{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"\n",
    "    border: 2px solid #4CAF50; \n",
    "    padding: 15px; \n",
    "    background-color: #f4f4f4; \n",
    "    border-radius: 10px; \n",
    "    align-items: center;\">\n",
    "\n",
    "<h1 style=\"margin: 0; color: #4CAF50;\">Supervised ML Modelle: Lineare Regression und logistische Regression</h1>\n",
    "<h2 style=\"margin: 5px 0; color: #555;\">DSAI</h2>\n",
    "<h3 style=\"margin: 5px 0; color: #555;\">Jakob Eggl</h3>\n",
    "\n",
    "<div style=\"flex-shrink: 0;\">\n",
    "    <img src=\"https://www.htl-grieskirchen.at/wp/wp-content/uploads/2022/11/logo_bildschirm-1024x503.png\" alt=\"Logo\" style=\"width: 250px; height: auto;\"/>\n",
    "</div>\n",
    "<p1> © 2024/25 Jakob Eggl. Nutzung oder Verbreitung nur mit ausdrücklicher Genehmigung des Autors.</p1>\n",
    "</div>\n",
    "<div style=\"flex: 1;\">\n",
    "</div>   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir werden uns nun mit dem linearen und logistischen Regressionsmodell auseinandersetzen. Dies wird auch Ausgleichsrechnung genannt.\n",
    " \n",
    "Dabei werden wir mit einem linearen Regressionsmodell beginnen und dieses dann zu einer logistischen Regression erweitern. Dies ermöglicht es uns dann, die ersten Klassifikationen durchzuführen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lineare Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Lineares Regressionsmodell](../resources/Lineare_Regression.png)\n",
    "\n",
    "(von https://de.wikipedia.org/wiki/Lineare_Einfachregression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problemstellung"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir haben (im 1d Fall) Daten der Form\n",
    "\n",
    "\\begin{equation*}\n",
    "    X=(x_1, x_2, \\ldots, x_n) \\quad \\text{und} \\quad Y = (y_1, y_2, \\ldots, y_n)\n",
    "\\end{equation*}\n",
    "gegeben, wobei $x_i\\in \\mathbb R$ und $y_i\\in \\mathbb R$ für das (einzige) Feature bzw. das Label des $i$-ten Datenpunktes stehen. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Insgesamt wollen wir eine Funktion $f(x)$ finden, welche am besten durch die gegebene Punkte passt.\n",
    "\n",
    "Im Fall der linearen Regression, ist dies eine *lineare* Funktion, sprich wir suchen die Parameter $k$ und $d$ jener linearen Funktion $f(x)=k \\cdot x + d$, welche am besten zu den gegebenen Daten passen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Fehler, der für die lineare Regression minimiert werden soll, nennt \n",
