02-linear-models_lsg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lineare Modelle\n",
    "\n",
    "In dieser Übung werden wir die linearen Modelle, die in den Vorlesungsfolien vorkommen, selbst implementieren.\n",
    "Wir starten mit den Iris-Daten, die Sie schon aus der Vorlesung kennen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLength</th>\n",
       "      <th>SepalWidth</th>\n",
       "      <th>PetalLength</th>\n",
       "      <th>PetalWidth</th>\n",
       "      <th>Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>146</td>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>147</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>148</td>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     SepalLength  SepalWidth  PetalLength  PetalWidth            Name\n",
       "0            5.1         3.5          1.4         0.2     Iris-setosa\n",
       "1            4.9         3.0          1.4         0.2     Iris-setosa\n",
       "2            4.7         3.2          1.3         0.2     Iris-setosa\n",
       "3            4.6         3.1          1.5         0.2     Iris-setosa\n",
       "4            5.0         3.6          1.4         0.2     Iris-setosa\n",
       "..           ...         ...          ...         ...             ...\n",
       "145          6.7         3.0          5.2         2.3  Iris-virginica\n",
       "146          6.3         2.5          5.0         1.9  Iris-virginica\n",
       "147          6.5         3.0          5.2         2.0  Iris-virginica\n",
       "148          6.2         3.4          5.4         2.3  Iris-virginica\n",
       "149          5.9         3.0          5.1         1.8  Iris-virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"iris.csv\", index_col=0)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wie in der Vorlesung können wir die Daten plotten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc9aeecd990>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot iris \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dfs = df.loc[df.Name != \"Iris-setosa\",:]\n",
    "\n",
    "plt.plot(dfs.loc[:,\"SepalWidth\"],dfs.loc[:,\"PetalLength\"],'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zunächst schauen wir uns das einfache lineare Modell an, das den Zusammenhang zwischen PetalLength und SepalWidth darstellt. Wir werden für das Fitten von linearen Modellen das Python-Paket statsmodels verwenden (`https://www.statsmodels.org`). Die Spezifikation von linearen Modellen funktioniert hier ganz ähnlich wie in den R-Beispielen, die in der Vorlesung vorkommen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>PetalLength</td>   <th>  R-squared:         </th> <td>   0.270</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   36.28</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 24 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>2.99e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:52:31</td>     <th>  Log-Likelihood:    </th> <td> -106.48</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   217.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   222.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>  <td>    1.2021</td> <td>    0.619</td> <td>    1.942</td> <td> 0.055</td> <td>   -0.026</td> <td>    2.430</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SepalWidth</th> <td>    1.2897</td> <td>    0.214</td> <td>    6.023</td> <td> 0.000</td> <td>    0.865</td> <td>    1.715</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 6.767</td> <th>  Durbin-Watson:     </th> <td>   0.895</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.034</td> <th>  Jarque-Bera (JB):  </th> <td>   6.222</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.575</td> <th>  Prob(JB):          </th> <td>  0.0446</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.414</td> <th>  Cond. No.          </th> <td>    28.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:            PetalLength   R-squared:                       0.270\n",
       "Model:                            OLS   Adj. R-squared:                  0.263\n",
       "Method:                 Least Squares   F-statistic:                     36.28\n",
       "Date:                Tue, 24 Nov 2020   Prob (F-statistic):           2.99e-08\n",
       "Time:                        16:52:31   Log-Likelihood:                -106.48\n",
       "No. Observations:                 100   AIC:                             217.0\n",
       "Df Residuals:                      98   BIC:                             222.2\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.2021      0.619      1.942      0.055      -0.026       2.430\n",
       "SepalWidth     1.2897      0.214      6.023      0.000       0.865       1.715\n",
       "==============================================================================\n",
       "Omnibus:                        6.767   Durbin-Watson:                   0.895\n",
       "Prob(Omnibus):                  0.034   Jarque-Bera (JB):                6.222\n",
       "Skew:                           0.575   Prob(JB):                       0.0446\n",
       "Kurtosis:                       3.414   Cond. No.                         28.2\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "results = smf.ols('PetalLength ~ SepalWidth', data=dfs).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Aufgabe*: Interpretieren Sie die Ergebnisse! Was bedeuten die Koeffizienten, $R^2$, p-Werte?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularisierung\n",
    "\n",
    "Betrachten Sie nun den stark korrelierten Datensatz von Seite 44 der Folien."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>-10.008379</td>\n",
