJ2e1ucr1lW4iYiEjBkD3/wmvPgiTJ8Ojz4Kl18OTz0FBw/Gu3Ui0ocOnytb1+SnOWAZ2j+jzXFZPi/lVXV91q7OtgMREUk9WVnOkOkll8A77zjDqJdcAoWFzly4447TliIiLldYkM990GaubLrXQ1OgbS98fXOAkXnZfdYuFW4iIu0xBk480fmpqoIXXoC774YBA5wC7qKLIDNT8VoiLnX4npGhlaZ1Tf42c9zmTh/XZ23S4gQRka4IBuG112DxYnjrLbadfi53mYlUDR7Wq5OVRSQxdbpivRu0qlSFm4j0hd27+d03H2Ty+lf5aOgo/nXK+fxn/GRq/Jb83EyeLjor3i0UkSTQlcJNQ6UiIt01fDi/OXk2g0+fzclbN3D+v1/m8//8E2smT2f5BBVtItKxUO+db8iYE6N9jgo3EZEeGJWXTUV1A+uPO4v1x53F8IoPOGP9Ch748w+g+d/OXLhTTtFiBhFpIzRfzuc1YIP+aJ+n7UBERHrg8C0Dtg0czu8Lv8THf1oMJ58MP/oRfOEL8OyzUFsb7+aKSIJYuHI7Pq9pk8wQDfW4iYj0QKQtA+ZOH8enC/Lh1LFw1VVONuqiRc4mvxdd5ITcT5gQ76aLSBztqqpjYJavy89T4SYi0kOHbxnQhjFw2mnOTygfdd485aOKpLjQNIuu9rhpqFREpK8MGQJFRc5+cF/8Ijz/PHz2s/CLX8CePfFunYj0ofBpFl2hHjcRkb4Wykc9/3zYuRP+8hcnH/Xkk51h1LPOAo++V4u4Wfg0C4wn6npM+7iJiCSC+nr4+9+dRQx1dfD5z8OcOU5Kg4i4mvZxExFJNspHFZEoqHATEUkk4fmoBw7A0qUR81FFJDVpEoWISKIaOBC+/GV47jn4+tfhlVdg9mz42c/ggw/i3ToRiQP1uImIJDqPB845x/nZvRv++lf46ledveCuvBKmTwevN96tFJE+oB43EZFkMnw43HwzvPgifO5z8NRTzp9PPAGVlfFunYjEmHrcRESSUXo6zJzp/JSVweLFTu/bWWcpH1XExbQdiIiIW9TUwLJlzopUY5w94WbPhpyceLdMRDrQle1ANFQqIuIW/fo52ajPPgt33gkbNjjJDD/6EWzdGu/WiUgv0FCpiIjbGAOnnur87NvnrEr9xjfg6KOdYdTzz1c+qkiSUo+biIibDRkC//Vfzn5wX/qS86fyUUWSlnrcRERSgfJRRVxBixNERFJVKB910SJnYcMVVygfVSQOlFUqIiKdC89H3bxZ+agiSUCFm4hIqjMGTjjB+Tk8H/WKK+Dii5WPKpIgNKFBREQ+cXg+akkJzJqlfFSRBKEeNxEROVKkfNQbboBjjlE+qkgcxaXHzRhzpTFmszEmaIxpdzKeMWaGMWaLMWabMeauvmyjiIi0COWj/u1vykcVibN4DZW+A1wOrGzvAGOMF/gFMBM4DrjGGHNc3zRPRESOEMpH/e1v4eGHoaLC6X27+24npcGFuxSIJJq4FG7W2nettVs6OewMYJu1dru1tgl4Brgk9q0TEZFOTZwI3/oWvPCCE2j/4x/DF77gxG3V1sa7dSKulciLE0YAu8Jul7fcJyIiiUL5qCJ9KmaLE4wxxcCwCA9921r7fDQvEeG+dvvhjTFFQBHA6NGjo2qjiIj0EuWjivSJmBVu1toLe/gS5cCosNsjgd0d/H2PA4+Dk5zQw79bRES6K5SP+pWvwMqVsHixs53IJZfA5Zc7xZyIdEsibweyFphgjBkLfAhcDXwxvk0SEZGoheejvv++8lFFekG8tgO5zBhTDpwNvGiM+XvL/cONMcsArLV+4Gbg78C7wLPW2s3xaK+IiPTQpz4Ft90GL74I554Lv/gFXHaZs7XIwYPxbp1I0lDIvIiI9D1rP8lHffVVp5i78ko4/njlo0rKUci8iIgktkj5qN/6FvTv7xRwykcViUiTC0REJL7C81FvvFH5qCIdUI+biIgkBuWjinRKPW4iIpJ4Ds9H/eMflY8qgnrcREQkkYXyUWfOhLIyZ0+4K6+EM890EhtOOUWLGSSlaFWpiIgkl5oaWLbMWZFqjLMn3KxZTvyWSBLqyqpSDZWKiEhyiZSP+rnPOfmoZWXxbp1ITGmoVEREklOkfNRbb1U+qriaetxERCT5hfJRX3gBrr3W2Rfus591Ehr27Il360R6jXrcRETEPbxeOO8850f5qOJCWpwgIiLuVl8Py5c7c+JqauDzn4c5c5yNf0USgCKvREREQrKy4JJLnGItlI966aXKR5WkpMJNRERSQ6R81G9/G3JzlY8qSUMD/SIiknpC+ahLljj5qK+++kk+6vvvx7t1Iu1Sj5uIiKSuw/NRlyxxVqcqH1USlHrcREREwMlHvekmJx91zhzlo0pCUo+biIhIuPR0mDHD+Tk8H/XKK2HKFC1mkLjRdiAiIiKdCc9HBaeAUz6q9BJllYqIiPSm8HzUu+5SPqrEjYZKRUREohWej1pZqXxU6XPqcRMREemOwYPhhhuOzEd99FFnhapIDKjHTUREpCci5aNeey2cdJLTC6d8VOlFWpwgIiLS25SPKl2grFIREZF4OjwfdfFiuOwyZ0Nf5aNKD6hwExERiZXwfNSDB5WPKj2mQXcREZG+MGAAXHed8lGlR9TjJiIi0pc6yke94go491zlo0q71OMmIiISL4fno/7v/zob+/7618pHlYjU4yYiIhJvykeVKGk7EBERkUQUykddvBisVT6qiymrVEREJNmF8lH//Ge4+254803lo4qGSkVERBKaMc5Q6ZQpbfNRhw1zeuEuuED5qClEPW4iIiLJIjwf9brrnD+Vj5pS1OMmIiKSbJSPmrK0OEFERMQNGho+yUetrlY+ahJRVqmIiEiqycx0CrXPfQ7+8x9YtAguvdTZ0Ff5qK6hwk1ERMRNjHGKtOOPVz6qC2kAXERExK3ay0d98EHloyYp9biJiIi4nfJRXUM9biIiIqlE+ahJTT1uIiIiqSg8H3XrVuWjJgltByIiIiKO2lp48cVP8lGvuAJmz1Y+aowpq1RERES6LienbT7qxo3KR00wGioVERGRtpSPmrDU4yYiIiLtOzwf9W9/Uz5qHKnHTURERDoXno/6wQfOPLjrroPJk5WP2oficoaNMVcaYzYbY4LGmHYn4xljdhpj3jbGbDTGaLWBiIhIIhg9Gm67zVnIcN558MtfOvFaf/gDHDgQ79a5Wrx63N4BLgcWRnHsedZabSwjIiKSaCLlo152GUyf7qxIPeEEbSnSy+JSuFlr3wUw+o8pIiKS/CLlo37nO842IqF81KyseLfSFRJ9MNoCy40x640xRR0daIwpMsasM8as27dvXx81T0RERNoIz0e96SZYudLZC075qL0iZj1uxphiYFiEh75trX0+ypeZaq3dbYzJB/5hjCm11q6MdKC19nHgcXA24O1Wo0VERKR3KB81JuKanGCMKQFut9Z2uvDAGPNdoMZa+9POjlVygoiISAJqaoJXXnHmwu3e7cyHu/RSGDIk3i2LK1ckJxhjcowxuaHfgYtwFjWIiIhIMkpPd+a7PfEEPPKIs7nvVVfBnXfCunVOzJZ0KF7bgVxmjCkHzgZeNMb8veX+4caYZS2HDQVWGWM2Af8GXrTWvhyP9oqIiEgvmzDBidX629/g1FPhJz/5JG6rpiberUtYCpkXERGR+LMW3nzTGUZ9/XX4zGecuXATJ8a7ZTHXlaFSJSeIiIhI/B2ej/r888pHjSBh57iJiIhIiho8GL76VScf9ctfVj5qGPW4iYiISGLyeqGw0PlRPiqgOW4iIiKSTBoaYPlyePZZOHTImQc3Zw4MHBjvlnWb5riJiIiIO7WXj/rpTzu9cC7PR1XhJiIiIsknRfNRU2tgWERERNwnhfJR1eMmIiIi7hCej7pnjyvzUdXjJiIiIu5z9NFw443OViKXXAJ/+pMzL+7Xv4Z9++Ldum5Tj5uIiIi4Vygf9eKLYetWZ0uRq66CM85w5sKdempSLWbQdiAiIiKSWmpr4cUXnSLOWmcYdfZsZ2FDHHRlOxANlYqIiEhqycn5JND+7rth0yZnGPVHP4Kysni3rkMaKhUREZHUFJ6Pun8/PPdcwuejqsdNREREZNCgpMhHVY+biIiISEh7+agnnuj0wp19dlzzUbU4QURERKQjoXzURYuclIZezkdVVqmIiIhIbwnlo86ZE/d8VPW4iYiIiHTVwYPOfLjFi51Vqj3IR9V2ICIiIiKxNGAAXHst/PWvcPPNbfNRd+6M2V+roVIRERGR7vJ4nAULZ5/9ST5qURGMH+/0wvVyPqp63ERERER6Q3g+6qWXOvmon/0sPP54r+WjqsdNREREpDfFMB9VixNEREREYq22FpYtc1akBoNOAdeSj6rtQEREREQSSWjl6RVXwJtvOr1wjz0Gn/lMl15GhZuIiIhIXzk8H3XZsi49XYsTREREROJh0CAnTqsLVLiJiIiIJAkVbiIiIiJJQoWbiIiISJJQ4SYiIiKSJFS4iYiIiCQJFW4iIiIiSUKFm4iIiEiSUOEmIiIikiRUuImIiIgkCRVuIiIiIklChZuIiIhIklDhJiIiIpIkVLiJiIiIJAljrY13G3qdMWYf8H4M/4rBQGUMXz9Z6Dw4dB4cOg8OnQeHzoPOQYjOg6Oj8/Apa+2QaF7ElYVbrBlj1llrT4t3O+JN58Gh8+DQeXDoPDh0HnQOQnQeHL11HjRUKiIiIpIkVLiJiIiIJAkVbt3zeLwbkCB0Hhw6Dw6dB4fOg0PnQecgROfB0SvnQXPcRERERJKEetxEREREkoQKt3YYY44yxvzDGLO15c+8CMeMMsa8Yox51xiz2RjzjbDHvmuM+dAYs7HlZ1bfvoOeMcbMMMZsMcZsM8bcFeFxY4xZ0PL4W8aYKdE+N1lEcQ6+1PLe3zLGrDHGnBT22E5jzNst/+3X9W3Le1cU56HQGHMw7LN+b7TPTSZRnIc7ws7BO8aYgDHmqJbH3PR5+K0xpsIY8047j6fCtaGzc5Aq14bOzkOqXBs6Ow+9e22w1uonwg/wE+Cult/vAh6IcMzRwJSW33OBMuC4ltvfBW6P9/vo5nv3Au8B44B0YFPofYUdMwt4CTDAWcAb0T43GX6iPAfnAHktv88MnYOW2zuBwfF+H310HgqBv3Xnucny09X3AnwOWOG2z0PLe5kOTAHeaedxV18bojwHrr82RHkeXH9tiOY8HHZsj68N6nFr3yXA71t+/z1w6eEHWGv3WGs3tPxeDbwLjOirBsbQGcA2a+12a20T8AzO+Qh3CfAH63gdGGiMOTrK5yaDTt+HtXaNtbaq5ebrwMg+bmNf6Ml/T7d8FqDr7+Ua4Ok+aVkfs9auBD7u4BC3Xxs6PQcpcm2I5rPQHtd8FqDL56HH1wYVbu0baq3dA06BBuR3dLAxZgxwCvBG2N03t3SV/zbSUGsCGwHsCrtdzpEFaXvHRPPcZNDV9/FVnF6GEAssN8asN8YUxaB9fSXa83C2MWaTMeYlY8zxXXxuMoj6vRhjsoEZwF/C7nbL5yEabr82dJVbrw3Rcvu1IWq9dW1Ii0XjkoUxphgYFuGhb3fxdfrh/Ie41Vp7qOXuXwHfx/mP8n3gQeD/dr+1fcpEuO/w5cftHRPNc5NB1O/DGHMezsV5WtjdU621u40x+cA/jDGlLd/Kkk0052EDTlxLjXHmcj4HTIjyucmiK+/lc8Bqa234N3C3fB6i4fZrQ9Rcfm2IRipcG7qiV64NKd3jZq290Fp7QoSf54GPWrr3afmzItJrGGN8OEXb/1pr/xr22h9ZawPW2iDwa5yu4WRRDowKuz0S2B3lMdE8NxlE9T6MMZOBJ4BLrLX7Q/dba3e3/FkBLCG5/vuH6/Q8WGsPWWtrWn5fBviMMYOjeW4S6cp7uZrDhkJc9HmIhtuvDVFJgWtDp1Lk2tAVvXJtSOnCrRNLgf/T8vv/AZ4//ABjjAF+A7xrrf3ZYY8dHXbzMiDiapMEtRaYYIwZa4xJx/mwLT3smKXAl1tWkJ0FHGwZUo7mucmg0/dhjBkN/BW4zlpbFnZ/jjEmN/Q7cBHJ9d8/XDTnYVjLvwWMMWfgXFf2R/PcJBLVezHGDADOJex64bLPQzTcfm3oVIpcGzqVIteGqPTmtSGlh0o7cT/wrDHmq8AHwJUAxpjhwBPW2lnAVOA64G1jzMaW532r5ZvFT4wxJ+N0/+4E5vZp63vAWus3xtwM/B1n9c9vrbWbjTFfa3n8MWAZzuqxbUAd8JWOnhuHt9EjUZ6De4FBwC9brk1+6wQIDwWWtNyXBvzJWvtyHN5Gj0V5Hq4Avm6M8QP1wNXWWS7lis8CRH0ewPmSttxaWxv2dNd8HgCMMU/jrBYcbIwpB/4b8EFqXBsgqnPg+msDRHUeXH9tgKjOA/TitUHJCSIiIiJJQkOlIiIiIklChZuIiIhIklDhJiIiIpIkVLiJiIiIJAkVbiIiIiJJQoWbiIiISJJQ4SYiIiKSJFS4iYiIiCSJ/w8QZMyLntQvoQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "import statsmodels.api as sm\n",
    "#ols(\"Diagnosis ~ radius1\", data).fit().summary()\n",
    "fitted=ols(\"Diagnosis ~ radius1\", data).fit().fittedvalues\n",
    "plt.figure(figsize=(10,6))\n",
    "sns.residplot(x=fitted, y='Diagnosis', data=data.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation between the residuals and the independent variable is a strong indication that the true relationship between the two variables is not correcly modeled. After all, from a purely predictive point of view, we are using a linear regressor which takes the form:\n",
    "\n",
    "$$f:\\mathbb{R} \\to \\mathbb{R}$$\n",
    "\n",
    "while the values `Diagnosis` variable belong to the set $\\{0,1\\}$ and we would need instead a function with the following form:\n",
    "\n",
    "$$f:\\mathbb{R} \\to \\{0,1\\}$$\n",
    "\n",
    "However, the linear regressor cannot directly predict **discrete values**. \n",
    "\n",
    "**In practice, while with a linear regressor we wanted to predict continuous values, now we want to assign observations $\\mathbf{x}$ to discrete bins (in this case only two possible ones). As we will better study later in the course, this problem is known as classification.**\n",
    "\n",
    "## From Binary Values to Probabilities\n",
    "If we want to model some form of continuous value, we could think to transition from $\\{0,1\\}$ to $[0,1]$ using probabilities, which is a way to turn discretized values to \"soft\" values indicating our belief in the fact that `Diagnosis` will take either a $0$ or $1$ value. We could hence think to model the following probability, rather than modeling `Diagnosis` directly:\n",
    "\n",
    "$$P(Diagnosis=1| radius1)$$\n",
    "\n",
    "However, even in this case, a model of the form:\n",
    "\n",
    "$$P(Diagnosis=1|radius1) = \\beta_0 + \\beta_1 radius1$$\n",
    "\n",
    "Would not be appropriate. Indeed, while $P(Diagnosis=1| radius1)$ needs to be in the $[0,1]$ range, the linear combination $\\beta_0 + \\beta_1 radius1$ will naturally output values **smaller than $0$** and **larger than $1$**. How should we interpret such values?\n",
    "\n",
    "Intuitively, we would expect to $P(Diagnosis=1| radius1)$ to assume values in the $[0,1]$ range for intermediate values (say `radius` $\\in [10,20]$), while for extremely low values of (say `radius` $<10$) the probability **should saturate to $0$** and for extremely large values (say `radius` $>20$) the probability should saturate to 1.\n",
    "\n",
    "when `radius1` takes large values (say larger than $20$), we expect **probability to saturate to $1$**.\n",
    "\n",
    "In practice, we would expect a result similar to the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "sns.regplot(x=data['radius1'],y=data['Diagnosis'], logistic=True, ci=None, line_kws={'color':'red'})\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be noted, the function above is not linear, and hence it cannot be fit with a linear regressor. However, we have seen that a linear regressor can be tweaked to also represent nonlinear functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Logistic Function\n",
    "Similarly to polynomial regression, we need to find a **transformation of the formulation of the linear regressor to transform its output into a nonlinear function of the independent variables**. Of course, we do not want *any* transformation, but one that has the previously highlighted properties. While different functions have similar characteristics, in practice the **logistic function has some nice properties that, as we will se in a moment, allow to easily interpret the resulting model in a probabilistic way**. The logistic function is defined as:\n",
    "\n",
    "$$f(x) = \\frac{1}{1+e^{-x}}$$\n",
    "\n",
    "and has the following shape:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the logistic (sigmoid) function\n",
    "def logistic_function(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# Generate x values\n",
    "x = np.linspace(-10, 10, 100)  # Creating 100 evenly spaced values from -6 to 6\n",
    "\n",
    "# Calculate y values using the logistic function\n",
    "y = logistic_function(x)\n",
    "\n",
    "# Plot the logistic function\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x, y, label='Logistic Function', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Logistic Function (Sigmoid)')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the function has the properties we need:\n",
    "* Its values are comprised between $0$ and $1$;\n",
    "* It saturates to $0$ and $1$ for extreme values of $x$.\n",
    "\n",
    "## The Logistic Regression Model\n",
    "In practice, we define our model, **the logistic regressor model** as follows (**simple logistic regression**):\n",
    "\n",
    "$$P(Diagnosis=1|X) = f(\\beta_0 + \\beta_1 X) = \\frac{1}{1+e^{-(\\beta_0 + \\beta_1 X)}}$$\n",
    "\n",
    "Or, more in general (**multiple logistic regression**):\n",
    "\n",
    "$$P(y=1|\\mathbf{x}) = \\frac{1}{1+e^{-(\\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n)}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is easy to see that:\n",
    "\n",
    "$$p=\\frac{1}{1+e^{-x}} \\Rightarrow p+pe^{-x} = 1 \\Rightarrow pe^{-x} = 1-p \\Rightarrow e^{-x} = \\frac{1-p}{p} \\Rightarrow e^{x} = \\frac{p}{1-p}$$\n",
    "\n",
    "Hence:\n",
    "\n",
    "$$e^{\\beta_0+\\beta_1x_1 + \\ldots + \\beta_nx_n} = \\frac{P(y=1|\\mathbf{x})}{1-P(y=1|\\mathbf{x})}$$\n",
    "\n",