    "sich **Methode der kleinsten Quadrate** und ist, wie im vorigen Notebook \n",
    "bereits gesehen, folgendermaßen definiert\n",
    "\\begin{equation*}\n",
    "    \\text{MSE} = \\frac{1}{n}\\sum_{i=1}^{n}(\\hat y_i-y_i)^2,\n",
    "\\end{equation*}\n",
    "erneut mit $\\hat y_i$ als der Model Output für den $i$-ten Datenpunkt und \n",
    "$y_i$ als der eigentliche (target) Wert an dieser Stelle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Methode der kleinsten Quadrate](../resources/Methode_der_kleinsten_Quadrate.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diesen Fehler wollen wir **minimieren**.\n",
    "\n",
    "Wir erinnern uns an das Kapitel *Kurvendiskussion* in Mathematik und \n",
    "wiederholen kurz, wie man das Minimum einer Funktion finden kann.\n",
    "\n",
    "* Wir berechnen die Ableitung der Funktion $\\textrm{MSE}$\n",
    "* Wir setzen diese Ableitung $0$ und lösen für die Koeffizienten $\\tilde \n",
    "k,\\tilde d$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die Summe der quadrierten Differenzen ergibt sich mit $\\hat y_i = kx_i + d$ (wir lassen die Division durch $n$ weg, weil dieses konstant ist):\n",
    "\\begin{equation*}\n",
    "    \\sum_{i=1}^{n}(\\hat y_i-y_i)^2 = \\sum_{i=1}^{n}[(kx_i+d)-y_i]^2.\n",
    "\\end{equation*}\n",
    "Die Summe der Abweichungsquadrate ist also eine Funktion\n",
    "\\begin{equation*}\n",
    "    f(k, d) = \\sum_{i=1}^{n}(kx_i+d-y_i)^2,\n",
    "\\end{equation*}\n",
    "die von 2 Variablen $k$ und $d$ abhängt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir berechnen nun die Ableitungen $\\partial f/\\partial k$ und $\\partial f/\\partial d$.\n",
    "\n",
    "\\begin{align*}\n",
    "    \\frac{\\partial f}{\\partial k} &= 2 \\cdot \\sum_{i=1}^{n} (kx_i+d-y_i) \n",
    "    \\cdot \n",
    "    x_i = 2 \\cdot (k\\cdot \\sum_{i=1}^{n}x_i^2 + d\\sum_{i=1}^{n}x_i - \n",
    "    \\sum_{i=1}^{n}x_i\\cdot y_i)\\\\\n",
    "    \\frac{\\partial f}{\\partial d} &= 2 \\cdot \\sum_{i=1}^{n}(kx_i+d-y_i) = 2 \n",
    "    \\cdot (k\\cdot \\sum_{i=1}^{n}x_i + d\\cdot \\sum_{i=1}^{n}1 - \n",
    "    \\sum_{i=1}^{n}y_i)\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Durch Nullsetzen erhalten wir nun folgendes Gleichungssystem\n",