       "      <td>-10.007781</td>\n",
       "      <td>-16.064194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-9.811091</td>\n",
       "      <td>-9.787912</td>\n",
       "      <td>-13.787926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-9.604869</td>\n",
       "      <td>-9.592039</td>\n",
       "      <td>-13.473252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-9.402045</td>\n",
       "      <td>-9.418639</td>\n",
       "      <td>-13.439822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-9.193054</td>\n",
       "      <td>-9.190633</td>\n",
       "      <td>-13.027876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>9.191319</td>\n",
       "      <td>9.195451</td>\n",
       "      <td>23.276237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>9.392459</td>\n",
       "      <td>9.377327</td>\n",
       "      <td>23.795605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>9.586266</td>\n",
       "      <td>9.604799</td>\n",
       "      <td>25.196303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>9.804099</td>\n",
       "      <td>9.800005</td>\n",
       "      <td>24.994132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>100</td>\n",
       "      <td>9.990538</td>\n",
       "      <td>10.007521</td>\n",
       "      <td>25.973731</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>101 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            x1         x2          y\n",
       "0   -10.008379 -10.007781 -16.064194\n",
       "1    -9.811091  -9.787912 -13.787926\n",
       "2    -9.604869  -9.592039 -13.473252\n",
       "3    -9.402045  -9.418639 -13.439822\n",
       "4    -9.193054  -9.190633 -13.027876\n",
       "..         ...        ...        ...\n",
       "96    9.191319   9.195451  23.276237\n",
       "97    9.392459   9.377327  23.795605\n",
       "98    9.586266   9.604799  25.196303\n",
       "99    9.804099   9.800005  24.994132\n",
       "100   9.990538  10.007521  25.973731\n",
       "\n",
       "[101 rows x 3 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"corr_data.csv\")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Aufgabe*: Fitten Sie ein lineares Modell mit y als abhängiger Variablen und x1 und x2 als unabhängigen Variablen. Interpretieren Sie erneut die Ergebnisse. Was ist das Problem?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.994</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.993</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7531.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 24 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>5.19e-108</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:18:51</td>     <th>  Log-Likelihood:    </th> <td> -136.69</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   101</td>      <th>  AIC:               </th> <td>   279.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   287.2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    4.9804</td> <td>    0.095</td> <td>   52.277</td> <td> 0.000</td> <td>    4.791</td> <td>    5.169</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>        <td>   -5.8432</td> <td>    7.006</td> <td>   -0.834</td> <td> 0.406</td> <td>  -19.746</td> <td>    8.059</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>        <td>    7.8352</td> <td>    7.006</td> <td>    1.118</td> <td> 0.266</td> <td>   -6.069</td> <td>   21.739</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.274</td> <th>  Durbin-Watson:     </th> <td>   1.815</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.529</td> <th>  Jarque-Bera (JB):  </th> <td>   0.769</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.015</td> <th>  Prob(JB):          </th> <td>   0.681</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.426</td> <th>  Cond. No.          </th> <td>    864.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.994\n",
       "Model:                            OLS   Adj. R-squared:                  0.993\n",
       "Method:                 Least Squares   F-statistic:                     7531.\n",
       "Date:                Tue, 24 Nov 2020   Prob (F-statistic):          5.19e-108\n",
       "Time:                        17:18:51   Log-Likelihood:                -136.69\n",
       "No. Observations:                 101   AIC:                             279.4\n",
       "Df Residuals:                      98   BIC:                             287.2\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      4.9804      0.095     52.277      0.000       4.791       5.169\n",
       "x1            -5.8432      7.006     -0.834      0.406     -19.746       8.059\n",
       "x2             7.8352      7.006      1.118      0.266      -6.069      21.739\n",
       "==============================================================================\n",
       "Omnibus:                        1.274   Durbin-Watson:                   1.815\n",
       "Prob(Omnibus):                  0.529   Jarque-Bera (JB):                0.769\n",
       "Skew:                          -0.015   Prob(JB):                        0.681\n",
       "Kurtosis:                       3.426   Cond. No.                         864.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = smf.ols('y ~ x1 + x2', data=df).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Aufgabe*: Verwenden Sie Ridge Regression, um ein lineares Modell zu fitten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    4.922549\n",
       "x1           1.963074\n",
       "x2           0.027962\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols('y ~ x1 + x2', data=df)\n",
    "results = model.fit_regularized(L1_wt=0.1,alpha=0.01)\n",