    "We note that the term on the right is the odd of $P(y=1|\\mathbf{x})$. We recall that the odd of $P(y=1|\\mathbf{x})$ is the number of times we believe the example will be positive (observed $\\mathbf{x}$) over the number of times we believe the example will be negative. For instance, if we believe that the example will be positive $3$ times out of $10$, then the odd will be $\\frac{3}{7}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By taking the logarithm of both terms, we obtain:\n",
    "\n",
    "$$\\log \\left(\\frac{P(y=1|\\mathbf{x})}{1-P(y=1|\\mathbf{x})}\\right) = \\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n$$\n",
    "\n",
    "The expression:\n",
    "\n",
    "$$\\log \\left(\\frac{P(y=1|\\mathbf{x})}{1-P(y=1|\\mathbf{x})}\\right)$$\n",
    "\n",
    "Is the logarithm of the odd (log odd), and it is called **logit**, hence the **logistic regression** is sometimes called **logit regression**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The expression above shows how a logistic regressor can be seen as **a linear regressor (the expression on the right side of the equation) on the logit (the log odd)**. This paves the way to useful interpretations of the model, as shown in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistical Interpretation of the Coefficients of a Linear Regressor\n",
    "\n",
    "Let's now see how to interpret the coefficients of a logistic regressor. Remember that the regression model (in the case of simple logistic regression) is as follows:\n",
    "\n",
    "$$\n",
    "\\log(\\frac{p}{1-p})=\\beta_0 + \\beta_1 x\n",
    "$$\n",
    "\n",
    "Applying what we know about linear regressors, we can write:\n",
    "\n",
    "$$x=0 \\Rightarrow \\ln(\\frac{p}{1-p})=\\beta_0$$ \n",
    "\n",
    "To have a clearer picture, we can exponentiate both sides of the equation and write: \n",
    "\n",
    "$$x=0 \\Rightarrow \\frac{p}{1-p}=e^{\\beta_0}$$ \n",
    "\n",
    "Remember that $\\frac{p}{1-p}$ is the odds that the dependent variable is equal to 1 when observing $x$ and, as such, it has a clear interpretation. For example, if the odds of an event are $\\frac{3}{1}$, then it is $3$ times more likely to occur than not to occur. So, **for $x=0$, it is $e^{\\beta_0}$ times more likely that the dependent variable is equal to 1, rather than being equal to 0**.\n",
    "\n",
    "It can be seen that:\n",
    "\n",
    "$$p=\\frac{odds}{1+odds}$$\n",
    "\n",
    "Hence, the probability of the event being true when all variables are zero is given by:\n",
    "\n",
    "$$p(y=1|x) = \\frac{e^\\beta_0}{1+e^\\beta_0}$$\n",
    "\n",
    "How can we interpret the **coefficient values**? \n",
    "\n",
    "We know that:\n",
    "\n",
    "$$odds(p|x) = \\frac{P(y=1|x)}{1-P(y=1|x)}$$\n",
    "\n",
    "We can write:\n",
    "\n",
    "$$\n",
    "\\log odds(p|x) = \\beta_0 + \\beta_1 x\n",
    "$$\n",
    "\n",
    "Hence:\n",
    "\n",
    "$$\\log odds(p|x+1) - \\log odds(p|x) = \\beta_0 + \\beta_1 (x+1) - \\beta_0 - \\beta_1 x = \\beta_1 (x+1) - \\beta_1 x = \\beta_1$$\n",
    "\n",
    "Exponentiating both sides, we get:\n",
    "\n",
    "$$e^{\\log odds(p|x+1) - \\log odds(p|x)} = e^{\\beta_1} \\Rightarrow \\frac{e^{\\log odds(p|x+1)}}{e^{\\log odds(p|x)}} = e^{\\beta_1} \\Rightarrow \\frac{odds(p|x+1)}{odds(p|x)} = e^{\\beta_1} \\Rightarrow odds(p|x+1) = e^{\\beta_1}odds(p|x)$$\n",
    "\n",
    "We can thus say that **increasing the variable $x$ by one unit corresponds to a multiplicative increase in odds by $e^{\\beta_1}$**.\n",
    "\n",
    "This analysis can be easily extended to the case of a multiple logistic regressor. Hence in general, given the model:\n",
    "\n",
    "$$P(y=1|\\mathbf{x}) = \\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n$$\n",
    "\n",
    "We can say that:\n",
    "\n",
    "* $e^\\beta_0$ is the odd of $y$ being equal to $1$ rather than $0$ when $x_i=0 \\forall i$;\n",
    "* An increment of one unit in the independent variable $x_i$ corresponds to a multiplicative increment of $e^\\beta_i$ in the odds of $y=1$. So if $e^\\beta_i=0.05$, then $y=1$ is $5\\%$ more likely for a one-unit increment of $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Geometrical Interpretation of the Coefficients of a Logistic Regressor\n",
    "Similar to linear regression, also the coefficients of logistic\n",
    "regression have a geometrical interpretation. We will see that, while\n",
    "linear regression finds a «curve» that fits the data, logistic\n",
    "regression finds a hyperplane that separates the data.\n",
    "\n",
    "Let us consider a simple example with bi-dimensional data\n",
    "$\\mathbf{x} \\in \\mathfrak{R}^{2}$ as the one shown in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lUGzb9nnuuq6IiNfFDYfZt5tyDIfZHZA5FW5dapb8otIgdpC8KXe0m2Ko+9dDWAxkToPEXF9H5T2RCXDGz80eu8ZKSBxpTm7W7YfgcJ0EFLdx556qrwObAS1Qi8jgFhQMc+6ApDz4/EnInA6Tr4aEHPPng23Jb/cH8MQlXbNvCTlw7fOQ1IteeG2N4Agd/MVTIxMgZ775fU0xfPB7WHG/mXk88xemlY3KY8gAueWrxLKsLOALwK+Bb7njmiIiPhWbDtOvh6nXDe6SCc218M7Pui9nVu2BopXHT6pqS2Hzy7DmMUgdC7NvMzNcg51tw9on4P3/NY8bK+GpK+DGN2H4bN/GJoOeZbuhKJ5lWUuA3wIxwHd6Wv6zLOtW4FaAlJSU6YsXLx7w6w429fX1REdH+zoMr9N9Bxbdt59xtkP5FvPrkWIze97AfVhdKdQf6HpsOSB5tFkuO4Lf3vexHPPvIwuiknt9mUF3324SqPe9cOHCVbZtzzjR8wY8U2VZ1nlAmW3bqyzLWnCs59m2fR9wH0BBQYG9YMExnzpkLV26FN134NB9Bxa/vW/bhvdXwtLfdo1Z1vFnZqoL4Z7Lob2l+/ilD8KEs7sN+e19H0tTDTzyc9i/rvv4xf+GSQt6fZlBd99uEqj33VvumNOeD1xgWdYe4GngNMuyHnfDdUVEZKAsyyxhnvI9iEgws01XPgUZU4/9OQ6Hy4yUGe9DEVVnBxzcbWpEdbSf+PneEhEHZ/zMzLwdFj8CMk84CSFyQgOeqbJt+4fADwEOzVR9x7btawd6XRERcZO4TFj4I5hxk0mWIhOO//zYTDjtf+C17x4xlmUqy/dGfZnZBP7xX8xertm3w5w7/ee0ZO4pcNNbZrYqPM60rUka6euoZAgY5Mc5RESkVyzLbL7vrYmXm9IS296E5HzIO733ZRh2f9C1ERxMaYqkPLPx3x8EhUD2TPMh4kZuTaps214KLHXnNUVExAci4qHgbPPRVxtfcB37/OnBf5LSkxrKoXi12USfPNqctIxO83VU0keaqRIREfdKnwxbXu4+ljldCdWxtDXBB3+E5f/sGpt6HZz9W1OsVQYN/Q8XEZFjO7jLNJd+6Wuw8T9mv9SJjD3f7Ms6LCoFJl/luRgHu8od8Nm/uo+teQwqtvkmHuk3zVSJiEjPavfD4uu7yg+sfgTmfQ1O/39mX9KxpI6BG1+HAxsBG1LHBVZbnL5qazSlL1zGm7wfiwyIkioREelZ+SbXek6f/sMsTaWMPv7nJowwH3JiCblmH9WRM1Nxw02PQhlUtPwnInI8LXWwf4PZQNze6utovKun+lJ2h/kQ94lOhcsehQmXQmQSjLsQrnoKYjN8HZn0kWaqRESO5eBueOMHsO0NcATB7Dth/l3mTTAQpI6BmHTTsuaw8ZdAfI7PQhqy0sbCRf+Apmpz8jI4zNcRST8oqRIR6Yltw9onTUIFpkL4sr+a2kbjLvBtbN4SPxyuXQIrH4bCT01CNeFiCI3wdWRDU3AYxKiMwmCmpEpEAodtmyKYvdFSD5tecB3f+3HgJFUAaRPgnN9DezOERvo6GhG/pqRKRPxbXRnUlZi+df3d+FyxHTY8D7uXwtgLYMwXzCzM8YREQPYc12Ptab1s1TKUOBxKqER6QUmViPivopWw5Gao3gPh8XDBX6HgCxDUh29ddfth8ZegbJN5vPcT83HRPyEs+tifFxQMc74CO97u2lM0fC7kntzfuxGRIU5JlYj4p/qyroQKoLkaltwIt34Iw8b3/jrlW7sSqsM2vwSnfA/STzDrlDYBbn4bKrZCUCikjAmcTeoi0mdKqkTEP9Xt70qoDnN2mLG+JFXWMSrH9HJrFfHZ5kNE5ARUp0pE/FNEgvk4Wl+bzKYUQPqU7mMTLw+8woqNB82HiHiMZqpExD/FZ8MFf4NnbwDnoSKUp/7ALMH1RXQqXPogbH0N9nwMoxdB/pkQGuX2kP1SUw1sew3e/715fMr3zL60iFjvxlG337S2iUzy7uuKeJGSKhHxXwXnwlc+hOq9EJVqEqqwfiRDSaNg3l3mI9Ds/Qj+c1vX4xdugyufNCcgvaHuAHz+JHzyNwiNhjN+BqPP1mlC6e7gHqjaDeFxkFzQv69zP6CkSkT8lyMI0saZD3+yfx0Urzb7tTJn+F98R1rzhOvYqke9l1Rtfgne+Zn5fWOlOWzwpZdg5Kn9u15LHZRthvoDED/CJNrBoW4LV3yg8DN44jJzGAVg7l1wyndMZflBRkmViEhfFK2ER86DtibzOCwGrn/VtzEdT1ym65i3Nt4318GK+13Hd/63f0lVSz18fDd88Afz2HLAxf+GiZcOLE7xncYqePVbXQkVwLK/weizIPcUn4XVX9qoLiLSF6se6UqowMycbHzed/GcyOSrIOSIpbaQCJhylXdeOzgU4npI4PrbKLh8S1dCBWA74ZVvmKUjGZyaq2H/etfx2hKvh+IOmqkSEekt2zb7u45WXQgp3g+nVzKnwc1vQdEKE3/2TBg2qXef21RtEpnWBrMvLSGnb68dHAYnfwt2vw8drWYsOrX/S38NFa5jLXXQXAX0MTZ3qC2FfZ9AyRrImGaKw8amez+OwSwyyXQuKPy0+/iJOh74KSVVIiK9ZVkw/QaTJBxp0mVQ6pOIemfYRPPRF3UH4M0fwYYl5nFkIlz7PGRM7dt1hs81BVT3r4fgcMiYAsn5fbvGYQkjTBHWwwkaQHwOxPawxOlpthPe+p+uvx9HMJx/tzltWbEV8s+CEfPM35scW3gsnPt7eOZaqN5nToie9v/6/v/VTyipEhHpi5EL4fy/mmUoRxAs+AGMmA+lq30dmXuVrO5KGMDUuHrnF3Dl430rR2FZJpHKmDLwmJIL4IrH4cU7oaEckvLh4nt9U+W+vbn738/s2+D9/zWJAcDqR+DMX5oTp71t4h2o0ifDze+YWeDwWEgcZZKrQUhJlYhIX0QmwPTrD52esyBqiNZdqil0HSteCc01vqvx5XCYOmO3fWKW/SLiICrZN7HYdvfHYdFdCdVh7/8Oxl80aJeyvComzXwMckqqRET6w1dv5t6S1MMSXf5Zvi3e2dYE+5bBZ/ebmYyZt0D2bN+UVAgOg+QxULHFPD46yQKzTOns8G5c4lM6/SciIq4ypsLCH5u9QmCWaE75rkkmfGXvJ/DYF2Hrq7DpBXj0fChc7ptYHMFw+SMmsUscaTbyh8d3f87MW3s+/ShDlmaqREQCWWujKaQZFtN99i0iHk76Joy9wDyOyfB+a5sj2baZoTp6bN0zkHuyb2JKHQPn/N4sRYbFmJmrz+6DA+th8tUw7gIIGkJvs23NPc/ISach9K8tIoB5k6zYZqpXJ4yApDxfRyT+qnwrvP3/YNsbZrblC3+C3FPN3iWAjjaoKYIV/za1rmbebJbbfLWJuKcExeGBWJwdZiN8SBSExxz/uY6grsrfGZPhgr+aZb+QCPfH5SutjbD7A/jkboi9GLa2mMKcajXkQst/IkNJS52pOH3fqfD4xXDvqeaboUhTNex8D1Y8CNvfgqpCePkbJqECOLgLnrzc1KU6bO9H8MQl5jkbn4dHzjeb1X3BsmDml7ufpHMEwaTL3fs6VXvg7Z/AP+aY5cXdH4DT2fvPdwQNrYQKzD62p64wy6+tDeb3+z7xdVR+STNVIkPJgY3mxNFhrfXw4lfNceUYHxw7l57V7Td7gfZvMPV4smd79uRTeyss+zt88PuusSnXum7w7miFyh2ml2FHm/mcI9lO2PiiqT3lC8PnwPWvwOdPmRmqyVea3ovu0t4GH/4ZVj9sHjdVmR9OvvzeoK2b5BarH3MdW/UI5J3h/Vj8nJIqkaGkrocKlNV7oemgkipP6WgziUhrg1kqi8s6/vNb6kyD4c+f6hqbeh2c8zsIjfZMjJU74MP/6z629nFTZHHX0u7jnU1sLbB6eIvw5R6h4FDIOcl8eEJdifl7OVJHm2ngHMhJVVgPS6BhPtxf58e0/CcylPRUDydlLET5aw+VQa61wTQM/tdJULkd7lsAhZ8d/3MqtndPqADWPAYVOzwWJq0NZpbpaEf/fxl3EaSON78PCoa5d3T/c0dw18Z1T2o8CPuWw95lPbem8ZTgsJ4roId5KNkdLKZe23UKFMzvp13nu3j8mGaqRIaS1HFw3l/gje9De4tpXHvhPUO3QKWvlW2CN37Q9bih3FT7vvGNY/+dtzf3bdwdEnIgebQ5wHBYVApkzTBLwwd3QFSq6Ql4ZNwj5sOXXjZJYEg4TLoSMqd7Lk4wzZFfvNPs5wLImglfvNeULPC0mGGw6Lfw3M1dY8Mm975X4lCVNRNuegO2vgmNaeb/d+Y0X0fll5RUiQwlIREw7UtmeaSpytTIUYNXz6nuoep4xTaTXB0rqUocZU5kVh4xM5U8xox7SnQKXPYwvPcb2Plfs4frjJ9BYq75yJ7Z8+eFhMPIU8yHt2x/oyuhAtMIetOLpjGzN4z5Atz4GuzfaEpMZM448ZLuUOdwmMQqayYsXXrs/y+ipEpkyHEE9b9hrfRNXA+NfBNyj191PCbN9K9bdo/ZzzTyNJh7p0l8PCltPFxyv1lai4j3XauZE9n5nuvYjrdNzSxv9NALiTAzdCPme/61ZMhRUiUi0l+p4+H0/wf//ZV5HB4PF/39xAlS6lizTNtcaxrIeqvuU0hEz4mgP8k/s6vMw2EF5w7+psT1ZWbTe0x6Vx0wGXKUVImI9FdYNMy50/TEW7cXFr0PiTm9+9ygEO1160n+WTD67K7EKnchjDnPtzENRGsDbH3dFFltqYXZt8OMG81+RxlylFSJiAxESLg5br+lsvcJlfSsttScjpz6JTj5O2YpO3EURMT5OrL+K1rZfeP7B783yfj8r/suJvEYJVUiIuJ7B/fAszdA6RrzOCIBvvTi4E6oAPZ+7Dq26mGTOEYmeD0c8SwlVSIicnzODjPjsn4JONtg4qWQNcu1IvtA7PmoK6ECc3r1k3vgwn9AsI96DbpDxjRY8INDdcIsWH4vxI8wM5wy5CipEhGR4ytaCQ+fY5IrMG1crnvJvaUWjuw5eFjJamhrgOB4972ON1VsN3XMqnabx2ExsPDHkD556PUHFEAV1UVE5ETWP9uVUAHYNnx2n/nVXXLmuY5NuPSItjmD0K6lXQkVmBZFhZ9Bpuo8DVVKqkREBru6Mtj9oVlCqy9z//U7Ws2m8fBD+5scwTDqNPj0n1BTCJtfNvWvBiJ7jpnFCQ4z5RPGXwxTrhp47L5UudN1rHwzdHiwer74lJb/REQGs4rtsPh6KNtoHmfOgIvvc29bl8lXmsr8jZUQPcwUDv3kbqjaAwU/h2e+aiq0z/9G/+tJRSbCyd+GCZeYfVtxIyB0kC+RjVoIy//ZfWzqdT03KJYhQUmViMhg0Npglo62vGZ61I1eBMMmwIbnuxIqgOKVpi7SvK+653Xry+C/v+7eOubUH5iZqyO9/3szu5Qwov+v5QjyTo8/b8meDef83hSHbW+CmV8xTatlyFJSJSIyGGx7C5bc0PX4k7/Cja/Drh7auuz9xH1JVdmm7gkVwMd/gTl3wEd/6hrraO2+7+p46vabmlSRiQNLwtzF2WH2hwW5+S0xIh5mfwXGnGteIzbL/a8hfkX/uiIi/q6xCt77dfex5mrTbHjchbBvWfc/yz/Tfa/d2uQ61t7senptxi0Qn33i6+37FJbcCLUlZo/WBfeYJsZHz3x5Q3srFH4Kn/7L3NPs2yBnvvv7Isb14u9FfK+2BErWmgMFKQWQNqHPSbCSKhERf2d3mOWjo3W0QcEXzCb1ra+asQmXQN4Z7nvtlHyT/DTXdI2NPtskQtWF0BYBZ/8vjD3/xD0Ma0tNgc+6UvO4uQaeuwm+8qHph+htxSvg0Qu6TjHufBeufhZGn+X9WMS3aorh2RuhaLl57AiCq57p8w8oSqpERPxdVDLM/ya89u2usaBQyJoOCcPhi/fCwV2mUW9iLoRGu++1k/Lguhfg/f+FkjUw/osw61az9+n8v8D7H8Cchb27Vl1pV0J1WEcbVO/zTVK1/nnXshDL/2lONg5kme7gHmisgOi03s3eie+Vru1KqMAs177+fVO8tQ89OpVUiYgMBuMvgrAoWH6fWU6aewekTzF/Fh4DGZM999qZ0+Cyh82ySGRS11KdI8ic9mtpMEneiSqfRyZCWKxpLHyk6DSPhH1CQT1UhA8K6/8JRqcTtr4GL9xu7jEyCS59EEYuGFCY4gVN1a5jNYXQ1sMM8XGoTpWICJiaQhueg7VPwf71vo7GVVQyTL7KbE6/9EEYPqf/b/79ERIB0and9z7VlkJDOTxwBjx/i6m8fjwJOXDhPabO1WFn/sLsX/GFCRd3j8WyYM7t/d/fVbndLGceThobK81yZ/W+AYcqHpY82vXradKVfU74NVMlIlK+FR69sGtpKjgcrn/JHIn3tupC2PGOKYuQM9/sXUrK6/pzf+kZ53TCygegNtqcECzbBNvfgi//9/hLeQVfgNs+hKp9EJMGKWN817Ilc7pJUjc8D+0tMPES09Owv2qLzXWO1FRlks/44QOLVTwrfTJc/hi8/j2oPwATr4CTv9nnvpNKqkREdi3tvtenvRk++itc9pB7mwafSGsDvPtz0xYGYPubZvbsmiVmlsif1JbAsntg5A+6xtoaYf+G4ydVQcGQOs58+JrDAdmzzIc7RKeZWa4jS0uERplZRvFvwaHmsEXWbHMoJCa9X1/7Wv4TEakpdB2r2gkdLa7jnnRwV1dCdVjp52YmzZPamqF4tZmx2bsMmmtP/DmOoJ5nmE50AtCXmmpcZ5LcKSkfzv0/sA69tQaFmJIRiSM995riXjGppnZaP3+Y0kyViMjI0+CTv3Ufm36T99uJHLM/cS8bF9u2aeDb1mSWm3oTv9NpErmXjigWetK34OTvmI3xxxKbDmf+CraUHzGWaZZR/E1NkZnxW/MYJI+Bk74BWTPc/zrBoTDlWsiaaQqcxmWZRMube9/Ep5RUiYhkz4SL/gXv/swswc29C8Zd4P04EnNNMc9NL3aNpY6D5F5s5G6pg7VPwDs/N8twuafCF/7PbMA9nqpd8Pp3u4999CezFJI5zfX57a1Qshr2fmxO8iXlwdyvQXwmjFxo7sGfdLTDsn/Cp/eYxxXbYdd/4ZZ3PVPGITgUhk00HxJwlFSJiITFwJSrIO90cLab/RS+mF0IizazPyPmw+aXIHeBKaUQc9QJpPoyaKk3PQBDI81YyRpTV+ew3e/Dh3+G8/96/M22TTU9HxtvrOz5+bvfhycv66rvNPbXsPAaSB3Ty5v0stpiWHFf97HWBjiw0Te1sWRIU1IlIoGjocKcxIqI77kooz9sBk8YbvrFzf6Keex0mj1V1fsgItHMSL14h0kWRp8LZ/4cUkZD+TbXa215BU77H4jLPPbrhcVAfA5U7+kaC4k05Q+O1lJnmgMfTqhCo02tp5K1vUuqnB3Q2miSR28lrY5gcz8drd3Hg/3kFKUMKUqqRCQwFK+B579saglFJMD5d0PBuf69sRpM65RnrjUnEgFm3GwSwtpi2PYaYJu6VbEZrp+bOh7CY13HO9oP/doCH/we5twGqx+Bss2msOh5f+lexuGw9lZTIgBg+o3m77E2yOzjqtxpqqwfy4FNpgTDng9hzHkw5Rqzgbtsk0kaw2LNktnRs3IDFZcJp/8UXv1m11jCSEif5N7XEUFJlYgEgoYK+M+tJqECkxgsuRFuff/4e19sGw7