    "\\begin{align*}\n",
    "    k\\cdot \\sum_{i=1}^{n}x_i^2 + d\\sum_{i=1}^{n}x_i &= \n",
    "    \\sum_{i=1}^{n}x_i\\cdot y_i\\\\\n",
    "    k\\cdot \\sum_{i=1}^{n}x_i + d\\cdot n &= \\sum_{i=1}^{n}y_i.\n",
    "\\end{align*}\n",
    "Dieses müssen wir lösen.\n",
    "\n",
    "Aus der zweiten Gleichung erhalten wir\n",
    "\\begin{equation*}\n",
    "    d = \\frac{\\sum_{i=1}^{n}y_i - k\\cdot \\sum_{i=1}^{n}x_i}{n} = \n",
    "    \\overline{y}- k \\cdot \\overline{x},\n",
    "\\end{equation*}\n",
    "wobei $\\overline{y}$ und $\\overline{x}$ das arithmetische Mittel von $y$ \n",
    "bzw. $x$ darstellen.\n",
    "\n",
    "Nun setzen wir dies in die erste Gleichung ein und erhalten\n",
    "\\begin{equation*}\n",
    "    k\\cdot \\sum_{i=1}^{n}x_i^2 + \\overline{y}-k\\cdot \n",
    "    \\overline{x}\\sum_{i=1}^{n}x_i = \n",
    "    \\sum_{i=1}^{n}x_i\\cdot y_i\n",
    "\\end{equation*}\n",
    "\n",
    "Umgeformt ergibt dies nun\n",
    "\\begin{equation*}\n",
    "    k = \\frac{\\sum_{i=1}^{n}x_iy_i - \n",
    "    n\\overline{x}\\overline{y}}{-\\overline{x}^2\\cdot n + \n",
    "    \\sum_{i=1}^{n}x_i^2}.\n",
    "\\end{equation*}\n",
    "\n",
    "Somit wissen wir nun, welchen Werte wir für $k$ und $d$ verwenden müssen, \n",
    "sodass wir die optimalen Parameter für die 1-dimensionale lineare \n",
    "Regression bekommen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Wir verwenden also\n",
    "\\begin{equation*}\n",
    "    k = \\frac{\\sum_{i=1}^{n}x_iy_i - n\\overline{x}\\overline{y}}{-\\overline{x}^2\\cdot n + \\sum_{i=1}^{n}x_i^2}, \\qquad \\qquad d = \\overline{y}- k \\cdot \\overline{x}.\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Wichtig:** Auch wenn wir dies jetzt nicht (händisch) berechnen, können wir auch für mehrdimensionale Funktionen und für Polynome vom Grad größer 1 (Grad 1 $\\hat =$ lineare Funktion $kx+d$) die optimalen Parameter bestimmen. Wir brauchen also beim Lernprozess für unser Model keinen iterativen Vorgang, sondern wir können die optimalen Parameter direkt berechnen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Wichtig:** Die direkte Berechnung der besten Lösung funktioniert leider nur für die wenigsten Machine Learning Modelle. In den meisten Fällen finden wir leider keine sogenannte Closed-Form Lösung. In diesen Fällen verwenden wir iterative Prozesse, wo unser Model dann versucht, das richtige Label zu erlernen, indem es Schritt für Schritt seine Parameter (sprich seine Klassifikationsregel) anpasst."