    "results.params #parameters for intercept, x1, x2: what we expect"
   ]
  },
  {
   "attachments": {
    "grafik.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![grafik.png](attachment:grafik.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistische Regression\n",
    "\n",
    "Schließlich wollen wir uns noch lineare Modelle als Klassifikatoren anschauen. Konkret wollen wir die Klasse (die Spalte `Name` im Data Frame) aus SepalWidth und PetalLength vorhersagen, indem wir ein lineares Modell mittels logistischer Regression fitten. \n",
    "\n",
    "*Aufgabe*: Erstellen Sie im Iris Data Frame eine neue Spalte `NameNum`, die 1 ist, falls Name=Iris-virginica, und 0 sonst. Führen sie dann regularisierte logistische Regression durch, wobei NameNum die abhängige Variable ist, und SepalWidth und PetalLength die abhängigen Variablen. Interpretieren Sie die Parameter. Was ist der Unterschied zwischen der Entscheidungsgrenze und der Regressionsgeraden?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 0.20012284998121793\n",
      "            Iterations: 44\n",
      "            Function evaluations: 45\n",
      "            Gradient evaluations: 44\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>NameNum</td>     <th>  No. Observations:  </th>  <td>   100</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>    97</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Nov 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.7657</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>17:46:33</td>     <th>  Log-Likelihood:    </th> <td> -16.242</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -69.315</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>8.930e-24</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <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>  -27.9927</td> <td>    7.608</td> <td>   -3.679</td> <td> 0.000</td> <td>  -42.905</td> <td>  -13.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SepalWidth</th>  <td>   -2.4863</td> <td>    1.619</td> <td>   -1.536</td> <td> 0.125</td> <td>   -5.659</td> <td>    0.687</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PetalLength</th> <td>    7.2231</td> <td>    1.609</td> <td>    4.490</td> <td> 0.000</td> <td>    4.070</td> <td>   10.376</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                NameNum   No. Observations:                  100\n",
       "Model:                          Logit   Df Residuals:                       97\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Tue, 24 Nov 2020   Pseudo R-squ.:                  0.7657\n",
       "Time:                        17:46:33   Log-Likelihood:                -16.242\n",
       "converged:                       True   LL-Null:                       -69.315\n",
       "Covariance Type:            nonrobust   LLR p-value:                 8.930e-24\n",
       "===============================================================================\n",
       "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercept     -27.9927      7.608     -3.679      0.000     -42.905     -13.081\n",
       "SepalWidth     -2.4863      1.619     -1.536      0.125      -5.659       0.687\n",
       "PetalLength     7.2231      1.609      4.490      0.000       4.070      10.376\n",
       "===============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"iris.csv\", index_col=0)\n",
    "dfs = df.loc[df.Name != \"Iris-setosa\",:].copy()\n",
    "\n",
    "dfs.loc[:,\"NameNum\"] = (dfs.loc[:,\"Name\"] == \"Iris-virginica\").astype(\"float\")\n",
    "dfs\n",
    "\n",
    "result = smf.logit('NameNum ~ SepalWidth + PetalLength', data=dfs).fit_regularized(alpha=0.1)\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8754466004607413\n",
      "0.34421752748033085\n"
     ]
    }
   ],
   "source": [
    "b=result.params[0]\n",
    "w1=result.params[1]\n",
    "w2=result.params[2]\n",
    "\n",
    "c = -b/w2\n",
    "m = -w1/w2\n",
    "print(c)\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistische Regression mit sklearn\n",
    "\n",
    "Im Machine Learning sind wir oft gar nicht so sehr an den Parametern des Modells interessiert, sondern daran, dass das Modell gute Vorhersagen liefert. Für solche Zwecke ist die logistische Regression aus dem Paket `sklearn` besser geeignet -- dort werden Dinge, die in statsmodels recht mühsam sind, wie das Encoding der Klasse, der Umgang mit mehr als zwei Klassen usw. direkt erledigt. Schauen Sie sich dafür die folgende Dokumentation an: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html\n",
    "\n",
    "Teilen Sie den Iris-Datensatz in zwei Teilmengen auf: Eine Trainingsmenge, die 80% der Daten enthält, und eine Testmenge, die die restlichen 20% der Daten enthält. Trainieren Sie dann ein Logit-Modell mit den Trainingsdaten und erzeugen Sie eine Vorhersage für die Klasse der Testdaten. Welcher Anteil der Testdaten wurde korrekt klassifiziert?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stefan/anaconda3/lib/python3.7/site-packages/sklearn/linear_model/logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n",
      "/home/stefan/anaconda3/lib/python3.7/site-packages/sklearn/linear_model/logistic.py:469: FutureWarning: Default multi_class will be changed to 'auto' in 0.22. Specify the multi_class option to silence this warning.\n",
      "  \"this warning.\", FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split \n",
    "\n",
    "X, y = load_iris(return_X_y=True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20) \n",
    "\n",
    "clf = LogisticRegression().fit(X_train, y_train)\n",
    "yhat = clf.predict(X_test)\n",
    "np.mean(yhat == y_test)"
   ]
  }
 ],
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