uhMaDJmmJy/JOvIfVlphZqcMJFZjEZOGPTWNigG2vm3IQGVMh7yzY8ZYZD42Gs37efbN6W7PZC7X8X+bx9BugfIvZwzXuAlMTq6HCnOrraSYpKgnm3GH6DNbvh1UPQcHP4f3fwbY34ZrFPc/21ZbAU1dC9V7zuHyrOW04/+vw5OVds0gjToaL7z3+zFp/TLzUxLX7A/NvOGKe6kaJRyipEpGhr24/VBy1PObsgKo9x06q2lth43/glW+Yjd9RKXDZo5Azz9PRdmk8aPZPucR2RFmAmGGmFlLMMPjiP82MUGs9JOebjyMVfgqPX9z1ePtbcNav4O2fwPolXeMTLj12TBMuNknPM9d2Hy9dY/6Oe0qqKrZ1JVSHRcTDW//TfVlu74emB5u7k6qq3SY5DY061Bjagutf7nkjvsgAqE6ViJ+pbWpjX2Ujdc1tvg5l6AiPM33YjhZ1nD1UFVvhhdtMQgWmHctzN5k9WZ5Uvs1UU9/7iYn76BpHlgXBYYd+74Bz/2gSKjBFJkeeAmPOdU2oAFY96jq2bxkMO6IMwrBJxz9tGJ0K8SN6/jOns+fxnnrsxWaaWcCjHWuD/ECsf84kU7UlZpN6az2secL9ryMBT0mViB9ZW1jFdQ8u55Q/vMcND61gfVGNr0MaGuKz4fy/de/zNv8bxz/9VVME9lFJQl2paWHhKXs/gftONUtlD50D//01XPh3k4CAmWm54O8wfC5c/G/TEmb0ot5fv6eChqHRZhlu1Olwxs9NFfmYE2zYTxwJY87vPpYy1myY70lKgWtT4fB4GH+x63N7SgYHqmq361hPCZ3IAGn5T8RPFFc1cfPDK6lsMMshq/ZW8eVHV/LCV+cxLNZHvdGGktGL4CsfwMHdEJ1i6j+FxZhN27VFYAWZ/TaH9xIdnv05UmRizzNe7tBUbUoiHJ4ZA1j3FEy6wiRPNcVmySxxZP9Pzk37Eqx7pitZtBxmX9WIeWZZr7fComHRb8xSaHEILPiR+fye/s7A/J1d8DfY85E5KTh8jikb0VpvSkNseclsel/0O0if0r97O55Jl5sSFUea9iX3v44EPCVVIn5i38HGzoTqsP21zRQebFJS5Q5BwZA23nwcVlsCy/4Bn/3LLFGd+kOYei1EJphGv4t+Y/b92E5zBP+if/VcisEdWmrhwAbX8bpiyFt47ISlL7JmmQbCG/9jNuFPuBgy+1lZPGG42bS+dCksWHDi58cPhylXm49OaWZjes1PTaNod++lOiznZFOva+lvzb/lKd91nTkTcQMlVSJ+IiY8GMvqKgEE4LAgJkxfph6z+WVYdqg9TUcbvP0/kJRrjvyHRMCMWyDnFGgoM0lB4nFKBgxUZArkLzKn+Y7kztcMCjazRMPnuO+aAxUSAclH3WNHm5k5dLhph0pEPEy/HgrOMY/9oR6ZDEn6bi3iJ0alRHHbqaP459KuvR5fPz2f3OTj9F+T/mtrNm1djla5Cwo/Mxuak/Ig3UvtRkIj4IyfmtN+JatMwcozf2E2jnvCwV3mdGHMMO+XijiWhkrY+Q6seNAUH531Zff26FMyJR6mpEr8UlVjK8t3VfLu5jLy06I5bUwaeanRvg7LoyJCg7nt1JGcnJ9MaXUzmQkRjE+PJSwkyNehDU1BIZA2AUo/7xqbeBkUrTQlBsCUUbjmOcjwUpPg1LFw3fNQXWjazwxk/9SxdLSbSusvfdVUSI9KgcsehpyT3Ps6/bHpBXj1W+b3hZ+ax7e8oz56Mmjo9J/4Hdu2eXZlEbc9vppnVxXxm9e2cP2Dy9l3sPHEnzzIxUWEMm9UMpdMz2LOyCRiIvy82vdg5giCWbeasgWHDZsAm49oZtxQDkt/A6099MbzlIh4MzuWNMozrVwqt8Pzt5iECsw9LrnRbIT3pfoy+PD/uo+1N5tK+P6mfKs5Bfr0NfD5M549ESqDipIq8Tsl1U3c/U73Qo3F1c1sLq31UUQyZGVMgVvehcsegaueBnqYFSxcDi3VXg7Mg6qLzJ6lI9WXmXIRvmQ5wNHDDxEOP5uprd4Hj19q/r62vGIq9X/6r67WPxLQlFSJ3+lw2rR12C7j7R3HKCwoMhDJ+TD+IrOJOW2c65/nnWUaGQ8VMWmuM2DhcaZwqC9FJcPCH3UfC4/zv6rnBzZCzb7uY8vuca0YLwFJSZX4ncyESG48KafbWGxEMGPTe2gMK33W3uGkqa3D12H4p4xpcNK3u2ZHhk2Ek7/VVcF8KEgeDWf/riuxCgo1BUYTcnwaFmB6D169GCZfDad+H65/9fgFWn3C9Qc+U/erh3EJONqoLn4nyGFx07wcsuIjeHZVEePSY7l2zghGpgztjeresK6omoc+3s22A/VcMTObRePTSFMNrC6RCbDgBzDpUmhrgoRcU/BzKAkJh2k3wPB5Zi9QXLZnqpifSEM5FK2Csk3m9bNmmVm00Yv6ViXe21LHQfRRNcNmfeXYrXskoCipEr+UFhfBdXNzuHxGNiFBDhwOD2zYDTDbDtRx1X2f0tBqZqn+34sbKatt5ltnFujv90jBoeaNs79qiqF4lWlzkzbOzH6F+9ksa0g4pHuoVENvtDXBB3+E5f/sGpt4OXzhj/73d3W0hBy47j+wfK2pCj/pclNfLEiHSkRJlfg5lRNwn637azsTqsP+/eFurpw1nKyESB9FNcTUl8GLX4Vd/+0aO/u3MPt2z5zkG6wqd5oq9kdavxhmf8W9dak8JW0cxJbBea+4r0CpDAn63yASIIJ7+OYfFuwgSG/27lO2uXtCBfDuL02/QenS1tS9dUDn+CArm6KESo6i/xEiAWJsRizpceHdxr6zqID0eO2pcpvWBtextkboaPZ+LP4sMbd7D0Ywe7uS8nwTj4ibaPlPJEDkJEXx6E2z+GBbObsqGjhtTCozchIGfN1d5fXsKm8gMjSIgmExboh0EEvOh9BoaK3vGht1OsQN911M/igqGS55ED6+G3a+a/YmnfxtiM3wdWQiA6KkSiSA5KfFkJ/mvsRnbWEV193/GXUtpvDhyfnJfCkngI+WJ+fDdS/Au7+AA+th3EUw76sQ5qOTq40HYd+nsOdDSCmA3FPNLJE/SB0D5/8VmqtMPaqhVLZCApaSKhHpl8bWdv7vzW2dCRXAh9sruCwj1IdR+YHsmXD106YNTGSS706FOTtgxf3w3q+7xoZNhKufhdh038R0tOAQNTmWIWXAe6osy8q2LOs9y7I2W5a10bKsr7sjMBHxb/XN7WwsqXEZb1XlewiNgphhvj1mX7XHtZfe/vVQttEn4YgEAndsVG8Hvm3b9lhgDnCnZVkDKPIiIoNBQlQo50xwnfEIVxkMV60NULEdaku895rOduhodR0/uu+fiLjNgJMq27ZLbdtefej3dcBmIHOg1xUR/xYS5ODLp+RySr7pGRce4uDH544lMlRJVTflW2Hx9XDPDLj3FNj4ArT3kOy4W/wImHBZ97GIBLO3SkQ8wrJ7qhXS34tZVg7wATDBtu3ao/7sVuBWgJSUlOmLFy922+sOFvX19URHB16rFd330Oa0oa3DiQWEBjsC5r6P1uN9206o2gstRy2TJo+GEC8UXO1ohaYq8xESCVEpEOLeEhr19fVER0WZ0hFtjWbJMyTS9BQcwvT/PLAsXLhwlW3bJ6xM67akyrKsaOB94Ne2bT9/vOcWFBTYW7dudcvrDiZLly5lwYIFvg7D63TfgUX3fYSDu+GvU1yffPG/TXsTb2muNclUWxNUbje9f5NGQUT8gC+9dOlSFiRVwnM3dQ2mjoern4H47AFf31/p/3lgsSyrV0mVW07/WZYVAjwHPHGihEqkw2lTXNWIw2GRGR+BpYreMlSFRkH8cKje1308wstNmsNjTQyvfge2v2nGchfC+X8eeIkFZzu8+cPuY2UbYf+6IZ1U+dT+DVD6OTiCIGOqlnT9yICTKsu8Iz4AbLZt+08DD0n8XX1zG5YFUWF9P9l0oLaJhz/Zw4Mf7SHYYfH1M0Zz+Yws4iOH9lKBBKjoVPjCn+CpK0yJA4CCc01pA2/b/lZXQgWw+z3Y/DLM/9rArms7oemg63hP1eVl4IpWwiPnmVlHMPvkrn/ZN/+nxIU7Tv/NB64DTrMsa+2hj3PdcF3xM/XN7by6rpTL713GZf9axmvrS2k4okZRb7y9qYx/Lt1FS7uThtYOfvPaZj7d1cM3ZB+rbWqjvC4wW4s4nTa1TW20qzSCe4w6DW59Hy59yBQGPf+vEJPm/Ti2v+06tu31nnvw9UVQCEy93nUsdczAriuunE747N9dCRWY/XJbXvNdTNLNgGeqbNv+CND6TQBYvruSO59c3fn4jidW89ANM1k4pnfF+1rbO3h2ZaHL+DubD3D2hGFui3Mg2jqcfLyjgt+/uZXy2haumzuCy2ZkkR4XGP3xdpfX8/SKQt7edICZuYncOC+HMemxvg5rcHMEmVkEX88kjFoI297oPpZ3Jgx4+d0ys12hUbD2cUjIhTN+BqkTBnhdcWF3QFUPzbmr9ng9FOmZKqpLrz312T6XsWdXFvY6qQp2OBibHsvnRd1PQuWn+s9Jkg3FNdz08Aqch354/9Pb2wCbr50+2qdxeUNtUxs/+s96lh2aOdxV0cBH28t59rZ5ZKjp8uA3+mzY9DLs/cg8zpoJ4y50z7UTRphEau6dEBoJYQHeA9JTgkJgxo1QuLz7+LiLfBKOuHLH8p8EiORo195cST2MHYvDYXHtnBHERnTl8hlx4Zw+1n/aVGworulMqA57dNleymqH/lLg3sqGzoTqsOLqZnaV1x/jM2RQSciBKx6Dm940H1c9bU4AuovDYZY1lVB5Vt6ZcPbvzH69uCy46J8wYq6vo5JDNFMlvXbFzGyeX13c2YYkLNjBJdP6Vud1QmYcL9wxny376whyWIxNj2V4ohfq9fRSTLjr5vvk6FDCQob+zx8hQQ4sy3WLTViwinkOGZGJMHyOr6OQgYhKhjm3w/iLwXJAdIqvI5IjKKmSXpuSHc+S2+aybFcllgVzRyYzIbPv+21GpkQzMsV/lvyONCU7nqyECIqqzEZQy4Lvnz2WuIihfzoxJzmKL80dwSOf7O0cOzk/mVF+tDwrIof44rCDnJCSKuk1y7KYlB3PpOx4X4cyIO0dTrbsr2NXRT1xESGMS48lJSYcMInFYzfPYu2+amqa25mYGcfEzDgfR+wd4SFBfHVhHnNyk1i1r4px6bHMzk0iMWroJ5THY9s2eyobOVDbRGpMODlJUTgcbj6b4+yAulIIDjNVz0VkUFJSJQHnw+0V3PLoSjoObZ5aOCaF318ymZQYsz8sNzma3OTAnJ1JiQnnnInpnDPRtVFyILJtm7c3HeDrT6+lqa2D8BAH/3fZZM6dkO6+xKp6H3z6L1j5AEQmwdm/hfxFEBLunuuLiNcM/Y0iIkeoqGvhJy9u6EyoAN7bUs7GkprjfJYEqj2VDXzjGZNQATS3Ofn24s/ZVeGmwpa2DasegU//Du3NUFsMi78EJWvcc30R8SolVRJQGlrbKa5uchmvamj1QTTi78rqWmhs7eg21tLu5IC7ToPWl8GaR13HS9e65/oi4lVKqiSgpMWGs2h890KjloXfbpwX30qNDiMipPvpx7BgB2mxvS8lclyhkRA33HVc+6pEBiUlVRJQwkOC+O5ZBZx+qGBpSkwY/7hmGmNVNVx6kJMcxZ+vmEz4oZIaYcFmT5Xb9tyFxcDpPwXHEdtbkwsgc7p7ru8O9eWw+0PY+R7UFPs6GhG/po3qEnBGpUZzz9XT2F/bTGRoEGmx2hAsPbMsi0Xjh/Ha107mQG0zqTHh5Ca7+fRfzklwy7tQttm0ekmfbCqU+4ODe+A/X4HCT83jhBxTNDR1rC+jEvFbSqrEIzqcNhuKa1ix5yCJDa1s3V9LwTD/mQ2KCA0iNznK12F4lNNps6awiudWFVPf3MZlM7OZkZNARIi+7PvCsizP1lZzOCBjivnwN7uXdiVUYIqHFq2EpDzTMkVEutF3V/GIVXsPcvW/l9PutPn2xHZ+9q9lPH3rXMZl+E9iNRTUNrWxYs9B3t1SxojESE4bk0p+mmkT8nlRNVfc+ynth046vrSutE8NsEUoWmV+DQqF034C+z6Bpb+F4pUw5w5IKfBtfCJ+RkmVuF1bu5N7P9jV+WYOUNvczntbywIyqWpp76C5raPfVdkbWsyJxbAgB9mJkd2Wnl5ZV8KP/rOh8/EDH+/mmS/PITclmnc3l3X7NwC494OdzM9LIlStZ6Q3ck8xpxNn3Aif3Qs1RWZ81cNQshau+4/nYyj9HNY+DZXbYMo1MPJUU89LxA8pqRK367BtyutaXMYr6wOvbMHqvVX8Y+kOdpY3cNn0LC6amklGfESvP393RT0/f3kTS7eWEx7i4LtnFXD5jGxiIkI4UNvMH97c2u35ZbUtbCqtJTclGvvoJn6A0+na289r2tvA2Wr2DYnv1JfBwV0QHA7JeRB6nGXN3JNh+k0QHteVUB1WutZcx5PKtsAj50PzoTpyO96Bc/4XZt/m2dcV6Sed/hO3Cw8J4vq5OS7jp48NrGWnlnYn19y/nHc2l7G7ooHfv7mVBz7aRfuhhtQn0t7h5IEPd7N0azlgCk/+8tXNrCs2bzBOp01ru+u12jtM1nT62DSCjtpQfespIwkL8fIslW1D4Wew5EZ44CxY+SDUHfBuDGKUbYZHLoAHF8F9p8IbP4b64/xbxAwzFd6Hz3X9M8syiZkn7V/XlVAd9v7/Qt1+z76uSD8pqRKPOG1MKr+9eCIjkiKJCAnivuumM31EvK/D8qrmto7OStyHPbpsL6U1vSscebChldc2uL55bC6tBWBYXDhfOXVktz+LDA1iTLrZUzU5O56nb53DxdMyOXNcKg/fOJN5eT5YNtm/AR45D7a8DAc2wCvfhM+f9H4cga69DZb9Hco3d42tfhgKVxz/80LCIWM6jLuo+/isr5gN617n5r6LgcDphMqdULoemtQ9wpO0/CcekRAVylWzhnP2hGGsWf4xpx1VcNOfOJ02eyobONjQSlpsONmJkQO+5pbSWtp6mJGKDA0mOKh3bwrR4cGMS4/lox0V3cYzDy0fWpbFlbOGkxQdxtOfFZKXGsX183I7T1kGOSxm5iQyMydxgHczQPvXQftRy8Ef3w2TroTYPvQYrC6EmkKISNDps/5oroad77qOH9gAY887/udGxMHZv4PxX4TyLTBsImTN8nx/wmGTzNLjkbNVp37fzKBJ77TUwdon4J2fQVsTZM+G8/8KqWN8HdmQpKRKPCohMhSH5b8/WbZ3OHltfSnfe24dzW1OYiOC+ftV0zh5dP8rWte3tPHTlzZy0TCb4YmR7DvY2Pln3z+7gPS43u2pigwN5ttnjWZtYTX1Le0AzB+VxOTs+M7npMaEc83sEVwyLYuQIIfLcp9fCO6h+nhIJAT14dvPvk/hmWugocIkU4t+A1Ovg5De708bNKr3mY+IREjKh2A3JY/h8ZC7wHWWMHVc7z4/Nh3GX+SeWHordQxc/zKsXwLl22DKVWbzfCBrrjWnMXub0JZ+Dq9/v+tx4XJ4/3dw0b/UtNsDlFRJQNtZ3sC3Fn/eeUqutqmdrz29hpfvOomshP7NWJXVtrB890FOju7gvEk52DZUNrRyUl4Sp/WxnMHU4Qm89NX57CyvJzI0mIK0GJJjXJOUcG/vk+qL9Mmm7UpDedfY6T/tfSuW+nL4z20moQLoaIPXvmuWpLL8qPK4O+xdBs9cDY0HTZX1s34F06437WwGKjgE5t1l6k4d3mA++Sozc+HP0iebj0BXtx82vgArH4C4bDjlO5A9x9Q5O57KHg4TbH3NfD3FZ3kk1ECmpEoCWmlNk0vZgarGNsrrWnqdVFU3trKxpJYDtc1kJ0SSmRBOVkIENnX8Y+lOIkKCiAkP5sIpGUSH933WYWRKNOlxEew72EhVUyuxEcGDqyRCcr6ZbdjxLtQWQ94ZkD2r95/fUA5Vu13Ha4uAIZRU1ZfBC7eZhArA2Q5v/ACyZkLWDPe8Rto4uPF1OLjTbDJPyofwwCtzMiitfRLe/bn5fcU22PMB3PzOiYvGRvfwg1zaRP27e4iSKgloabHhBDksOo5IrGIjgkmO7l3D3PqWdu5+dzsPfbync+wXF47j11+cyPqVywBoauvg/MnpjOtnf8Giqkb+782tvPh5CQ7L4ktzR3D7qaNIHUztdVLH9r+1SWSy+cm8prD7eEzGwOPyJw0VULXHdbym2H1JFZj9SNqTNLjU7Ydlf+s+1tEG+9efOKnKmGoOGWx6wTwOjYZFv1ZS5SFKqsQtyuua+XhHJe9sOsDErDjOGJfGKE+19XCjUSnR/OqiCfzkhQ20O23CQxz88bIpvd6svqOsrltCBfCrV7bwxjdOpjk1mvuuG0d8ZAij02KIj+xf8c83NuznhbUlgKkB9tDHe5icFc9FUzP7db1BJyYVvvgvePpqs2HZcsAZP+v9XiBPqC83e1UayiBxpNlQPVBRyRCfA9V7uo/HDrHkUfrOEQyhMV2zmIf1Zk9UTBqc92eYdSu01JpDHsn5nolTlFTJwLV1OPn3h7u57wOzdv/K+lKeWVHI47fM7lOhS18IDXZw6fQspg6Pp6KuhfS4iD71BKxtancZa+1wUtvURliwgwUDPPXY2t7By5+XuIy/t7UscJIqME2Hb33fbOCOTDLLViG9m010u6YqePNHsH5x19j5dwM5A7tudCpc9E+zp6qpChxBcMYvzJKdBLaoZDjj57Dkhq6x6GGQPq13nx+ZCDnzPRKadKekSgas8GAjD37Ufc/LrooGth2o8/ukCiAkyMGYYbHQj/xneGIkMWHB1LV0JVcjkiLJSoik2g2xhQYHMTMnkc+LuteWmZwV74arDzKJuebD18o2d0+owCRZsx8e+LVz5sGtS035iMjDp//6N8MpQ8zoRfCll2D3+xCdDiNPgeRRvo5KjqKkSgbMaYOzp5YovmqH4kU5yVE8dONMfvLCBjbvr2NmTgI/u2B8jyf0+uuyGdm8tqGUkmpTNHTssBgWFKSwo6yO4qomkqPDyEuN9n6l9EDVXO061toAdu8q5Z9QQo75EDlSaKTpezjyVF9HIsehpEoGLDsxgitmDuepz/Z1jg2LC2N0mv/vqXKHGTmJPH3rHKqb2kiKCu3XCb/jKRgWw5Lb5rHtQB1BDouCtBjWF9dwxxOraWl3Ylnw43PHcu2c4YSH6Eva4xJHmfpYbU1dYxnTVYxURJRUycCFBQdx12l5jE2P4YU1JUwfEc+l07P6XedpMIqLDCXuBBvRS6ub2FhSS2NrB6PToikYFoPVy8KoGfERnUupxVVNfOfZz2k51PfPtuFXr25mVm4ikwJxWdDbUgrgmufg1e9AxWbIX2Q2zm9SP0ORQKekStwiIz6CL83N4epZwwkOCqyWkg2H9lNFhR37y6nwYCO3PbaKjYf69oUFO3js5lnMyu17L76Dja1UNba5jJfVmlYwlfUtbCqppby+hZzkKMalx/ptcdD1RdU8t6qYPZUNXD4zi3mjkvt9StKrcubDja+Z01RRKWZpRkmVSMBTUiVuFUgJVWNrOx9tr+Ce/27HacPtC/I4dXQK0eGuX1Zr9lV1JlQALe1Ofv/mVh65YRZRPTz/eFJjwhgWG87+2q7GzEEOi8z4CKobW/nFy5t48YgTg/932WQune5/lZO3lNZy5X2f0tBqmk4v3VbOb744gatnj/BxZL0UmWA+REQOCZx3QBE3W7HnILc+top1xbVsKKnlzidX8+muyh6fW1bX4jK2p6KBhjbXkgwnkhYbzt+umkrKoQKlkaFB/PGyyeSlRbNlf123hArg5y9tpPCI/oP+YkNJbWdCddjd726nooe/q4Bi26bP3fa3oXg1tDT4OqKhoe6AqUr++CXw7i/hwCZfRyRDkGaqRPrpuVVFLmOPf7qX08emuuyVmpAZ5/LcS6ZlkRzVv1OCM3MTefGr89lf00xiVCgjkiKxLIvaJtdlwbqW9s4lSn/S024yq8fRALP7fXjqyq6N8Cd9C076pipgD4SzA5b/Cz76k3m84x1Y8zjc9IZ/lOmQIUMzVSL9lBjpmhAlRYf2uPl8UlYcf7xsMgmRIQQ5LK6cmc21c0bgcPQ/iciIj2DaiARykqM6XzMnOYqw4O5f1tOGx/tlvbAJmbFEH7UP7etn5Lm1HMWgU3cAXryz+8nCj/4EZRt9F9NQUL0Plt3Tfax+P5RptkrcSzNVIr3Q0taBw7IIOSJhuWhaBk+t2Nd5Ci8kyOLqWcN7/PzI0GAumZ7FvLwkWtudpMeFe6Qpcn5qNA/eMJOfvLCeXRWNLChI4UfnjiU2wv+O+xcMi+WpL8/mxbUl7KlsMH8/I5N9HZZvNVVBjesMKLX7vR+LiPSZkiqR46htauX9bRU89PFu4iJCuPWUUczISSAkyMHkrHiW3DaXj3ZU4rRtTspLZmIPy3xHSo/z7IyRZVnMz0tmye3zqG9uJzkmjMhQ//0yn5gVz0SVgegSnQqp411nphIGyeZ9fxU/HOZ+tWv5D0ybF1/2j5QhyX+/24r4gfe2lvP1p9d2Pn5/WzmLvzKXGTmJWJblt0lBYlQYib3Yr+V02uwsr6fwYCOJUaHkpcW4LMmJF0UmwoX3wLPXmyWrkAg45w968x8oRxDMvs00El7/LGRMhQmXaj+VuJ2+e4ocQ0NLe2eT6MOcNnywvZwZOYk+isq9PthezlceW9W5hHn7qSO5c2Ge26vCSx9kToOb34HaIgiPMxXce1kkVo4jJg2mXG0+RDxEG9VFjiHIsogMdd33FDFEWsEcqGnme0vWdSZUAP98fxdb9tf1+5pOp01zm5PX1pfy0Y5yKusDvDxCf8WkQeZ0SMpTQiUyiCipEjmG8NAg7lyY120sIiSIk/OHxmbq6qa2Hutn9TTWW5/srGBHeT13PLGaa+//jB88v57yuuYTf6KIpznd1PBa5DiGxo/cIh4yd2QST986h7c27icuIoTTx6b1WHPqRHZXNLB6bxU1zW1MzopjYmY8ocG+/ZkmNSaMgmExbD1iZsqyYHhi/3o2Hmxo4f+9uIEvptudY29vOsA1s4ezoCB8wPFKAGhrhtK1ULENIpMgfQrEZQ7smmVbYP1i2PsJTLgECs6BOP/rMCBDg5IqkeMICwlizsgk5ozse4++w3ZX1HPt/csprjYzNpYFD14/k4VjUt0VZr8kRIXyh0sncddTa9hb2UhUaBC/vGgCo9Oi+3W9+pYOdlc2Qnr38cr6VjdEKwFhy6vw3E1dj4fPhUsfgtj0Y3/O8VQXwpOXQ/Ve83jfMij9HM79PwgZYKLvbIeDuyA2E4IDuLaadKOkSsTD1u6r7kyowHQh+d83NjNtRDxxEb5tHjwpK57nbptHaU0TsREhjEiK6ve1UqLDOGtsGlDcbTw3uf/XlABSWwpvfL/72L5lsH99/5Oq8i1dCdVhax835RVSx/Tvmm3NsPU1KC+Bv11mZr8W/AiSRvbvejKkaE+ViIfVNru2iKmsb+u2QdyXkmPCmJgVP6CECiAiNIjvnj2msyRDfGQIf7liCuMz1F5FeqGtCRorXMdbal3Hesvq6S3OGtjm/9LPYcmNZqbKdpoSDR//BTpcW0RJ4FFSJeJhE7PiOLobzfXzRpAaM/T2GeWlRjMiKYq3v3kKr33tZC6amklYiPsrx8sQFJcJ477YfSwoBFIK+n/N1LGQPLr72IybIWEA9akqtrqOrV8M9Qf6f00ZMrT8J+JhEzPjeOjGWfzhzS2U1bZw/bwRXDIt29dheYzDgvy0GF+HIYNNcBic9j8QGg0bnoWEkXD2b0yF+f6KzYArnzR7tYpWwJgvwMiFEDyAZfeIHmrUxedCiJa5RUmVeIHTtimtaSIpKtQj/e78XUiQg1NHpzAtO56WdmdgNwwWOZ6kUfCFP8GC75vkKiJ+4NdMzoeTvjHw6xyWMdVsoD/MEWySv8gE972GDFpa/hOPWr23ij0VjZz1pw/40X82sLO83tch+UxMRIgSKpETCQ4xJQ/ckVB5QlymOZGYOBIuuR++vBRyT/V1VOInNFPlR0prmthZVk+ww0FeWjTJ0f17A27vcLJ6XzWLV+yjtcPJlTOHM31Egtf3tuwqr+e6B5ZzW0E7dS2wZFURpTVN3HvddKLD1AbFkyrrWyipaSYuPJjhA9yALiJHiU2HsFiYuMDXkYifUVLlJ7YdqOOWR1aw72ATAFOz47n7yqkMT+p7IcY1hdVced8ynIdqML70eSmP3zKLk/JS3BnyCe0sb6ChtaPb2Mc7Kik62MSYdCVVnrK+qJqvPb2G3RWNxIQF