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hinweis:** Es gibt auch eine mehrdimensionale Regression. Hier besitzt jeder Datenpunkt $n\\geq 2$ Features. Dies funktioniert in Python genau gleich, weswegen wir da jetzt nicht genauer in die Details eingehen (Referat?)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir probieren nun die lineare und logistische Regression in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LogisticRegression, LinearRegression\n",
    "from sklearn.metrics import accuracy_score, classification_report, mean_squared_error, confusion_matrix\n",
    "from sklearn.datasets import make_classification, make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wir starten mit Regression\n",
    "\n",
    "# Erzeugen von Daten (Dummy Dataset)\n",
    "\n",
    "X, y = make_regression(n_samples=100, n_features=1, noise=10, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 3,
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   "source": [
    "X"
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  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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    "X.shape"
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  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisierung der Daten\n",
    "plt.scatter(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train und Test set erzeugen\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) # 80/20 split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardisieren der Features (optional; welche anderen Methoden gibt es?)\n",
    "\n",
    "# Standardisieren = z-score normalisieren\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f629b729160>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NwB4LFy7UG2+8oR07dvQYZCRp7NixkqSqqiqfzycnJystLa3TDQDiwd6ak4aDjHTmqHZvqgPH2wkqWJPpYcbtdmvhwoV69dVXtX37duXm5gZ8TXl5uSQpO5tpSwDoKNhu1L0NGmZ1yQY6Mn0D8IIFC7R+/Xpt2rRJqampqq8/c2TQ6XSqX79+qq6u1vr16/Uv//IvysjI0P79+7Vo0SKNHz9eF198scmjBwBrCaVAXKCg0dMpJQrXwQpMDzOrVq2SdKYwXkdr167V3LlzlZSUpK1bt2rlypVqampSTk6OZs+erYceesiE0QKAtXlONPW09NNVT0Ej0CmlQCeoPHtmKFyHSDI9zATaf5yTk6O33347SqMBAHtLTHBo5iXZevadmoDXBgoaRvs8Fc7I1/ziMjmkTtdSuA7RYvqeGQBA+LS1u/X6+3WGr/cXNAL1eZK+2TzsKVzncnae4XE5UziWjagwfWYGABA+gU4XeaSf1Vc//f5FfoNGMKeUCvIyKFwHUxFmACCGGD01tOy7I3