88uLJnDuxGEBufQqIuJNWv7zA7Zts3hFYWdCBSYx+mB7eb+u9+Ka4s6E6rCHP96D8+hBD4sO66lvXhAROg3mMVWNrXx3yTp2VzQCUNfSzjcXr2Xrgf738xMRkd5RUuUHWtqdfLq70mV8bWF1v67n3dTp2EanxbBwTPfZse+dXdCv2TfpnbLaFpeGyLYNhUck7CIi4hlKqvxAeEgQ50xwrRh8Ul7/GvdeNDWzh7pIOTiOHjyG5rYO1hdX8+7mA2wuraWto39FKpOiw/jdFycyIimKX1w4nie/PJvLpmdjDaTwnhxXfEQIqT1shk+J9m3ldhGRQKA9VX7i/EkZrNlXxTuby7AsuGrmcOaO6l+/uSnZ8Tz15Tk8+dk+2jucXDVrBDNzenfct6WtgyeW7+VXr27GtiHIYfGnyydzweSMfiVDaXERxIYHc8HcnD5/rr9oam1nT2UjHU6bnKRIosP9dz9YWlw4v790Erc+uorWQ8nwraeMZMwwVTUXEfE0JVV+YnhSJHdfMZU9BxsIcljkJkX1+7ReSJCD2SOTmN2PJsA7yuv59aGECqDDafPD59czOSuenADs4Xagpok/vb2NZ1YWAXDq6BR+ceH4Abd08aRT8lN49WsnsbeykaToUPLTYjpbx4iIiOfoO60fiQoPZnxGnE9jqKhvcdnk3tjawcGG1oBMqj7ZWdmZUAG8v62cl9aWcNfp+f2+ZktbB5v317HvYAMp0WGMTY8lPtJ9y3MOh0V+WoyqmouIeJmSKukmMz6CsGBHt2a/ydGhpMcNvT51vfHxTtcDBG9s3M+XTxlJeD9mEm3b5uV1JXzn2XWdY1+aM4LvLCogNsI7y4r7a5qxbZv0+AivvJ6ISKDQRnXpZmRyNH+/ehrxkeYNPjUmjL9fPS1g34CnZse7jM0blURYcP++dPYdbOSnL27sNvbop3vZXub5kgdVja08+NFuFv3lA8768wfc+/5OKutbPP66IiKBQjNV0o3DYXHGuDReueskDja0khobxrBYzyRUm0tr+c+aYjYU1/DFqZksKEghJca/ZsROHp3CzJwEVuypAmBkchSXz+j/Cca65naXgqgA1Y1tA4qzN5btrOAXr2zqfPzb17eQFhvORVMzPf7aIiKBQEmV9CgrIZKsBM/Vk9pT0cC19y+nsqEVMHuXvnZaHt84Y3SvSz94w/DESP517XR2lNXT4bQZlRJN2gCWQjPiwxmdFs22A109EMOCHQxP9Hztrpc+L3UZW7yykAun9O9kp4iIdKflP/GJzaW1nQnVYfd+sIviav8rUpkUHcbskUnMy0seUEIFkBgVxl+umMK04fEAZCVE8MD1M8hLjXZDpMc3KsX1oMHotBglVCIibqKZKvEJRw9v5IPtvb2mqQ1sm7hjnNxr63Cys7yejLgIIkK7NrWPy4jjkRtnUVbfQmx4CCk9FOv0hPMmZfDk8n1UHVpqjA0P5tLpWW659o6yOt7eVMbm0hpOj2+jsr6FpH42BBcRGayUVIlPjEmPITU2jLLaro3SdywYReYg2BDf0NLO+9vK+cs722jrsLljwSjOHJfWWRahsbWdl9eWUFlWz5f/+D6LxqXxg3PHkJvcNRsVExFCjJdO+x02Nj2WJbfPY1NJLbYNY9PdU3ahqKqRGx78jKLqZgDyJ7bzxPK9fHVhvl8t5YqIeJqSKvGJEUlRPHbTLF5dX8qmklrOn5zB2PQY3t9WTmRYEKNTY0iI8s/WKiv3HuSOJ1Z3Pv7uknX87aqpnD85A4D1RTV8//n1fHuiKfj15qYDJEWH8fMLxxMS5NsV91Ep0YxKce9S4+bSus6E6rB/LN3JRVMyGe7HRVJFRNxNSZX4TMGwWAoOtU9ZV1jNZf/61CypAWeOS+NXF40nzUMnD3vS2NpOS7uThBMU4nxtneuG78eW7eHsCcMICXKw7YBreYSXPy/ha6fnM2wI1vvqcLr2huxw2n7T2FtExFu0UV18rrG1nT+8ubUzoQJ4e9MBPi+s6dXn27bN9gN1vL1pP5/trqS6sfXEn3SEDqfNsp0V3PjQCi6852Pu/3AXB2qbj/n8nso+pMWFE3RoU1hPe6TyUqOJCutf2yF/N2ZYLIlHzSreMC9nUCzlioi4k2aqxK3WFlbz3KpCSqqbuXxmNvN60X+wrrmddcWuCVRRVe9OAn6ys5KbHl5BS7uTa2cPZ1hcOBtKapmTm8jCMakn7NO3obiG6x74jPZD/Xl+9epmWto7uHNhPqXVTby/rZy3Nx1gZk4iZ41P4+wJw3jo492d9aZCgxxcPzenc//Q5Ox45oxMBMoAUzLhh+eOIcZNjZh3lNWzbGcF5fUtzBuVzOTsOCJCfPelnJMcxeM3z+aZFftYX1xDZnwDl5+US/ARS51Op8364ho+2VlJkAPmjUpmQqZvWzKJiLibkipxmw3FNVx53zKa28xy0Ltbyvjz5ZNJOMHnJUaGcua4NJasKuo2np924r0/lfUt/PiF9bS0OzklP5mi6iYeX74PgDc27OeV9aXcd910EqOOfRJtU0ltZ0J12IMf7eGLUzP589vbefZQXO9uKeOFtUU8dtNsltw+j5V7qmjrcDIzJ6FbgpAeF8Ffr5zKZ8s+4h/XjCMvNYbRburDt6u8nqv+/SnldWaD/1/f3cE/r53GORPS3XL9/hqXEcvPL5xAW4eTjz/8gLS47rNUawqruPK+T2nrMH/PYcEOFn9lLpN7qFgvIjJYaflP3GbV3qrOhOqwv/53Bx1Hd2g+Skiwg9tPHcmMHJN+hQY5+N6iAiZnnXgmo765nT0VjQBMG5HA0q3l3f585Z4qdpQ1HPcaR5Y7OCwuMoTa5naWrO6e6G3ZX8+2snrGpsdy3dwR3HRSLhOz4l1qPaXGhhMdFsy5EzPcllCBmQk8nFAd9oc3t/Z5ydNTjrUR/9FlezsTKoCWdievrCvxVlgiIl6hmSpxm54Oz/f2QP2o1BgevH4mhVWNhIcEMSIxstvy0bEkx4RxUl4yH+2owD5G7uY81h8cMikrjmFxYeyv6UpWvrdoDBb0eM0TXc+TmtpcW9zUNrXR2u66WdxfOJ02Bxtck76Kev9IBAebAzXNbCurw7YhPzU6YPtyivgjJVXiNtNzEggPcXSbrbrr9HyCarb36vNjI0IYH9G3fTZRYcH85LyxfG/JOjaV1jJnZCKf7jrY+edj02NOWEJgZEo0T9w8h+W7K6msb2VmbiJTs+Nx2nDhlAxeXNs1ozIqJapXy5KeMiEjjmCH1W258uaTckmN9d9ThQ6HxbVzRvDh9opu4+o52He7yuu5/fFVbD3U5ig7IYIHb5jplnpjIjJwSqrEbcZnxPH0rXN5blUR+2uauHxmNnNyk1i1vHdJVX8VDIvl0ZtnUVLdjNO2+Wh7BW9uPMApo5O5YHJGryqWj0qNZlQPrWK+t2gM04cn8Or6UuaOSuL8SRkeazDdGxMz43j8ltn87b/b2V/TzHVzczh3wjCfxdNb80Ym8berpvKPpTsIdlh89bR8ZuacaLedHO2dzQc6EyqAwqomXlhTzHfPHuPDqETkMCVV4lZTsuOZ4oPNx3ERocRFmGP94zPiuOXkkQS5oZp3ZkIEX5qXw5fm5Qz4Wu7gcFjMGZnE5Kx4Wjs6Ou/Z38VEhHD+5AwWFqRgWRZRYfrW0x+r91a5jH26+yBOp63q9SJ+QN/ZZEhyR0LVF3sqGlhbWE1NUxsTs+KYkOHZcgERoUFEMPjqXkW7qaxEoDp9XBpvbDzQbez8SelKqET8hJIqkQHaU9HAtQ8s76yrZVlwz1VTqa1p5t8f7GJBQYr2vIhbnJKXzHVzhvPE8n3YwMVTMzlznP8v/4oECiVVQ0R7h5PS2maCLWtQnwYqr2vms91VrNhTyfjMOOaOTCIrIdLXYR3XmsLqboVKbRvufnc7145w8uvXNvPvj3ax+Na55CSrD54MTFpcBP9z3ji+NDcHpw0jkiII92HhVxHpTl+NQ0BpdRMPfrybRz7ZS3iog+8uKuCiyZnERAyupZaW9g7u+e8OHlm2t3Ns7qgk7rlqKknRJ95s7in7KhvYUVZPaEgQBWkxLhvf65rbXD7nYEMrwQ4LsCmrbWFjSY3Pk6r65jZaO2yXljIyuIQFB2nmU8RPKakaAl5ZX8K/P9wNQGuTk5+8sJHshEgWFKT6OLK+2V3RwGOf7u02tmxnJTvK6n2WVG0sMS1sDtdZmjY8nruvmkr2EbNnEzLisKzuNa3OmZBOXfNuDtfXPbLwpbe1tjv5ZGcFf3p7GwcbWrnppFzOn5TeYw9DERHpP1VUH+Tqmtt4ZkWRy/hHR9UEGgzaO2x6Kr7e1uH+wpYH61sorWnCeZxq723tTv79wa5uhStX76vms0N1sLYdqOON9aXUt7Tz9JfnMDY9lpToMG47dSTtTieth+KOCAlibLrvZhbWFVVz48MrWFdUQ1FVE794eROvrCv1WTwiIkOVW2aqLMs6G7gbCALut237d+64rpxYWLCD0WnR7Cir7zY+Itm/9yH1ZERSJCflJbOzvJ5LpmcBEBUa1GP9qP5qaevgv1vL+PWrm6lqaOXauSO4fm4OGT3sQ2tsbWdtYbXL+I6yOj7bXcl1D3xGy6FK5vNHJfHPa6YRFRaEhcUbG/bTXBjE+ZPSuemkXAqGxbrtHvpq5d4ql8rwD368m4umZJKgpUAREbcZcFJlWVYQ8HfgTKAIWGFZ1ku2bW8a6LXlxEKDg7j1lJEs3VpOY6tpYZKdEMH8Uck+jqzvYsJD+M0XJ/DRjkp+8cpGmtuchAU7yEqI5NyJ4W4pk7CuqIbbH1/d+fje93cRERzE18/Id+nfFxsRwnmTMrjnvR3dxk8dncKvX9vcmVABfLyzkm0H6jhrvDmJde3cEbzXvJsbTpnSq3Y7R6ptamN9cQ0l1Y1kJ0ZxoLaZ9g6bsekxjE2PdYnzRGLDXb/Mk6LCCAkeGsfw65vb2FnRQEtbBzlJUX5dXV5EhjZ3zFTNAnbYtr0LwLKsp4ELASVVXjIlO4EX7pzP1v11hAY5GJcRS3bi4JupAmh32vzylU2drW5a2p1859nPGZseS54bZqzWFde4jD3x2T6umTPcZY+RZVlcNiOLbQfqeGvTAUKCLG5fkEdabDg7DtS7XOfoRseWRZ8TqrZ2J48s28Mf39rGXafl8ce3trO/thkws5JP3DKbGTmJfbrmzJxEkqNDO3vtWRZ884x8osMG10GGnpTVNvO/b2zhudXFAOQmR/Kva2dQMEwbuUXE+yx7gM1hLcu6FDjbtu1bDj2+Dpht2/ZXj3rercCtACkpKdMXL148oNcdjOrr64mO9l3fOHdq67Cpa26jtrmd6LAgYsNDCA3uOYHoy303tHawq9w1YRmZHOWWKtzVTW0UHmzsNhYZGkRuchSOY8wAOW2zr8sCQoMd2EBJVRMHG7s3BB6ZEk1UaFdBzv78e7e0O9l+oB7LgqToUJdELTY8hOFJkb1uVA3m36q2uY32DidOG4KDLCJDgjxW1dyb/89rm9vYW9n93zMhMpTMhIg+/R25w1D6+u4L3XdgCdT7Xrhw4Srbtmec6Hnu+K7a0/cul0zNtu37gPsACgoK7AULFrjhpQeXpUuXMhTuu6G1nR88t46XPz+82bmdCRmRPHTjrB777PXlvneX1/Odv35EU1tH51hYsIPXvjbHLXur9lQ2cPdDK9hd0QBAsMPikZtmMT+vb8ul64tq+NPbW3lvazmx4cH88NyxLJySQWRo15dUf/691+yr4ivvfEJabBinjk5l8frCbn8+KiWS/3xhPrF9qEz+1sb9fPuxVYQFOwgNclDX0s7IlDCW3DbPI+UVvPn//C/vbOMv67v3lkyPC+WVu+Z6/cToUPn67ivdd2AJ1PvuLXckVUVA9hGPs4ASN1xX/NTeioYjEipjQ0ktO8rqe9W8+HhykqP4yxVT+ObitTS2dhAe4uCPl00m9xg1ng7UNvP5oeKbeanRTM6KJy7y2AlHTlIUj9w0iw1FNTS2tVOQFsO4PraU2VvZwJ1PrmJ4YhR3nZZHU1sHmfHh3RKq/hqeGMmolCh2ljeQk+S6hHvN7BHHTahs22Z/TTMhQQ6SD/1b1DSZOlot7c7OfWDFVU3dEtfBaly66wGAU/KT+5R0ioi4izuSqhVAvmVZuUAxcCVwtRuuK37qWAvGNjY1jW2s2HOQj3dWMDI5mpPykvp0bcuyOGt8Gq9+7WQO1DaTGhNGbnJUj5uzq5ta+cXLG3l1/f7OsW+ekc8dC/MIOc5epuGJkQzv556zmiZzf/sONrHvYBMf7TClK97dfIDnb48f8Gm6pOgw7rl6Gr9/YwtLt5bxg3PG8PDHe2hoaefmk3P5wsRjtyQ5UNPEk58Vcv+Hu4gOD+YH54zhrHHDyEuNdqmjdfG0LFIHmAD7g6nD47lyZjZPrzAzevlp0dx88khCjrEULSLiSQNOqmzbbrcs66vAm5iSCg/atr1xwJGJ38pJiuKcCcN4fUNXMjN2WAz5qdEsXlnIr1/b3Dk+KjmKH0ztW50py7LITY4iNSYM27aPedpt+4H6bgkVwD3v7eDcSenkp7p/o/LeigZ+9MJ6pg5PcPmzyoZWWtrdM/MzNj2Wv18zjaqGVuIiQrh0WhZtHU6GxYUf9+TfK+v3c/e7ZimsobWDbz7zOU/cHM7M3ETuvXY6P3tpI2V1LVw8LZPbTh153MRzsEiJCecn54/jmjkjOk//JQ+BZFFEBie37FS1bfs14DV3XEv8X1RYMD/+wlhm5ybyxsb9nJSXzLkT02lpd/Lnd7Z1e+7Oigaa2/r2JtfY2s6H28v527s76LBt7liQx4LRKS5tdxpb2l0+t63DptlDy1ovrSvh4x2VzB+VTJDDouOIwqHXz80hzY1H+SNDgzuXE6N7cdnapjaeXL7XZfyTnRXMz0/mrPHDmDY8geb2DlJjwggNDurhKoNTVGgwEzP7toQrIuIJalMj/ZKVEMkN83O5YX5u59ieigZa211npfp6wnTFniq+8lhXLam7nlrDvddNZ9H47ktfI1OiSYwK7VbxfHJ2HMM90IC5tb2DtzYeAODpFYX86NwxPL+6mPK6Fq6ZPZzLZmT3uX6UO4UFO8hOiGRneUO38SOba2sGR0TEswb//L/4jcz4CK6ald1tLDY8mLCQvs2KFFc1ctdpeXzzjHxm5ZqaTI8t2+vSUiY7MZJHbpzJqaNTiIsI4eJpmfzfZZOJi3T/ibbQ4CBOyTcnBPcdbOR3r28hMz6C3148ga+fMbrHiuzeFBYSxFdPyyPsiL1EGfHhzB3Ztz1tIiLSf5qpErcJCXZw+4I8shIiWbKqiLHpsXz55Fwqd6zt9TXWF1Xz57e3U15v6jNdNCWTM8elERUahKOHiuoTs+L557XTqGtqJyEqxKPLWhdPy+K/W8rYvL+Otg6b+pZ2Rqf5rv3M0aaPSOD5O+axpbSOsGAHEzPjGHGMU5MiIuJ+SqrkhOpb2tlUUkNhVRPDYsMZnxFL/DFmgzLiI/jKqaO4ZvZwwkOCCA5ysHRHj0910dDczq9e3dyZUAG8sLaY75w1mjnHmXE5cv+RJ41KjebRm2exq7yBIIfFqNRoEjwwK9ZflmUxPiOO8X0sESEiIu6hpEqOq73DyVPL93U70XfjvBy+vaiA6ONU5I7uR52g6qZWVu2tchmPiwhhWg8n7nwhJSbcpZ2NiIgIaE+VnMCeygZ+/+aWbmMPfbKHnWWurWQGKj4qlLmjXGekRqZE97j0JyIi4k+UVMlx1TW309bhenrvcJVud4oKDeZH54whO9Fs+nZY8LXT8piQ6T/7lkRERI5Fy39yXNkJkeQkR7KnoqtpbWxEMCN6aKHSW4UHGymsaiQ+IpRRKVHdTgeOzYjjudvmse9gI9FhweQmR/X59KCIiIgvKKmS40qOCeMfV0/j5y9vYvnug4xLj+WXF41nRFL/TpWt2HOQWx5ZSU1TG5YF3zpjNDfOzyU6vOu/YmpsOKluLKTZG06nTWVDC5GhwUQdZ6+YiIjIsejdQ05oXEYcD1w/g4MNbcRFBPe7DlRlfQvfX/J559KhbcMf397G3FFJzMhJdGfIfVJ4sJEnlu/luVXF5KZE8d2zCpiRk+CzYp7ldc00tnaQHhtOqBtn6eqb21izr5pV+6rITohkRk5Cv5NjERFxpaRKeiU6PKRfJ/qOVNXYxq4jlhEPK61pHtB1B6K1vYN7/rudZ1YWAVBe38KP/7Oef103nZEp0V6Oxcn728r4y9vbuGhaFhuLa2hoaefKWcOZPTLpuKcte+M/a4r5yYtdbTnHDovlwRtmdKu6LiIi/aeN6uI1ESEObpiX063qN+DTauSlNc0sWV0MQGiQg+8uKmB8ZhzfeGYt93+4i+Iq1yTQUzaX1nLrY6s4b3IGf3hjKy+sLeHtzWXc/MhKPthWPqBrF1c18fs3tnZ/vf21bCqtHdB1RUSki2aqxOPanTYPfrSbBz7aTVxEMN9bVMDilUXsLK/n+2ePYcywGJ/FFhrsICY8mOrGNq6fl8Ojy/ZwoNYUH11XVMOW/XX8+qIJXtksv7O8npjwYA7UttDa0b2H4j3/3c4p+cn9ni1s63DS2EOj6ZYeejWKiEj/aKZKPK6mqY1fvLKJ4uomNpXW8ctXN/P9cwp49Wsnc8P8HJ9uDE+Pi+B/vjAWgMjQoM6E6rDnVhex76B3ZqviIkzC1NNWLsuyehzvrYz4cC6dntltLDI0iPxU7y5xBrryuhaW7azk4x0VlNX6btlbRDxDM1XiUTWNrVTWt3B0/r6xpJbTxqT5JqijnDMhncz4SIp6WOoLsiwcXtqwPiEzlokZcaTGhBEW7Og2i3Tnwjyiwvq/py00OIivLswnLSac59cUk58azV2n5ZOf5rtZwkCzu6Kerz25lvUlNQDkp0bzz2unkZeqfwORoUJJlXhUSLCDYIfrhKg/9cyLCgtm7qgk9tdEUpAWzdYDXdXib5yfy/DE/tfk6ou02Aj+dMUUth+o5e9XT+XdzWVUNbZy+YzhzBo58NOR2YmRfPPM0dwwP5fI0CDCVf/Lq97dXNaZUAFsL6vn5c9L+OaZBT6MSkTcSUmVeFRkaDCpsWE4rBachwqzJ0WFMjvXdyUUjmVYXAT/um4G720pY11RNQvHpDJvVBIhwd5bJU+LDSftUI2uM8YNc/v1LcsiMcp/EtpA8tnugy5jH++o5Btn2D4r3yEi7qWkSjwuOiyYJbdPZ+2+aqLCgpg+IsFvlzxyk6PIPSnX12HIEHTamFTe2nSg29g5E9OVUIkMIUqqxCumDU9g2vAEX4ch4jOnjE7hkmmZPHeohMe5E4axaJx/7CsUEfdQUiUi4gUZ8RH86qKJ3HLySGzbZkRyFFGh+hYsMpToK1pExEsiQoMYmx7r6zBExEOUVIlIv9i2zfriGlbtrSLE4WB6ToISBhEJaEqqRKRfVu+r4qr7lndWf48OC+bpW+f4OCoREd9RRXUR6bMOp81DH+3p1k6nvqWdtzbt92FUIiK+pZkqET+0q7yej3dWsKeikfl5yUwfEU9chP/Ul+qwnezvoc1KWW0LJPkgIBERP6CkSsTPFFU1ctPDK9hTadrmPPDRbn56/jhunO8/9bNCg4L40twRrNxb1W383InpOEtci1yKiAQCLf+J+JnNpbWdCdVhf3xrG8VH9SZsbe+gpLqJmqY2b4bX6ZTRKfzvJRMZkRRJflo0/7hmGtNHqBaZiAQuzVSJ+JnWdttlrKW9g3Zn1/juinr+/t5OXllXwqiUaH5y3jhm5yZ6tTp3fGQoV8wczqLxw3BYFrER/W/4LCIyFGimSsTPFAyLJjqs+88718weQUZ8BACNre385tUtLFlVRHObk40ltVz/4GdsO6IRtDfFR4YqoRIRQUmViN/JS43hyS/P5vxJ6eSnRvPjc8dw6ykjCQkyX66l1c28vbl7D7mWdie7yn2TVImIiKHlPxE/NCkrnj9dPoWW9g6iw7vPAoWHBBEbEUxtU3u38aNnt0RExLs0UyUBZ0dZHS9/XsKr60r8enYnJNjhklABZCZE8JMvjOs2dnJeMmNUzVxExKf0o60ElI0lNVz17087Z3mSokJ54pbZgy4hOW9SOiOSItlZ3kBydBgTM+NIiQnzdVgiIgFNSZUElMUrCrstm1U2tPL6htJBl1RFhAYzKzeJWblDp9JmRV0LDgsSo5UcisjgpKRKAobTabNlf53L+I6yBh9EI4dVNbTyyroS/vbfHQQ7LL515mgWjR9GjE4Uisggoz1VEjAcDovLZ2S7jH9hUrrLmNPpWitKPOOD7eX85MWNlNW1UFLTzHeWrGP5HlVlF5HBR0mVBJRTC1L47qICIkODiAkL5n++MJZ5o7qW0Lbtr+O3r2/msnuX8eiyPZRUN/kw2qGvw2nz5PJ9LuMvrS32QTQiIgOj5T8JKMnRYdyxYBRfnJqJBaQfKqgJpufe9Q99RmmNaRS8am8Vm0vr+NkF4wgLDvJRxENbkMNiRFIky3d3n5kanhjlo4hERPpPM1UyaBRVNfL86iL+9/XNvLVxP5UNLf26jmVZZMRHdEuoALYfqOtMqA57ZsU+Cg9qtsqTrp49goiQrqQ1NjyYcyYO82FEIiL9o5kqGRQq61v4zrOf8+murhmNOxaM4ptnjCYk2D0/G/TUN89hWTi8104vIE3Jjue52+eyoaQWh2UKn45Oi/F1WCIifaakSgaFbQfquiVUAPd9sIuLp2WSl+qeN+DRaTHkJkexu6LrNOD180aQnRDpluvLsY3LiGNcRpyvwxARGRAlVTIotLQ7XcbanTatHa7j/ZURH8H9X5rB25sOsLaomrPGpTE/L9ltM2EiIjK0KamSQSEvNZqU6DDK67v2UZ06OoXhbp5FGpUazajUaLdeU0REAoOSKhkUshIiefimmdz/wS5W7avm3InDuGLm8B5744mIiPiCkiovOdjQSmu7k7rmNmKUCPTL+Iw4fn/pZBpa24kND8GhHeQyCJVUN1FS3URCZCg5yVEE6f+xyJChzSJesHxXJZf96xO2HqjjxodWsLGkxtchDVohwQ7iI0OVUMmgtGL3QS645yMu/dcyzv3rhzy7spCWtg5fhyUibqKkysN2l9dz08Mr2FluTpSt3FvF155aQ2V9/2osyYnZts2u8no+3F7OppJavWmJXyiva+abi9dSUd8KmMMXP/zPeraVufajFJHBSct/Hrb3YCMNrd3f1HeWN1Bc1URSdJiPohraPtxewW2Pr6KxtQOHBT88dyzXzh5ORKj+u4vvVNS3UlTVvZCsbUNJVTMTM30UlIi4lWaqPCwuwnX/VHiIg+hwvcF7QmlNE99e/DmNhxJZpw2/fnUz2w7U+zgy6a/aprYhMbObGBlKaozrD1JpsfrhSmSoUFLlYfmpMdw4L6fb2I/PHUtOknqbecLBhtZuZRcOO1Db3MOzxZ+1tHXw9qYDXH7vJ5z/t4946OPdVAzi5CotLpw/XT6ZqFDTksdhwY/OHcPoYaoeLzJUaLrEw6LDg/n6GfmcOS6Nsu1reO72GYxNj9FGaw9JiQ4jIy6ckiN6+FkWZB7V50/835rCar786MrOxz9/eROhwQ6umT3Ch1ENzEn5Kbz6tZMpqmokMSqMUSlRhIWoWbfIUKGZKi+IjwxlXl4y8REhTB+RQKT29nhMamw4f7lyCklRoQCEBTv4/SWTyFNBz0Hn4x0VLmMPfbyHuqY2H0TjPjnJUZyUn8K4jFglVCJDjN7dZciZlZvEy3edZGoBRYWSmxSlmcFBKPFQYnyktNgwtQ0SEb+lpEqGpIz4CDK05DeozR+VTGJUKAcbTAmCIIfFXQvzCdfsjoj4KSVVIuKXRg+L4Zlb57B6XxWNrR1MzY5nYla8r8MSETkmJVUi4rfy02LIT9PpOBEZHLQ5QURERMQNNFMlXld4sJGNJTU0tzkpGBbDmGExWJY2kouIyOCmpEq8andFPTc+tII9lY2AKXnwxC2zmZGT6OPIREREBkbLf+JVn+0+2JlQgWkq+9d3t9PUqqbHIiIyuGmmSk6oqKqR7QfqCQ6yGJ0WQ1pseL+vVVrj2i5md2UDze0dRIQG9lH5uuY2LCA63LVfpIiI+D8lVXJcW/fXcsNDKzqToXHpsfzjmmnkJPevd+HMHpb5rpw5nIRI10KPgaK+uY33tpbz9/d2EOSw+OppeZySn0JUmL48RUQGEy3/yTHZts0zKwq7zS5tKq3l/W3l/b7m1Ox4/njZZJKjQwkLdvDlk0fyxamZ7gh30Fq2q5K7nlrDlv11bCyp5fbHV7Nyz0FfhyUiIn2kH4XlmFrbnazYU+Uyvq6out/XjAwL5pLpWZycn0xrh5P0uAiCAriFjG3bPPHpPpfx51YXcWpBqg8i8ryGlnY2l9ayt7KBtNhwxmfEkdBDSxoRkcFGSZUcU1hIEOdPTmd9cU238VNHpwz42qkD2Jc1lFiWRXJMmMt4crTr2FDgdNosWVXIT1/a1Dl2zezh/OCcMcRoL5mIDHJa/pPjOndCOhdOycCyTO+1L5+cy9xRSb4Oa0i5atZwQoO6vhTDgh1cMGVoLonuqWzgN69t6Tb2xPJ9bD9Q76OIRETcRzNVclxZiZH87uJJ3LEgjyCHxYjESEKClYu707Th8Sy5bS7LdlUS5LCYMzKRCZnxvg7LIxpa2mlpd7qM1zS1+SAaERH3UlIlJxQRGkTBMPVf8xTLspiUHc+k7Hhfh+JxGfER5KdGs72sa2YqKjSIEUmRPoxKRMQ9NOUgIl6TFB3GX6+ayrxDS8hjhsXw8I2zGJkS7ePIREQGTjNVIuJVY9Nj+fd1M6hsaCE2IoT4AK5RJiJDi5IqEfG6qPBgosL17UdEhhYt/4n4udb2Dlrb1RtRRMTf6UdFET/V2t7BZ3uquO/9nTS1dXDzSbmclJdCtGZ4RET8kr47i/ipNfuque6B5di2ebxiTxX3XjudRROG+TYwERHpkZKqIaKiroV1RdUUVzeRkxzFxMw4bQAe5N7cuL8zoTrsgY92s3BMCqHBQb4JSkREjklJ1RBQ19zGb1/fwnOrizrHvnFGPncuyFOhzkEsMtT1yzMyLAiHFbi9EkVE/JnecYeA7WX13RIqgHv+u4PdlQ0Dum5VQyvLdlbw+vpStpTW0uG0T/xJ4jZnjksj7Iik2LLgyyePJDhIX7YiIv5IM1VDQENLu8tYu9OmsbX/J8YqG1r45cubeGFtCQDBDov7r5/BgoLUfl9T+mZSVhzPfmUu72w5QGNLB4vGpzE5O8HXYYmIyDEMKKmyLOsPwPlAK7ATuNG27Wo3xCV9kJscRWJUKAcbWjvHxgyLYXhiRL+vubmktjOhApOk/ej59bz41fmkxIQPKF7pHX9tX2PbJmGPDA3C0lKkiEinga4jvA1MsG17ErAN+OHAQ5K+ykqI5JEbZ3JyXjJRoUGcO3EYf71qKolRYf2+ZuURCdphJTXN1De7zopJ4NhZVs//vrGFi//xCb97fQs7j+jhJyIS6AY0U2Xb9ltHPPwUuHRg4Uh/TcyK519fmk5tUxuJkaGEhQzsdFhOUhSWRbfTZyflJZMaq1mqQFVZ38I3n1nLuuIaALYeqOOjHRU8etMskqL7n8CLiAwVln30me3+XsiyXgaesW378WP8+a3ArQApKSnTFy9e7JbXHUzq6+uJjh4cjWNtoLapjZLqJtqdNlGhwWQmRHTbON1bg+m+3Wmo3Xdjawc7y11npkalRBMZ2pXED7X77i3dd2DRfQeWhQsXrrJte8aJnnfCpMqyrHeAnqoN/ti27RcPPefHwAzgYrsXWVpBQYG9devWEz1tyFm6dCkLFizwdRh9UlLdRH1LO+lx4cSEh/TrGoPxvt1hqN3354XVXPj3j13GX7hzPlOO2Pc11O67t3TfgUX3HVgsy+pVUnXC5T/bts84wQtdD5wHnN6bhEoGl4z4/m92l6FlZEoU50wYxusb9neOnT1+GCOTo3wYlYiI/xjo6b+zge8Dp9q23eiekETEH8WEh/CT88Zx5rg0Vu6pYvqIeOaOSiY2on8zmCIiQ81A61TdA4QBbx86Wv2pbdu3DTgqEfFLGfERXDwti4unZfk6FBERvzPQ03957gpEREREZDBTvwsRERERN1BSJSIiIuIGSqpERERE3EBJlYiIiIgbKKkSERERcQMlVSIiIiJuoKRKRERExA0GWvxTRPqoqqGVXRX1OCyLkSlRxEWE+jokERFxAyVVIl60u6Ke7yz+nFX7qgE4OT+Z33xxItmJkb4NTEREBkzLfyJe9Oq60s6ECuDD7RUs3Vruu4BERMRtlFSJeElHh5P/bnFNoD7eoaRKRGQoUFIl4iVBQQ5OH5vqMj4/P8UH0YiIiLspqRLxoi9MTGdWbkLn44UFKSwcraRKRGQo0EZ1ES/KSY7ivutmsKu8AYcFuSnRxEWE+DosERFxAyVVIl4WHxnKtBEqoyAiMtRo+U9ERETEDZRUiYiIiLiBkioRERERN1BSJSIiIuIGSqpERERE3EBJlYiIiIgbKKkSERERcQMlVSIiIiJuoKRKRERExA2UVImIiIi4gZIqERERETdQUiUiIiLiBkqqRERERNxASZWIiIiIGyipEhEREXEDJVUiIiIibqCkSkRERMQNlFSJiIiIuIGSKhERERE3UFIlIiIi4gZKqkRERETcQEmViIiIiBsoqRIRERFxA8u2be+/qGXVAVu9/sK+lwxU+DoIH9B9Bxbdd2DRfQeWQL3vAtu2Y070pGBvRNKDrbZtz/DRa/uMZVkrdd+BQ/cdWHTfgUX3HVgsy1rZm+dp+U9ERETEDZRUiYiIiLiBr5Kq+3z0ur6m+w4suu/AovsOLLrvwNKr+/bJRnURERGRoUbLfyIiIiJu4LOkyrKsX1qWtc6yrLWWZb1lWVaGr2LxJsuy/mBZ1pZD9/4fy7LifR2TN1iWdZllWRsty3JaljWkT45YlnW2ZVlbLcvaYVnWD3wdj7dYlvWgZVlllmVt8HUs3mRZVrZlWe9ZlrX50P/xr/s6Jk+zLCvcsqzPLMv6/NA9/9zXMXmTZVlBlmWtsSzrFV/H4k2WZe2xLGv9offtXp2GGwosy4q3LGvJoffuzZZlzT3Wc305U/UH27Yn2bY9BXgF+H8+jMWb3gYm2LY9CdgG/NDH8XjLBuBi4ANfB+JJlmUFAX8HzgHGAVdZljXOt1F5zcPA2b4OwgfagW/btj0WmAPcGQD/5i3AabZtTwamAGdbljXHtyF51deBzb4OwkcW2rY9JcDKKtwNvGHb9hhgMsf5t/dZUmXbdu0RD6OAgNjcZdv2W7Zttx96+CmQ5ct4vMW27c22bQdCwddZwA7btnfZtt0KPA1c6OOYvMK27Q+Ag76Ow9ts2y61bXv1od/XYb7hZvo2Ks+yjfpDD0MOfQTE93DLsrKALwD3+zoW8TzLsmKBU4AHAGzbbrVtu/pYz/fpnirLsn5tWVYhcA2BM1N1pJuA130dhLhVJlB4xOMihvgbrHSxLCsHmAos93EoHndoCWwtUAa8bdv2kL/nQ/4CfA9w+jgOX7CBtyzLWmVZ1q2+DsZLRgLlwEOHlnzvtywr6lhP9mhSZVnWO5Zlbejh40IA27Z/bNt2NvAE8FVPxuJNJ7rvQ8/5MWbZ4AnfRepevbnvAGD1MBYQP8EHOsuyooHngG8cNRM/JNm23XFo+0YWMMuyrAk+DsnjLMs6DyizbXuVr2Pxkfm2bU/DbG+407KsU3wdkBcEA9OAf9q2PRVoAI65V9ajbWps2z6jl099EngV+KkHw/GaE923ZVnXA+cBp9tDqKZFH/69h7IiIPuIx1lAiY9iES+xLCsEk1A9Ydv2876Ox5ts2662LGspZj/dUD+kMB+4wLKsc4FwINayrMdt277Wx3F5hW3bJYd+LbMs6z+Y7Q5Dep8s5nt60REzsUs4TlLly9N/+Uc8vADY4qtYvMmyrLOB7wMX2Lbd6Ot4xO1WAPmWZeValhUKXAm85OOYxIMsy7Iw+y0227b9J1/H4w2WZaUcPrlsWVYEcAYB8D3ctu0f2radZdt2DuZr+7+BklBZlhVlWVbM4d8DZzH0k2hs294PFFqWVXBo6HRg07Ge76uGygC/OxSkE9gL3ObDWLzpHiAMeNt8L+ZT27aH/L1blvVF4G9ACvCqZVlrbdte5OOw3M627XbLsr4KvAkEAQ/atr3Rx2F5hWVZTwELgGTLsoqAn9q2/YBvo/KK+cB1wPpDe4wAfmTb9mu+C8nj0oFHDp12dQCLbdsOqPICASgN+M+h961g4Enbtt/wbUhecxfwxKEflHcBNx7riaqoLiIiIuIGqqguIiIi4gZKqkRERETcQEmViIiIiBsoqRIRERFxAyVVIiIiIm6gpEpERETEDZRUiYiIiLiBkioRERERN/j/V8gaN42QIq8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "x=np.array(list(np.random.normal(0,1,100))+list(np.random.normal(3,1,100)))\n",
    "y=np.array(list(np.random.normal(0,1,100))+list(np.random.normal(3,1,100)))\n",
    "l=np.array([0]*100+[1]*100)\n",
    "plt.figure(figsize=(10,8))\n",
    "sns.scatterplot(x=x,y=y,hue=l)\n",
    "plt.xlim([-3,6])\n",
    "plt.ylim([-3,7])\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us assume that we fit a logistic regressor model to this data\n",
    "\n",
    "$$P\\left( y=1 | \\mathbf{x} \\right) = \\frac{1}{1 + e^{- {(\\beta}_{0} + \\beta_{1}x_{1} + \\beta_{2}x_{2})}}$$\n",
    "\n",
    "and find the following values for the parameters:\n",
    "\n",
    "$$\\left\\{ \\begin{matrix}\n",
    "\\beta_{0} = - 3.47 \\\\\n",
    "\\beta_{1} = 1.17 \\\\\n",
    "\\beta_{2} = 1.43 \\\\\n",
    "\\end{matrix} \\right.\\ $$\n",
    "\n",
    "We know that these parameters allow to find a probability value according to the formula above.\n",
    "We can use these values to **classify the observations** $\\mathbf{x}$. In practice, a reasonable criterion to classify observations would be:\n",
    "\n",
    "$$\\hat y = \\begin{cases}1 & \\text{if } P(y=1|\\mathbf{x}) \\geq 0.5\\\\0 & \\text{otherwise}\\end{cases}$$\n",
    "\n",
    "This makes sense as we are assigning the observations to the group for which the posterior probability $P(y|\\mathbf{x})$ is higher. \n",
    "\n",
    "To understand how the data is classified, we can look at those points in\n",
    "which the classifier is uncertain, which is often called **the decision boundary**, i.e.,\n",
    "those points in which $P\\left( y=1 | \\mathbf{x} \\right) = 0.5$.\n",
    "\n",
    "We note that:\n",
    "\n",
    "$$P\\left(y=1 | \\mathbf{x} \\right) = 0.5 \\Leftrightarrow e^{- (\\beta_{0} + \\beta_{1}x_{1} + \\beta_{2}x_{2})} = 1 \\Leftrightarrow 0 = \\beta_{0} + \\beta_{1}x_{1} + \\beta_{2}x_{2}$$\n",
    "\n",
    "This last equation is the equation of a line (in the form\n",
    "$ax + by + c = 0$). We can see it in explicit form:\n",
    "\n",
    "$$x_{2} = - \\frac{\\beta_{1}}{\\beta_{2}}x_{1} - \\frac{\\beta_{0}}{\\beta_{2}}$$\n",
    "\n",
    "So, we have found a line which has a\n",
    "\n",
    "-   Angular coefficient equal to $- \\frac{\\beta_{1}}{\\beta_{2}}$;\n",
    "\n",
    "-   Intercept equal to $- \\frac{\\beta_{0}}{\\beta_{2}}$;\n",
    "\n",
    "If we plot this line, we obtain the **decision boundary** which\n",
    "separates the elements from the two classes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "lr = LogisticRegression()\n",
    "lr.fit(np.vstack([x,y]).T,l)\n",
    "xx = np.linspace(-3,6)\n",
    "yy = -lr.coef_[0][0]/lr.coef_[0][1]*xx-lr.intercept_/lr.coef_[0][1]\n",
    "plt.figure(figsize=(10,8))\n",
    "sns.scatterplot(x=x,y=y,hue=l)\n",
    "plt.xlim([-3,6])\n",
    "plt.ylim([-3,7])\n",
    "plt.plot(xx,yy,'r', label='decision boundary')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, the decision boundary found by a logistic regressor is a\n",
    "line. This is because **a logistic regressor is a linear classifier**,\n",
    "despite the logistic function is not linear!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation of the Parameters of a Logistic Regressor\n",
    "\n",
    "To fit the model and find suitable values for the $\\mathbf{\\beta_i}$\n",
    "parameters, we will define a **cost function**, similarly to what we have\n",
    "done in the case of linear regression. \n",
    "\n",
    "Even if we can see the logistic\n",
    "regression problem as the linear regression problem of fitting the\n",
    "$logit(p) = \\mathbf{\\beta}^{T}\\mathbf{x}$ function, differently from\n",
    "linear regression, **we should note that we do not have the ground truth probabilities p**. \n",
    "Indeed, our observations only provide input examples\n",
    "$\\mathbf{x}^{(i)}$ and the corresponding labels $y^{(i)}$.\n",
    "\n",
    "Starting from the definition:\n",
    "\n",
    "$$P\\left( y = 1 \\middle| \\mathbf{x}; \\mathbf{\\beta} \\right) = f_{\\mathbf{\\beta}}\\left( \\mathbf{x} \\right) = \\frac{1}{1 + e^{- \\mathbf{\\beta}^{T}\\mathbf{x}}} = \\sigma(\\mathbf{\\beta}^{T}\\mathbf{x})$$\n",
    "\n",
    "We can write:\n",
    "\n",
    "$$P\\left( y = 1 \\middle| \\mathbf{x};\\mathbf{\\beta} \\right) = f_{\\mathbf{\\beta}}(\\mathbf{x})$$\n",
    "\n",
    "$$P\\left( y = 0 \\middle| \\mathbf{x};\\mathbf{\\beta} \\right) = 1 - f_{\\mathbf{\\beta}}(\\mathbf{x})$$\n",
    "\n",
    "Since $y$ can only take values $0$ and $1$, this can also be written as follows in a more compact form:\n",
    "\n",
    "$$P\\left( y \\middle| \\mathbf{x};\\mathbf{\\beta} \\right) = \\left( f_{\\mathbf{\\beta}}\\left( \\mathbf{x} \\right) \\right)^{y}\\left( 1 - f_{\\mathbf{\\beta}}\\left( \\mathbf{x} \\right) \\right)^{1 - y}$$\n",
    "\n",
    "Indeed, when $y = 1$, the second factor is equal to $1$ and the\n",
    "expression reduces to\n",
    "$P\\left( y = 1 \\middle| \\mathbf{x};\\mathbf{\\beta} \\right) = f_{\\mathbf{\\beta}}(\\mathbf{x})$.\n",
    "Similarly, if $y = 0$, the first factor is equal to $1$ and the\n",
    "expression reduces to $1 - f_{\\mathbf{\\beta}}(x)$.\n",
    "\n",
    "We can estimate the parameters by maximum likelihood, i.e., choosing the\n",
    "values of the parameters which maximize the probability of the data\n",
    "under the model identified by the parameters $\\mathbf{\\beta}$:\n",
    "\n",
    "$$L\\left( \\mathbf{\\beta} \\right) = P(Y|X;\\mathbf{\\beta})$$\n",
    "\n",
    "If we assume that the training examples are all independent, the\n",
    "likelihood can be expressed as:\n",
    "\n",
    "$$L\\left( \\mathbf{\\beta} \\right) = \\prod_{i = 1}^{N}{P(y^{(i)}|\\mathbf{x}^{(i)};\\mathbf{\\beta})} = \\prod_{i = 1}^{N}{f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)^{y^{(i)}}\\left( 1 - f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right) \\right)^{{1 - y}^{(i)}}}$$\n",
    "\n",
    "Maximizing this expression is equivalent to minimizing the negative\n",
    "logarithm of $L(\\mathbf{\\beta})$ (negative log-likelihood - nll):\n",
    "\n",
    "$$nll\\left( \\mathbf{\\beta} \\right) = - \\log{L\\left( \\mathbf{\\beta} \\right)} = - \\sum_{i = 1}^{N}{\\log\\left\\lbrack f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)^{y^{(i)}}\\left( 1 - f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right) \\right)^{{1 - y}^{(i)}} \\right\\rbrack} =$$\n",
    "\n",
    "$$= - \\sum_{i = 1}^{N}{\\lbrack y^{(i)}\\log{f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)}} + \\left( 1 - y^{(i)} \\right)\\log{(1 - f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)})\\rbrack$$\n",
    "\n",
    "Hence, we will define our cost function as:\n",
    "\n",
    "$$J\\left( \\mathbf{\\beta} \\right) = - \\sum_{i = 1}^{N}{\\lbrack y^{(i)}\\log{f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)}} + \\left( 1 - y^{(i)} \\right)\\log{(1 - f_{\\mathbf{\\beta}}\\left( \\mathbf{x}^{(i)} \\right)})\\rbrack$$\n",
    "\n",
    "This can be rewritten more explicitly in terms of the $\\mathbf{\\beta}$\n",
    "parameters as follows:\n",
    "\n",
    "$$J\\left( \\mathbf{\\beta} \\right) = - \\sum_{i = 1}^{N}{\\lbrack y^{(i)}\\log{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}} + \\left( 1 - y^{(i)} \\right)\\log{(1 - \\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right)})\\rbrack$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly to linear regression, we now have a cost function to minimize in order to find the values of the $\\beta_i$ parameters. Unfortunately, in this case, $J(\\mathbf{\\beta})$ assumes a nonlinear form **which prevents us to use the least square principles** and **there is no closed form solution for the parameter estimation**. In these cases, parameters can be estimated using some form of **iterative solver**, which begins with an initial guess for the parameters and iteratively refine them to find the final solution. Luckily, the logistic regression cost function **is convex, and hence only a single solution is admitted, independently from the initial guess**.\n",
    "\n",