ucMQnllFKku2QD/rDMBAAxxOipIVdaz9dxSgl2QpgBgBjiOV3kb3HHoTOnkQKdLvp7U6t6WiEy+j5ANBBmACCGJCY4VDgjX5K6BRqjp4tKKuq0YH2ZAhUG5pQSrIIwAwAxpjeni3o6xeSR4JCeuekyTinBMtgADAAxKNTTRUZOQ7W7pXPOSg7ncIFeIcwAQIwK5XQRvZZgRywzAQC8OMUEO2JmBgBM4mngWN/wlU42tSr97GS50swtNkevJdgRYQYATOCrgaNHx0aO0eY5DUWvJdgJy0wAEGWeBo7+NtrW/aORY0mF8R5L4USvJdgNMzMAEEWtX7frJ6/+tcejzx5Fmys1Jd8V9CyIZ/mqNz2S6LUEOyHMAECUlFTU6SevVuhk0+mA13Zt5BjMZ3Rdvgp12YpeS7ALlpkA2FZbu1ul1Se0qfywSqtPqC1QyVoTeZaWTja1BvW6YI5A+1u+qjd52QqINGZmANhSOGcgIs1IVV1/PEegAy0d9fQZbp3ZvBvqshVgdYQZALbjmYHo+sPtmYGw2iZVI1V1u+p4BNpIcAv0GaEuWwF2wDITAFsJNAMhnZmBsNKSU6jVcgtn5GtLZb2hpSOjn/HHijrLL8kBwSLMALCVYGYgzNRxP89nn7cE9drsfxyBnpLvMhzcjFbk/W3px7rxN3t0zYrt7KFBzGCZCYCt2KF3kK9loQTHmQaN/qSl9FHhjJEaPKCfdz9MafUJw8EtUOXerqy6JAeEgjADwFas3jvI334ef0HGsxX3iesv7hYqjAay3VXHdezzZv3wyhw9tfVv3Sr3+hLqpuBw1LABwo0wA8BWrNw7yMippa4zNK4eTmAZDWRP76j2/nlA/76SpFNfhr+WjZ1OkCG+EGYA2IqVewcZObXU7paWXXehBqYmB5zZCHbpSJIa/hFiFk0+XyeaWvTb0o8DvsbIDJDdTpAhvrABGIDtWKF3kK+CfUaXhQamJut7l/6TCvIyegxdnuAmfRPUAvGEjZfeq9W0kS5Drwk0A2THE2SIL8zMALAlM3sH+Vtu+eGVOYZeH8x+Hk9w89dh2xfP8pHcCsuSHDVsYHWEGQC21dveQaFsZu1pueWprX/TgP591fDlaUPhwejndw1ufzv6hZ7eURXw73fsi5awLMnZ4QQZ4hthBkBcCmUzq5Hlltav270nhXoKD8F+fsfgVlp9wlCYefSND/TT71/kc2anp43HXVn9BBngcLvdMb/I2djYKKfTqYaGBqWlpZk9HAAm8ze74gkc/vbdlFaf0I2/2WPoM7qeWuoYVEL9fI+2dreuWbHd0MZgxz/erzdLcoE+zzPjtGvJJI5pI6yM/n6zARhAXAl1M2tbu1u7qz4z/Dmel99x9TD9bt5V2rVkkqaPyg7LZtpgNwYXba6UJBXkZRjaeBzM55l9ggyQCDMA4ozRzazrdtd4A0VJRZ2uWbHd0NJORw5Jf6io7zQLEq52DJ6NweecldTjdeFq72CFE2SAP+yZARBXjG5SffTND/XcrhrNvCRbv36nxnCdl458nfIJ52ba6aOy9VVrmxa9/H5Y3s/I55l1ggzoiW1mZp555hkNGzZMKSkpGjt2rPbu3Wv2kADYUDCbVOsbmvVsiEGmo45BItybaV3OfmF9v0A8G5FDWa4CIsUWYWbDhg1avHixCgsLVVZWpksuuUTTpk3TsWPHzB4aAJvxVNU18hMcrtMRHYNEoM936MxmYaPtGML9foAd2SLM/PznP9e8efN02223KT8/X6tXr1b//v21Zs0as4cGwGZCqaobKl9BItybadmcC9ggzLS2tmrfvn2aPHmy97GEhARNnjxZpaWlPl/T0tKixsbGTjcA8PC3mbU3ggkSRjfT+mqZ4AubcxHvLL8B+LPPPlNbW5sGDRrU6fFBgwbpwIEDPl+zfPlyFRUVRWN4AGzKs5l13e4aPfrmhyG9h6e+yrLr8vXom8EVpQu0mTbYonpszkU8s3yYCcWDDz6oxYsXe+83NjYqJ8dYzxQA8SMxwaG5V+fquV01QXWmljrPvEwfla1po4IPEv7aMYTaobq37R0Au7L8MtPAgQOVmJioo0ePdnr86NGjcrl8d4RNTk5WWlpapxsA+BJoz4lD0t3jc5UdYAknXKd8AhXVc4sO1UBXlp+ZSUpK0ujRo7Vt2zbNmjVLktTe3q5t27Zp4cKF5g4OQEzw15m641LRA9MvjMoSTqCietKZ2jVPb/+b/s/k88P++YAdWT7MSNLixYs1Z84cXXHFFRozZoxWrlyppqYm3XbbbWYPDUCMCLTnJFpLOEaL2z219W+6wJXK5l5ANgkz//qv/6rjx4/r4YcfVn19vS699FKVlJR02xQMAG3t7pBnUMIRWHrz+VJwxe2KNldqSr6LTb6Ie3TNBhAzgj0BZMXP93