    "Different iterative solvers can be used in practice. The most commonly used is the **gradient descent algorithm**, which requires the cost function to be differentiable. We will not see this algorithm in details, but an introduction to it and its application to the estimation of the parameters of a logistic regressor are given in the following (hidden) section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{toggle}\n",
    "## Estimating the Parameters of a Logistic Regressor through Gradient Descent\n",
    "\n",
    "Given the cost function $J(\\mathcal{\\beta})$ above, we want to find suitable values $\\mathbf{\\beta}$ by\n",
    "solving the following optimization problem:\n",
    "\n",
    "$$\\mathbf{\\beta} = \\arg_{\\mathbf{\\beta}}\\min{J(\\mathbf{\\beta})}$$\n",
    "\n",
    "As we already discussed, since $J$ is nonlinear, we cannot find a closed form solution for the estimation of the parameters.\n",
    "\n",
    "Alternatively, we could **compute**\n",
    "$\\mathbf{J}\\left( \\mathbf{\\beta} \\right)$ **for all possible values\n",
    "of** $\\mathbf{\\beta}$ **and choose the values of** $\\mathbf{\\beta}$\n",
    "**which minimizes the cost**. However, this option is unfeasible in\n",
    "practice as $\\beta$ may assume an infinite number of values. Hence, we\n",
    "need a way to **find the values of** $\\mathbf{\\beta}$ **which\n",
    "minimize** $\\mathbf{J(}\\mathbf{\\beta}\\mathbf{)}$ **without computing**\n",
    "$\\mathbf{J(}\\mathbf{\\beta}\\mathbf{)}$ **for all possible values of**\n",
    "$\\mathbf{\\beta}$**.**\n",
    "\n",
    "In these cases, we can use **gradient descent**, a numerical optimization strategy\n",
    "which allows to **minimize differentiable functions** with respect\n",
    "to their parameters.\n",
    "\n",
    "We will introduce the gradient descent algorithm considering initially\n",
    "the problem of minimizing a function of a single variable $J(\\theta)$.\n",
    "We will then extend to the case of multiple variables.\n",
    "\n",
    "**The gradient descent algorithm is based on the observation that, if a\n",
    "function** $J(\\theta)$ *is defined and differentiable in a neighborhood\n",
    "of a point* $\\theta^{(0)}$*, then* $J(\\theta)$ *decreases fastest if one\n",
    "goes from* $\\theta^{(0)}$ *towards the direction of the negative\n",
    "derivative of* $J$ *computed in* $\\theta^{(0)}$*.* Consider the function\n",
    "$J(\\theta)$ shown in the plot below:\n",
    "\n",
    "\n",
    "In these cases, we can use **gradient descent**, a numerical optimization strategy\n",
    "which allows to **minimize differentiable functions** with respect\n",
    "to their parameters.\n",
    "\n",
    "We will introduce the gradient descent algorithm considering initially\n",
    "the problem of minimizing a function of a single variable $J(\\theta)$.\n",
    "We will then extend to the case of multiple variables.\n",
    "\n",
    "**The gradient descent algorithm is based on the observation that, if a\n",
    "function** $J(\\theta)$ *is defined and differentiable in a neighborhood\n",
    "of a point* $\\theta^{(0)}$*, then* $J(\\theta)$ *decreases fastest if one\n",
    "goes from* $\\theta^{(0)}$ *towards the direction of the negative\n",
    "derivative of* $J$ *computed in* $\\theta^{(0)}$*.* Consider the function\n",
    "$J(\\theta)$ shown in the plot below:\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd1.png)\n",
    "\n",
    "Let us assume that we are at the initial point $\\theta^{(0)}$. From the\n",
    "plot, we can see that we should move to the right part of the x axis in\n",
    "order to reach the minimum of the function.\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd2.png)\n",
    "\n",
    "\n",
    "The first derivative of the function in that point $J'(\\beta^{(0)})$\n",
    "will be equal to the angular coefficient of the tangent to the curve in\n",
    "the point $(\\theta^{(0)},J\\left( \\theta^{(0)} \\right))$. Since the curve\n",
    "is decreasing in a neighborhood of $\\beta^{(0)}$, the tangent line will\n",
    "also be decreasing. Therefore, its angular coefficient\n",
    "$J'(\\theta^{(0)})$ will be negative. If we want to move to the right, we\n",
    "should follow in the *inverse direction* of the derivative of the curve\n",
    "in that point.\n",
    "\n",
    "The gradient descent is an iterative algorithm; hence we are not trying\n",
    "to reach the minimum of the function in one step. Instead, we would like\n",
    "to move to another point $\\theta^{(1)}$ such that\n",
    "$J\\left( \\theta^{(1)} \\right) < J(\\theta^{(0)})$. If we can do this for\n",
    "every point, we can reach the minimum in a number of steps.\n",
    "\n",
    "At each step, we will move proportionally to the value of the\n",
    "derivative. This is based on the observation that larger absolute values\n",
    "of the derivative indicate steeper curves. If we choose a multiplier\n",
    "factor $\\gamma$, we will move to the point:\n",
    "\n",
    "$$\\theta^{(1)} = \\theta^{(0)} - \\gamma J'(\\theta^{(0)})$$\n",
    "\n",
    "For instance, if we choose $\\gamma = 0.02$, we will move to point\n",
    "$\\theta^{(1)} = 0.4 + 0.02 \\cdot 1.8 = 0.436$. The procedure works\n",
    "iteratively until the derivative is so small that no movement is\n",
    "possible, as shown in the following figure:\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd3.png)\n",
    "\n",
    "In the next step, we compute the derivative of the function in the\n",
    "current point $J\\left( \\beta^{(1)} \\right) = - 0.8$ and move to point\n",
    "$\\beta^{(2)} = \\beta_{1} - \\gamma J'(\\beta^{(1)})$.\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd4.png)\n",
    "\n",
    "\n",
    "Next, we compute the derivative of the function in the current point\n",
    "$f\\left( \\theta^{(2)} \\right) = - 0.4$ and move to point\n",
    "$\\theta^{(3)} = \\theta^{(2)} - \\gamma J'(\\theta^{(2)})$:\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd5.png)\n",
    "\n",
    "\n",
    "We then compute the derivative of the current point\n",
    "$J\\left( \\theta^{(3)} \\right) \\approx 0$:\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd6.png)\n",
    "\n",
    "\n",
    "This derivative is so small that we cannot advance further. We are in a\n",
    "local minimum. The optimization terminates here. We have found the value\n",
    "$\\theta^{(3)} = \\arg_{\\theta}\\min{J(\\theta)}$.\n",
    "\n",
    "In practice, the algorithm is terminated following a **given termination\n",
    "criterion**. Two common criteria are:\n",
    "\n",
    "-   A maximum number of iterations is reached.\n",
    "\n",
    "-   The value $\\gamma J'(\\theta)$ is below a given threshold.\n",
    "\n",
    "\n",
    "### Global vs Local Minima\n",
    "\n",
    "It is important to note that gradient descent can be applied only if the\n",
    "cost function is **differentiable with respect to its parameters**.\n",
    "Moreover, the algorithm is guaranteed to converge to the global minimum\n",
    "**only if the cost function is convex**. In the general case of\n",
    "non-convex loss function, the algorithm may converge to a **local\n",
    "minimum**, which may represent a **suboptimal solution**. Nevertheless,\n",
    "when the number of parameters is very large, gradient descent **usually\n",
    "finds a good enough solution**, even if it only converges to a local\n",
    "minimum.\n",
    "\n",
    "\n",
    "### One Variable\n",
    "\n",
    "The gradient descent algorithm can be written in the following form in\n",
    "the case of one variable:\n",
    "\n",
    "1.  Choose an initial random point $\\beta$;\n",
    "\n",
    "2.  Compute the first derivative of the function $J'$ in the current\n",
    "    point $\\theta$: $J'(\\theta)$;\n",
    "\n",
    "3.  Update the position of the current point using the formula\n",
    "    $\\theta = \\theta - \\gamma J'(\\theta)$;\n",
    "\n",
    "4.  Repeat 2-3 until some termination criteria are met.\n",
    "\n",
    "\n",
    "### Multiple Variables\n",
    "\n",
    "The gradient descent algorithm generalizes to the case in which the\n",
    "function $J$ to optimize depends on multiple variables\n",
    "$J(\\theta_{1},\\theta_{2},\\ldots,\\theta_{n})$.\n",
    "\n",
    "For instance, let's consider a function of two variables\n",
    "$J(\\theta_{1},\\theta_{2})$. We can plot such function as a 3D plot\n",
    "(left) or as a contour plot (right). In both cases, our goal is to reach\n",
    "the point with the minimum value (the 'center' of the two plots). Given\n",
    "a point $\\mathbf{\\theta} = (\\theta_{1},\\theta_{2})$, the direction of\n",
    "steepest descent is the **gradient** of the function in the point.\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd7.png)\n",
    "\n",
    "\n",
    "The gradient is a multi-variable generalization of the derivative. The\n",
    "gradient of a function of $n$ variable computed in a point\n",
    "$\\mathbf{\\theta}$ is a vector whose $i^{th}$ variable is given by the\n",
    "partial derivative of the function with respect to the $i^{th}$\n",
    "variable:\n",
    "\n",
    "$$\\nabla J\\left( \\mathbf{\\theta} \\right) = \\begin{pmatrix}\n",
    "J_{\\theta_{1}}(\\mathbf{\\theta}) \\\\\n",
    "J_{\\theta_{2}}(\\mathbf{\\theta}) \\\\\n",
    "\\begin{matrix}\n",
    "\\ldots \\\\\n",
    "J_{\\theta_{n}}(\\mathbf{\\theta}) \\\\\n",
    "\\end{matrix} \\\\\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "In the case of two variables, the gradient will be a 2D vector (the\n",
    "gradient) indicating the direction to follow. Since in general we want\n",
    "to optimize multi-variable functions, the algorithm is called 'gradient\n",
    "descent'.\n",
    "\n",
    "The following figure shows an example of an optimization procedure to\n",
    "reach the center of the curve from a given starting point:\n",
    "\n",
    "![](/_static/lecture_specific/gradient_descent/gd8.png)\n",
    "\n",
    "The pseudocode of the procedure, in the case of the multiple variables\n",
    "is as follows:\n",
    "\n",
    "1.  Initialize\n",
    "    $\\mathbf{\\theta} = (\\theta_{1},\\theta_{2},\\ldots,\\theta_{n})$\n",
    "    randomly.\n",
    "\n",
    "2.  For each variable $x_{i}$:\n",
    "\n",
    "3.  Compute the partial derivative at the point:\n",
    "\n",
    "4.  $\\frac{\\partial}{\\partial\\theta_{i}}J\\left( \\mathbf{\\theta} \\right)$\n",
    "\n",
    "5.  Update the current variable using the formula:\n",
    "\n",
    "$$\\theta_{i} = \\theta_{i} - \\gamma\\frac{\\partial}{\\partial\\theta_{i}}J(\\mathbf{\\theta})$$\n",
    "\n",
    "6.  Repeat 2-3 until the termination criteria are met.\n",
    "\n",
    "### Logistic Regression and Gradient Descent\n",
    "It can be shown that, in the case of the logistic regressor, the update rule will be:\n",
    "\n",
    "$$\\beta_{j}\\mathbf{=}\\beta_{j}\\mathbf{-}\\gamma\\sum_{i = 1\\ }^{N}{x_{j}^{(i)}\\left( \\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right) - y^{(i)} \\right)}$$\n",
    "\n",
    "For the most curious, the details are in the following section.\n",
    "\n",
    "#### Derivation of the Update Rule\n",
    "\n",
    "Let us first consider the derivative of the logistic function:\n",
    "\n",
    "$$\\sigma(x) = \\frac{1}{1 + e^{- x}}$$\n",
    "\n",
    "This will be:\n",
    "\n",
    "$\\sigma^{'}(x) = - \\frac{1}{\\left( 1 + e^{- x} \\right)^{2}}D\\left\\lbrack e^{- x} \\right\\rbrack = \\frac{e^{- x}}{\\left( 1 + e^{- x} \\right)^{2}}$\n",
    "\\[Applying the rule\n",
    "$D\\left\\lbrack \\frac{1}{f(x)} \\right\\rbrack = - \\frac{D\\left\\lbrack f(x) \\right\\rbrack}{f(x)^{2}}$\\]\n",
    "\n",
    "$\\sigma^{'}(x) = \\frac{1 + e^{- x} - 1}{\\left( 1 + e^{- x} \\right)^{2}}$\n",
    "\\[Summing and subtracting $1$ to the numerator\\]\n",
    "\n",
    "$\\sigma^{'}(x) = \\frac{1 + e^{- x}}{\\left( 1 + e^{- x} \\right)^{2}} - \\frac{1}{\\left( 1 + e^{- x} \\right)^{2}}$\n",
    "\\[Splitting the numerator in two terms\\]\n",
    "\n",
    "$\\sigma^{'}(x) = \\frac{1}{1 + e^{- x}}\\left( 1 - \\frac{1}{1 + e^{- x}} \\right)$\n",
    "\\[making the $\\frac{1}{1 + e^{- x}}$ factor explicit\\]\n",
    "\n",
    "$\\sigma^{'}(x) = \\sigma(x)\\left( 1 - \\sigma(x) \\right)$ \\[replacing the\n",
    "formula $\\sigma(x) = \\frac{1}{1 + e^{- x}}$\\]\n",
    "\n",
    "##### Partial Derivatives of the Cost Function\n",
    "\n",
    "We now need to obtain the partial derivatives of the cost function with\n",
    "respect to the j-th parameter:\n",
    "\n",
    "$$\\frac{\\partial J\\left( \\mathbf{\\beta} \\right)}{\\partial\\beta_{j}}$$\n",
    "\n",
    "Remember that the cost function is defined as:\n",
    "\n",
    "$$J\\left( \\mathbf{\\beta} \\right) = - \\sum_{i = 1}^{N}{y^{(i)}\\log{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}} + \\left( 1 - y^{(i)} \\right)\\log{(1 - \\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right)})$$\n",
    "\n",
    "Let us first compute the derivative of the first term of the addition:\n",
    "\n",
    "$\\frac{\\partial}{\\partial\\beta_{j}}y^{(i)}\\log{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}$\n",
    "\\[Initial expression\\]\n",
    "\n",
    "$= y^{(i)}\\frac{1}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\frac{\\partial}{\\beta_{j}}\\left\\lbrack \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right\\rbrack$\n",
    "\\[Applying\n",
    "$D\\left\\lbrack \\log\\left( f(x) \\right) \\right\\rbrack = \\frac{1}{f(x)}f'(x)$\\]\n",
    "\n",
    "$= y^{(i)}\\frac{1}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)\\frac{\\partial}{\\beta_{j}}\\left\\lbrack {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right\\rbrack$\n",
    "\\[Applying\n",
    "$\\sigma^{'}\\left( f(x) \\right) = \\sigma\\left( f(x) \\right)\\left( 1 - \\sigma\\left( f(x) \\right) \\right)f'(x)\\rbrack$\n",
    "\n",
    "$= y^{(i)}\\frac{1}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)x_{j}^{(i)}$\n",
    "\\[Applying\n",
    "$\\frac{\\partial}{\\beta_{j}}\\left\\lbrack {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right\\rbrack = x_{j}$\\]\n",
    "\n",
    "The derivative of the second term will be:\n",
    "\n",
    "$\\frac{\\partial}{\\partial\\beta_{j}}{(1 - y}^{(i)})\\log\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)$\n",
    "\\[Initial Expression\\]\n",
    "\n",
    "$= \\left( 1 - y^{(i)} \\right)\\frac{1}{1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\frac{\\partial}{\\beta_{j}}\\ \\lbrack 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\rbrack$\n",
    "\\[Applying\n",
    "$D\\left\\lbrack \\log\\left( f(x) \\right) \\right\\rbrack = \\frac{1}{f(x)}f'(x)$\\]\n",
    "\n",
    "$= \\left( 1 - y^{(i)} \\right)\\frac{1}{1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}( - 1)\\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right)\\left( 1 - \\sigma\\left( \\mathbf{\\beta}^{T}x^{(i)} \\right) \\right)x_{j}^{(i)}$\n",
    "\\[Applying $\\sigma(x)\\left( 1 - \\sigma(x) \\right)$ and\n",
    "$\\frac{\\partial}{\\beta_{j}}\\left\\lbrack {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right\\rbrack = x_{j}$\\]\n",
    "\n",
    "$= \\frac{y^{(i)} - 1}{1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right)\\left( 1 - \\sigma\\left( \\mathbf{\\beta}^{T}x^{(i)} \\right) \\right)x_{j}^{(i)}$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "We can write the sum of the last two derivatives as follows:\n",
    "\n",
    "$\\frac{\\partial}{\\partial\\beta_{j}}y^{(i)}\\log{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)} + \\frac{\\partial}{\\partial\\beta_{j}}{(1 - y}^{(i)})\\log\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)$\n",
    "\\[Initial Expression\\]\n",
    "\n",
    "$= \\frac{y^{(i)}}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)x_{j}^{(i)} + \\frac{y^{(i)} - 1}{1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}\\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right)\\left( 1 - \\sigma\\left( \\mathbf{\\beta}^{T}x^{(i)} \\right) \\right)x_{j}^{(i)}$\n",
    "\\[Replacing derivatives\\]\n",
    "\n",
    "$= \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)x_{j}^{(i)}\\left\\lbrack \\frac{y^{(i)}}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)} + \\frac{y^{(i)} - 1}{1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)} \\right\\rbrack$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "$= \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)x_{j}^{(i)}\\left\\lbrack \\frac{y^{(i)}\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right) + (y^{(i)} - 1)\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)} \\right\\rbrack$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "$= \\frac{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)}{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)}x_{j}^{(i)}\\left\\lbrack y^{(i)}\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right) + (y^{(i)} - 1)\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right\\rbrack$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "$= x_{j}^{(i)}\\left\\lbrack y^{(i)} - y^{(i)}\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) + y^{(i)}\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right\\rbrack$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "$= x_{j}^{(i)}\\left( y^{(i)} - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)$\n",
    "\\[Simplifying\\]\n",
    "\n",
    "The derivative of the cost function with respect to the j-th parameter\n",
    "will hence be:\n",
    "\n",
    "$$\\frac{\\partial J\\left( \\mathbf{\\beta} \\right)}{\\partial\\beta_{j}} = - \\sum_{i = 1}^{N}{\\frac{\\partial}{\\partial\\beta_{j}}y^{(i)}\\log{\\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right)} + \\frac{\\partial}{\\partial\\beta_{j}}{(1 - y}^{(i)})\\log\\left( 1 - \\sigma\\left( {\\mathbf{\\beta}^{T}\\mathbf{x}}^{(i)} \\right) \\right)} = \\sum_{i}^{N}{x_{j}^{(i)}\\left( y^{(i)} - \\sigma\\left( \\beta^{T}x^{(i)} \\right) \\right)}$$\n",
    "\n",
    "The gradient descent update rule for each parameter will be:\n",
    "\n",
    "$$\\beta_{j}\\mathbf{=}\\beta_{j}\\mathbf{-}\\gamma\\sum_{i = 1\\ }^{N}{x_{j}^{(i)}\\left( \\sigma\\left( \\mathbf{\\beta}^{T}\\mathbf{x}^{(i)} \\right) - y^{(i)} \\right)}$$\n",
    "\n",
    "```"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example of Logistic Regression\n",
    "\n",
    "Let us now apply logistic regression to a larger set of variables in our regression problem. We will consider the following independent variables:\n",
    "* `radius1`\n",
    "* `texture1`\n",
    "* `perimeter1`\n",
    "* `area1`\n",
    "* `smoothness1`\n",
    "* `compactness1`\n",
    "* `concavity1`\n",
    "* `symmetry1`\n",
    "\n",
    "The dependent variable is again `Diagnosis`.\n",
    "\n",
    "Once fit to the data, we will obtain the following parameters:\n",
    "\n",
    "|$R^2$|Adj. $R^2$|F-statistic|Prob(F-statistic)|Log-Likelihood|\n",
    "|-|-|-|-|-|\n",
    "|0.670|0.666|142.4|1.16e-129|-78.055|\n",
    "\n",
    "All values have interpretations similar to the ones obtained in the case of linear regression. The Log-Likelihood reports the value of the logarithm of the likelihood which was used to train the data.\n",
    "\n",
    "The estimates for the coefficients are as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>   -2.6591</td> <td>    0.224</td> <td>  -11.896</td> <td> 0.000</td> <td>   -3.098</td> <td>   -2.220</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radius1</th>      <td>    0.4688</td> <td>    0.133</td> <td>    3.532</td> <td> 0.000</td> <td>    0.208</td> <td>    0.730</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>texture1</th>     <td>    0.0219</td> <td>    0.003</td> <td>    7.376</td> <td> 0.000</td> <td>    0.016</td> <td>    0.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>perimeter1</th>   <td>   -0.0473</td> <td>    0.021</td> <td>   -2.272</td> <td> 0.023</td> <td>   -0.088</td> <td>   -0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>area1</th>        <td>   -0.0009</td> <td>    0.000</td> <td>   -3.985</td> <td> 0.000</td> <td>   -0.001</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>smoothness1</th>  <td>    5.1389</td> <td>    1.221</td> <td>    4.208</td> <td> 0.000</td> <td>    2.740</td> <td>    7.538</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>compactness1</th> <td>    0.3080</td> <td>    0.854</td> <td>    0.360</td> <td> 0.719</td> <td>   -1.370</td> <td>    1.986</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>concavity1</th>   <td>    2.0973</td> <td>    0.414</td> <td>    5.065</td> <td> 0.000</td> <td>    1.284</td> <td>    2.911</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>symmetry1</th>    <td>    1.2739</td> <td>    0.568</td> <td>    2.244</td> <td> 0.025</td> <td>    0.159</td> <td>    2.389</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols(\"Diagnosis ~ radius1 + texture1 + perimeter1 + area1 + smoothness1 + compactness1 + concavity1 + symmetry1\",data).fit().summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that not all variables have a statistically relevant relationship with the dependent variable. Applying backward elimination, we remove `compactness1` and obtain the following estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>   <td>   -2.6708</td> <td>    0.221</td> <td>  -12.086</td> <td> 0.000</td> <td>   -3.105</td> <td>   -2.237</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radius1</th>     <td>    0.4360</td> <td>    0.097</td> <td>    4.517</td> <td> 0.000</td> <td>    0.246</td> <td>    0.626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>texture1</th>    <td>    0.0219</td> <td>    0.003</td> <td>    7.405</td> <td> 0.000</td> <td>    0.016</td> <td>    0.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>perimeter1</th>  <td>   -0.0419</td> <td>    0.014</td> <td>   -2.915</td> <td> 0.004</td> <td>   -0.070</td> <td>   -0.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>area1</th>       <td>   -0.0010</td> <td>    0.000</td> <td>   -4.477</td> <td> 0.000</td> <td>   -0.001</td> <td>   -0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>smoothness1</th> <td>    5.3093</td> <td>    1.125</td> <td>    4.719</td> <td> 0.000</td> <td>    3.099</td> <td>    7.519</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>concavity1</th>  <td>    2.1479</td> <td>    0.389</td> <td>    5.517</td> <td> 0.000</td> <td>    1.383</td> <td>    2.913</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>symmetry1</th>   <td>    1.3132</td> <td>    0.557</td> <td>    2.359</td> <td> 0.019</td> <td>    0.220</td> <td>    2.407</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols(\"Diagnosis ~ radius1 + texture1 + perimeter1 + area1 + smoothness1 + concavity1 + symmetry1\",data).fit().summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are now all statistically relevant. For instance, we can see that:\n",
    "* When all variables are set to zero, the odds of the benign tumor are $e^{-2.6708} \\approx 0.07$, or $\\frac{7}{100}$. This is a base value.\n",
    "* An increment in one unit of `texture1` increments the odds of a benign tumor multiplicatively by a factor of $e^{0.0219} \\approx 1.02$ (a +$2\\%$).\n",
    "* An increment of one unit of `perimeter1` decrements the odds of benign tumor multiplicatively by a factor of $e^{-0.0419} \\approx 0.96$ (a -$4\\%$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multinomial Logistic Regression\n",
    "\n",
    "In many cases, we want to study the relationship between a set of **continuous or categorical independent variable and a non-binary categorical dependent variable**. \n",
    "\n",
    "### The Iris Dataset\n",
    "An example is given by Fisher's Iris dataset.\n",
    "\n",
    "The dataset was introduced by Ronald Fisher in 1936 and contains observations related to 150 specimens of iris flowers belonging to 3 different species: \"setosa\", \"versicolor\", and \"virginica\". Example images of the three flowers are given below:\n",
    "\n",
    "![](/_static/lecture_specific/iris/iris.png)\n",
    "\n",
    "For each of the observations, the dataset provides measurements of 4 physical characteristics (length and width of sepals and petals), as illustrated in the image below:\n",
    "\n",
    "![](/_static/lecture_specific/iris/sepal_petal.png)\n",
    "\n",
    "All the variables in the dataset are numeric, except for `species`, which is categorical. Here are some observations from the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "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>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_length  sepal_width  petal_length  petal_width    species\n",
       "0             5.1          3.5           1.4          0.2     setosa\n",
       "1             4.9          3.0           1.4          0.2     setosa\n",
       "2             4.7          3.2           1.3          0.2     setosa\n",
       "3             4.6          3.1           1.5          0.2     setosa\n",
       "4             5.0          3.6           1.4          0.2     setosa\n",
       "..            ...          ...           ...          ...        ...\n",
       "145           6.7          3.0           5.2          2.3  virginica\n",
       "146           6.3          2.5           5.0          1.9  virginica\n",
       "147           6.5          3.0           5.2          2.0  virginica\n",
       "148           6.2          3.4           5.4          2.3  virginica\n",
       "149           5.9          3.0           5.1          1.8  virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "iris = sns.load_dataset('iris')\n",
    "iris"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the scatterplots we can see how the measurements have different ranges (same units, all centimeters):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "iris.plot.box(figsize=(8,6))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us observe the scatter matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 804.75x720 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(iris, hue='species')\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additional Limitations of a Linear Regression in the Presence of More than Two Classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider again a case with a single independent feature. We will select `petal_length`. The following image plots it with respect to the three classes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x='petal_length', y='species', data=iris)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the figure above, one may think that a linear regressor, even if not perfect, could still be an option. However, **to fit a linear regressor, we should first convert species values to numeric values**. A possible outcome could be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris2 = iris.copy(); \n",
    "iris2['species'] = iris2['species'].replace({'setosa':2, 'versicolor':1, 'virginica':0})\n",
    "sns.scatterplot(x='petal_lerngth', y='species', data=iris2)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, also the following mapping would be valid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris2 = iris.copy(); \n",
    "iris2['species'] = iris2['species'].replace({'setosa':1, 'versicolor':2, 'virginica':0})\n",
    "sns.scatterplot(x='petal_length', y='species', data=iris2)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even if the two mappings should be equivalent, we can see how a linear model would find very different results.\n",
    "\n",
    "This is an example of how the linear model is **even more limited when more than two possible outcomes of the dependent variable are possible**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Multinomial Logistic Regression Model\n",
    "When the dependent variable can assume more than two values, **we can define the multinomial logistic regression model**. In this case, we select one fo the values of the dependent variable $Y$ as **a baseline class**. Without loss of generality, let $K$ be the number of classes and let $Y=1$ be the baseline class. Recall that in the case of the logistic regressor, we modeled the logarithm of the odd as our linear function:\n",
    "\n",
    "$$\\log \\left(\\frac{P(y=1|\\mathbf{x})}{1-P(y=1|\\mathbf{x})}\\right) = \\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n$$\n",
    "\n",
    "Since we have more than one possible outcomes for the dependent variable, rather than modeling the odds, a multinomial logistic regressor models the logarithm of the ratio between a given class $k$ and the baseline class $1$ as follows:\n",
    "\n",
    "$$\\log\\left( \\frac{P(Y=k|X=\\mathbf{x})}{P(Y=1|X=\\mathbf{x})} \\right) = \\beta_{k0} + \\beta_{k1} x_1 + \\ldots + \\beta_{kn} x_n$$\n",
    "\n",
    "Note that, in practice, we need to define a different linear function for each class $k = 1 \\ldots K$, hence we need $(n+1) \\times (k-1)$ parameters.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $P(k)=(Y=k|X=\\mathcal{x})$ for brevity, $\\mathbf{\\beta_k}=(\\beta_0,\\beta_1,\\ldots,\\beta_k)$ and $\\mathbf{X}=(1,x_1,\\ldots,x_n)$. We can see that:\n",
    "\n",
    "$$\\log\\left(\\frac{P(k)}{P(1)}\\right) = \\mathbf{\\beta_k}^T\\mathbf{X} \\Rightarrow P(k)= e^{\\mathbf{\\beta_k}^T\\mathbf{X}} P(1)$$\n",
    "\n",
    "We can divide the last term by $1=\\sum_{l=1}^K P(l)$:\n",
    "\n",
    "$$ P(k) = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}} P(1)}{\\sum_{l=1}^K P(l)} = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}}}{\\sum_{l=1}^K \\frac{P(l)}{P(1)}} = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}}}{\\frac{P(1)}{P(1)}+\\sum_{l=2}^K \\frac{P(l)}{P(1)}} = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}}}{1+\\sum_{l=2}^K \\mathbf{e^{\\beta_l^T\\mathbf{X}}}} \\text{   (A)}$$\n",
    "\n",
    "Note that the expression above can also be seen as:\n",
    "\n",
    "$$ P(k) = \\frac{\\frac{P(k)}{P(1)}}{1+\\sum_{l=2}^K \\mathbf{e^{\\beta_l^T\\mathbf{X}}}}$$\n",
    "\n",
    "Hence:\n",
    "\n",
    "$$ P(1) = \\frac{1}{1+\\sum_{l=2}^K e^{\\mathbf{\\beta}_l^T\\mathbf{X}}} \\text{   (B)}$$\n",
    "\n",
    "We can rewrite the results (A) and (B) in the full form:\n",
    "\n",
    "$$ P(Y=k|X=\\mathbf{x}) = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}}}{1+\\sum_{l=2}^K \\mathbf{e^{\\beta_l^T\\mathbf{X}}}}$$\n",
    "$$ P(Y=1|X=\\mathbf{x}) = \\frac{1}{1+\\sum_{l=2}^K \\mathbf{e^{\\beta_l^T\\mathbf{X}}}}$$\n",
    "\n",
    "These two expressions can be used to compute the probabilities of the classes once that the parameters have been estimated and $\\mathcal{x}$ is observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Estimating the Parameters of the Multinomial Logistic Regressor Model\n",
    "We can estimate the paramters of the multinomial logistic regressor model again by maximizing the likelihood of the model on the data. Assuming that all observations are i.i.d., we can write:\n",
    "\n",
    "$$L(\\mathbf{\\beta}) = \\prod_{i=1}^N P(Y=y^{(i)}|X=\\mathbf{x}^{(i)};\\mathbf{\\beta})$$\n",
    "\n",
    "Again, we minimize the negative log likelihood:\n",
    "\n",
    "$$nll(\\mathcal{\\beta})=-\\log L(\\mathbf{\\beta}) = -\\sum_{i=1}^N \\log P(Y=y^{(i)}|X=\\mathbf{x}^{(i)};\\mathbf{\\beta}) = -\\sum_{i=1}^N [y^{(i)} \\neq 1](e^{-\\mathbf{\\beta}_k^T\\mathbf{X}} - \\log(1+\\sum_{l=2}^K {\\beta}_k^T\\mathbf{X})) + [y^{(i)} = 1] (- \\log(1+\\sum_{l=2}^K {\\beta}_k^T\\mathbf{X}))$$\n",
    "\n",
    "Where $[\\cdot]$ denotes the Iverson brackets:\n",
    "\n",
    "$$[x] = \\begin{cases}1 & \\text{if } x \\text{ is true} \\\\ 0 & \\text{otherwise}\\end{cases}$$\n",
    "\n",
    "Similarly to the logistic regressor, there is no close form for the estimation of the parameters, but iterative algorithms such as **gradient descent** are in general used for optimization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpretation of the Parameters of a Multinomial Logistic Regressor\n",
    "The statistical interpretation of the parameters of a multinomial logistic regressor is similar to the one of a logistic regressor, but we should pay attention to the choice of the baseline. \n",
    "\n",
    "Let us consider our example of studying the relationship between `sepal_lenght` and `species`. We will map `virginica` to $0$, `versicolor` to $1$ and `setosa` to $2$. Once the model is fit, we will find the following values:\n",
    "\n",
    "|Pseudo $R^2$|LogLikelihood| LLR p-value|\n",
    "|-|-|-|\n",
    "|0.4476|-91.034|9.276e-33|\n",
    "\n",
    "The value of LLR p-value is telling us that the model is statistically relevant, even if the pseudo $R^2$ is not very high. The relationship is not completely explained by the multinomial logistic regressor.\n",
    "\n",
    "The coefficients will be as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.606893\n",
      "         Iterations 8\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <th>species=1</th>     <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>   12.6771</td> <td>    2.906</td> <td>    4.362</td> <td> 0.000</td> <td>    6.981</td> <td>   18.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sepal_length</th> <td>   -2.0307</td> <td>    0.466</td> <td>   -4.361</td> <td> 0.000</td> <td>   -2.943</td> <td>   -1.118</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <th>species=2</th>     <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>   38.7590</td> <td>    5.691</td> <td>    6.811</td> <td> 0.000</td> <td>   27.605</td> <td>   49.913</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sepal_length</th> <td>   -6.8464</td> <td>    1.022</td> <td>   -6.698</td> <td> 0.000</td> <td>   -8.850</td> <td>   -4.843</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.formula.api import mnlogit\n",
    "iris2 = iris.copy(); \n",
    "iris2['species'] = iris2['species'].replace({'setosa':2, 'versicolor':1, 'virginica':0})\n",
    "mnlogit(\"species ~ sepal_length\", iris2).fit().summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that there are two sets of coefficients. One for `species=1` (versicolor) and one for `species=2` (setosa). No coefficients have been estimated for `virginica`, because it has been chosen as the baseline. We can see that all p-values are small, so we can keep all variables. Let us see how to interpret the coefficients:\n",
    "* The intercept for `species=1` is $12.6771$. This indicates that the odd of `versicolor` versus `virginica` is $e^{12.6771}=320327.76$, when `sepal_length` is set to zero. This is a very large number, probably due to the fact that `sepal_lenght=0` is not a realistic observation.\n",
    "* The intercept for `species=2` is $38.7590$. This indicates that the odd of `setosa` versus `virginica` is $e^{38.7590}=6.8e+16$, when `sepal_length` is set to zero. Also in this case, we obtain a very large number, probably due to the fact that `sepal_lenght=0` is not a realistic observation.\n",
    "* The coefficient $-2.0307$ of `sepal_length` for `species=1` indicates that when we observe an increase in one centimeter of `sepal_length`, the odd of `versicolor` versus `virginica` decreases multiplicatively by $e^{-2.0307} = 0.13$ (a large -$87\\%$!).\n",
    "* The coefficient $-6.8564$ of `sepal_length` for `species=2` indicates that when we observe an increase in one centimeter of `sepal_length`, the odd of `setosa` versus `virginica` decreases multiplicatively by $e^{-6.8464} = 0.001$ (a large -$99.9\\%$!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Softmax Regressor\n",
    "Softmax regression is an alternative formulation of multinomial logistic regression which is designed to avoid the definition of a baseline and it is hence symmetrical. In a softmax regressor, the probabilities are modeled as follows:\n",
    "\n",
    "$$ P(Y=k|X=\\mathbf{x}) = \\frac{e^{\\mathbf{\\beta_k}^T\\mathbf{X}}}{\\sum_{l=1}^K \\mathbf{e^{\\beta_l^T\\mathbf{X}}}}, \\ \\ \\ \\forall k=1,\\ldots,K$$\n",
    "\n",
    "So, rather than estimating $K-1$ coefficients, we estimate $K$ coefficients.\n",
    "\n",
    "The optimization of the model is performed defining a similar cost function and optimizing it with iterative methods.\n",
    "\n",
    "The softmax formulation is widely used in predictive analysis and machine learning, but less pervasive in statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "* Chapter $4$ of \\[1\\]\n",
    "\n",
    "\\[1\\] James, Gareth Gareth Michael. An introduction to statistical learning: with applications in Python, 2023.https://www.statlearning.com"
   ]
  }
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