SoDrTU5PG7eVex6Rcxi67ZAOKK5wRQ1xDgOQFUUlFni8/vuCHZiHD0XALsjjADwPYCnQCSInsCKNyfP31UthYZ3Nwbrp5LgJ0RZgDYXqATQB27V9vl8xdOOk+utGS/z9NzCfgGYQaA7Rldaul4nZFWAUbbCYTy+YEkJjj0yMyR3lo3HdFzCejMFqeZAKAnRpdaPNcZ2agbzGbeYD/fKCP1bwBwmglADPCcAPLXksDTQ2nXkknaUlnvs1WA57pVN18uST6v8cyBdG0nEMznhzKT0tvj3oBdcZoJQNwI1JJAkvd5fxt1pTN7Wx7c+Fc98voHQW3mNfr5HQOI0SUsz/uHo1UCEKtYZgIQcdGYWTCyJFNafSJg/Za/f3m6x+c7bubtWN8lmCUhs+vhALGGMAMgoqL5wx2oJUE4a7L4eq9Any+F3hEbgH+EGQARY8YPd08tCcJZk8Xfe/X0+YHq0ThEiwIgFOyZARARZhey82VMbroG9Ovbq/foTX0Xs+vhALGKMAMgIqz4w52Y4NBtV+cavj7c9V0iUY8GAGEGQIRY9Yd74aTzNKC//9kZz8zLr266TC5n56UklzOlV0tjkapHA8Q79swAiAgr/HD7O0X1+A8u0j3FZd2u7zjzMn1UtqaNyg7rKawxuenKdqYErEdDiwIgOIQZABFh9g93oFNUqw0co+5pM28oPPVo5heXySF1+l5oUQCEjgrAACLGc5pJ8v3DHaljyP5OUXX9XLMq61JnBjDG6O83YQZAREX7h9vTWsDf5uPethYIF1oUAIEZ/f1mmQlARBkpJBdOwZyiCucSUrDCvYQFxDPCDICIi+YPt1VPUQGIHI5mA4gpVjhFBSC6CDMAYornFJW/RazeVPAFYE2EGQAxxXP8WQp/BV8A1kSYAWBJbe1ulVaf0KbywyqtPhFUD6fpo7K16ubLw17BF4A1sQEYgOWE4zj39FHZmjRikP5v6SF9fPJLDU3vr1sKhimpD/8OB8Qa6swAMF3HmiuHPvtSK7f+v4AF7wKhMB1gfxTN64AwA1iXr9Dhj9GCdyUVdT32XmKpCbAHo7/fzLcC6NX+lN7wtB0wEmSkzgXv/Glrd2vpxr/6fb0kFW2ujNrfEUDksWcGiHNmLce0tbtVtLnSZxPKQHoqePf09iqd+vK03+etUgEYQPgwMwPEMX8zI/UNzZpfXKaSirqIfG5bu1vrdtcYnpHpyl/Bu7Z2t9burjH0HlQABmIHMzNAnOppZsStM/tLijZXakq+K6w1WYLZI+PP35tafD6+t+akTn3lf1amIyoAA7GDmRkgTgXTkDFcgt0j48+jb37oc8+L0dmWAf36UgEYiCGEGSBORbshY2/2yHTlL2QZnW257ephVAAGYohpYebQoUO64447lJubq379+ikvL0+FhYVqbW3tdI3D4eh227Nnj1nDBmJGtBsyBpoJCpavkBWoL5MkndO/rxZO+lbYxgHAfKbtmTlw4IDa29v17LPP6rzzzlNFRYXmzZunpqYmPfnkk52u3bp1q0aOHOm9n5HBCQSgtzw//PUNzT5nSzw1XcK1HBPuDbe+QpanL9P84jI5JJ+F95b/4CJmZYAYY9rMzPTp07V27VpNnTpVw4cP18yZM/WjH/1IGzdu7HZtRkaGXC6X99a3b18TRgzElmg3ZAzXDE+grtf++jJl05cJiFmWOs3U0NCg9PTu/4CaOXOmmpubdf755+uBBx7QzJkze3yflpYWtbR8c9qhsbEx7GMFYoHnh7/r6SJXBOrMGJ0JevL6S7TtwFGt2X2o2+yK0ZA1fVS2puS7vC0SslLPhB9mZIDYZJl2BlVVVRo9erSefPJJzZs3T5L02Wef6be//a2uvvpqJSQk6JVXXtETTzyh1157rcdA88gjj6ioqKjb47QzAHzr2Bspkj/8ntNMku+Q0nHmhN5KAEzrzbR06VKtWLGix2s+/PBDjRgxwnv/8OHD+s53vqMJEyboueee6/G1t956q2pqavTnP//Z7zW+ZmZycnIIM4AFBBNSohWyAFiTaWHm+PHjOnHiRI/XDB8+XElJSZKkI0eOaMKECbrqqqu0bt06JST0vI3nmWee0X//93+rrs54ZVIaTQLWQkgBYITR3++w75nJzMxUZmamoWsPHz6siRMnavTo0Vq7dm3AICNJ5eXlys5mihmws8QEB32RAISNaRuADx8+rAkTJmjo0KF68skndfz4ce9zLpdLkvTCCy8oKSlJl112mSRp48aNWrNmTcClKAD2EGiGJpIzOMwOAbHDtDCzZcsWVVVVqaqqSkOGDOn0XMeVr0cffVQff/yx+vTpoxEjRmjDhg26/vrroz1cAGEWaO9MJDcAs7kYiC2WOc0USeyZASIr2FkOz6kmX0XtJOmu8bn69Ts1fp/vTb2YQJ9NLRrAOkzbMwMgvgQ7y2GkW/dv/tw9yHR8PtRu3mZ1CgcQWTSaBBAyf12w6xuaNb+4TCUV3U8dGunW7aMhdqfnQ+3mbUancACRR5gBEJJAsxzSmVmOti7JJFw9mkJ5n2h3CgcQHSwzAQhJMLMcY3LTvXtqPvu8xe9rghFKr6dodwoHEB2EGQAh2VJZb+i6rZX1Wvxyeafgk+Dwv5TkkOQI8Hyo3byj3SkcQHSwzATYSFu7W6XVJ7Sp/LBKq090W8KJlpKKOq3ZfcjQtc/vPtRtBqenoCJJ876deybU+Hk+1G7e0e4UDiA6mJkBbMIqtVE8e2WM6GkGxtfzHbt1X3buORHp5h3NTuEAooM6M4ANWKk2Smn1Cd34mz1he79l112oganJVAAG0A11ZoAYYbXaKEZP+nzn/IF6+/99FvC6ganJ+t6l/+TzuUj2cKI/FBA72DMDWJzVaqMYPekz/lvGGs5ycghAbxFmAIszOhOyu+qzqGwI9pwI8jcH5NCZvTy3FAwzdB0nhwD0FmEGsDijMxdP76jSNSu2+6y6G05GTgT98Mpz9ceKOv3wynN7vI6TQwDCgQ3AgMW1tbt1zYrtfmujdBStDcFt7W49vb1Ka3fX6NRXp72Pn9O/r9ySTn35zWMD+veVujxGh2oARrABGIgRnpmQ+cVlckg9BppobAj2dUR8QL+++va3MrR5f/dCeg1fnpZb0qLJ39KwgWdxcghA2LHMBNiApzaKyxl4ySmSG4L9NZZs+Oq0zyDjGY9D0kvvfaLvXjxYBXkZBBkAYUWYAWxi+qhs7VoySQsn5hm6PtzNEo00lvSHbtQAIokwA9hIYoJDV59nzpHnQEfEjaAbNYBIIMwANmP0aHS4jzyHI4hQUwZAJBBmAJsxq1lib4IINWUARBJhBrAhfxuCXc6UiB3LDjQj5A81ZQBEGnVmABsLplliOBorek4zSZ03/Xre5a7xuXr9/TrTO3sDiA1Gf78JM4BFhbOrs6/aMKGGjEDvRTdqAOFCmOmAMAO7CXf4mF9c1u34dG+qBRNYAEQDYaYDwgzsJJzhw9MKwd+RaofO7LPZtWQSYQSA5Rj9/WYDMGAhRgrTFW2uNNwdO1BtGIrZAYgFhBnAQsIdPozWhqGYHQA7I8wAFhLu8GG0NgzF7ADYGV2zAQsJd/jw1Iapb2j2uXTl2TPTsZgdm3sB2A1hBrCQUMJHTzzVgucXl8kh37VhOhazC+cpKgCIFpaZAAuJRKsCo9WCPaeouu7ZqW9o1vziMpVU1AX1dwGAaOFoNmBBkZgh6Wn5iCPcAKzI6O83y0yABU0fla0p+a6w7l1JTHCoIC/D53PBnKLy9x4AYBZTl5mGDRsmh8PR6fb44493umb//v369re/rZSUFOXk5OiJJ54wabRAdHnCx/cu/ScV5GVEdEaEI9wA7Mz0mZn/+q//0rx587z3U1NTvX9ubGzU1KlTNXnyZK1evVp//etfdfvtt2vAgAG66667zBguEJM4wg3AzkwPM6mpqXK5XD6fe/HFF9Xa2qo1a9YoKSlJI0eOVHl5uX7+858TZoAwCvcpKgCIJtNPMz3++OPKyMjQZZddpp/97Gf6+uuvvc+VlpZq/PjxSkpK8j42bdo0HTx4UH//+9/9vmdLS4saGxs73QD4F4lTVAAQLaaGmf/4j//QSy+9pB07dujuu+/WT3/6Uz3wwAPe5+vr6zVo0KBOr/Hcr6+v9/u+y5cvl9Pp9N5ycnIi8xcAYojRI9wAYDVhP5q9dOlSrVixosdrPvzwQ40YMaLb42vWrNHdd9+tL774QsnJyZo6dapyc3P17LPPeq+prKzUyJEjVVlZqQsvvNDn+7e0tKilpcV7v7GxUTk5ORzNBgygAjAAqzDtaPb999+vuXPn9njN8OHDfT4+duxYff311zp06JAuuOACuVwuHT16tNM1nvv+9tlIUnJyspKTk4MbOABJPR/hBgArCnuYyczMVGZmZkivLS8vV0JCgrKysiRJBQUF+s///E+dPn1affv2lSRt2bJFF1xwgc4555ywjRkAANiXaXtmSktLtXLlSr3//vv66KOP9OKLL2rRokW6+eabvUHlpptuUlJSku644w598MEH2rBhg37xi19o8eLFZg0bAABYjGlHs5OTk/XSSy/pkUceUUtLi3Jzc7Vo0aJOQcXpdOqtt97SggULNHr0aA0cOFAPP/wwx7IBAIAXvZkAAIAlGf39Nr3ODAAAQG8QZgAAgK0RZgAAgK0RZgAAgK0RZgAAgK0RZgAAgK0RZgAAgK0RZgAAgK0RZgAAgK2Z1s4AiGdt7W7trTmpY583Kys1RWNy05WY4DB7WABgS4QZoAeRCB0lFXUq2lypuoZm72PZzhQVzsjX9FHZvR0yAMQdwgzgRyRCR0lFneYXl6lrQ7T6hmbNLy7TqpsvJ9AAQJDYMwP44AkdHYOM9E3oKKmoC/o929rdKtpc2S3ISPI+VrS5Um3tMd/7FQDCijAD/ENbu1ul1Sf0atmn+smrFWEPHXtrTnYLR13fu66hWXtrTgb1vgAQ71hmAuR7ScmfjqGjIC/D8Gcc+zzwewdzHQDgDMIM4t4f9tfp39eXBf26YENHVmpKWK8DAJzBMhPi2h/2H9HC3wUfZKTgQ8eY3HRlO1Pk7yyUQ2c2GI/JTQ9pPAAQrwgziFslFXX69/V/UbD7bUMNHYkJDhXOyPe+R9f3lKTCGfnUmwGAIBFmEJc8J4uC1dvQMX1UtlbdfLlczs6zOi5nCseyASBE7JlBXAp0ssgfVxiK200fla0p+S4qAANAmBBmEJeC2bybflZfLfvuSLnSwhc6EhMcQZ2EAgD4R5hBXApm8+5Pv38Ryz8AYGHsmUFcCnSySJISHNKvbmIfCwBYHWEGcamnk0UeT994mf7lYoIMAFgdYQZxy9/JomxnilbffLmmjcpWafUJbSo/rNLqE/RMAgCLYs8M4pq/k0VbKut1zYrtYe2YDQCIDIfb7Y75f91sbGyU0+lUQ0OD0tLSzB4OLM7TMbvr/zE8y1HUgwGA6DD6+80yE9CBp5heuDtmAwAihzADdBComF7HjtkAAGsgzAAdGC2mF2zHbABA5BBmgA6MFtMLtmM2ACByCDNAB4GK6YXaMRsAEDmmhZmdO3fK4XD4vL333nuSpEOHDvl8fs+ePWYNGzGup2J6ve2YDQCIDNPCzLhx41RXV9fpdueddyo3N1dXXHFFp2u3bt3a6brRo0ebNGrEA3/F9FzOFI5lA4AFmVY0LykpSS6Xy3v/9OnT2rRpk+699145HJ3/rTcjI6PTtUCk+Sumx4wMAFiPZSoAv/766zpx4oRuu+22bs/NnDlTzc3NOv/88/XAAw9o5syZPb5XS0uLWlpavPcbGxvDPl7EvsQEhwryMsweBgAgAMtsAH7++ec1bdo0DRkyxPvY2Wefrf/5n//R73//e7355pu65pprNGvWLL3++us9vtfy5cvldDq9t5ycnEgPHwAAmCTs7QyWLl2qFStW9HjNhx9+qBEjRnjvf/rppxo6dKhefvllzZ49u8fX3nrrraqpqdGf//xnv9f4mpnJycmhnYENtbW7WeoBgDhltJ1B2JeZ7r//fs2dO7fHa4YPH97p/tq1a5WRkRFw+UiSxo4dqy1btvR4TXJyspKTkwO+F6ytpKJORZsrafYIAOhR2MNMZmamMjMzDV/vdru1du1a3Xrrrerbt2/A68vLy5WdzQ9ZrPPX7LG+oVnzi8s4VQQA8DJ9A/D27dtVU1OjO++8s9tzL7zwgpKSknTZZZdJkjZu3Kg1a9boueeei/YwEUWBmj06dKbZ45R8F0tOAADzw8zzzz+vcePGddpD09Gjjz6qjz/+WH369NGIESO0YcMGXX/99VEeJaIpmGaPnDYCAJgeZtavX+/3uTlz5mjOnDlRHA2sgGaPAIBgWOZoNuBBs0cAQDAIM7Acmj0CAIJBmIHl0OwRABAMwgwsiWaPAACjTN8AjNgTrqq9NHsEABhBmEFYhbtqL80eAQCBEGYQko6zLwPPTpbc0rYDR7Vm96Fu11K1FwAQSYQZBM3X7EtPqNoLAIgkNgAjKJ6eSUaDjEfHqr0AAIQTYQaG9dQzySiq9gIAwo0wA8MC9Uwygqq9AIBwY88MDOvNrIpDZ2rEULUXABBuzMzAsFBnVajaCwCIJMIMDAvUM8kfqvYCACKJZSYY5umZNL+4TA4p4EbgO64epsn5Lqr2AgAiipkZBMVfz6SOsp0pWn3z5Vo2Y6QK8jIIMgCAiGJmBkHr2jPJUwH4s6YW+icBAKKOMIOQ0DMJAGAVLDMBAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbI8wAAABbi1iYeeyxxzRu3Dj1799fAwYM8HlNbW2trrvuOvXv319ZWVn68Y9/rK+//rrTNTt37tTll1+u5ORknXfeeVq3bl2khgwAAGwoYmGmtbVVN9xwg+bPn+/z+ba2Nl133XVqbW3Vu+++qxdeeEHr1q3Tww8/7L2mpqZG1113nSZOnKjy8nLdd999uvPOO/WnP/0pUsMGAAA243C73e5IfsC6det033336dSpU50e/+Mf/6jvfve7OnLkiAYNGiRJWr16tZYsWaLjx48rKSlJS5Ys0ZtvvqmKigrv6374wx/q1KlTKikpMTyGxsZGOZ1ONTQ0KC0tLSx/LwAAEFlGf79N2zNTWlqqiy66yBtkJGnatGlqbGzUBx984L1m8uTJnV43bdo0lZaWRnWsAADAuvqY9cH19fWdgowk7/36+voer2lsbNRXX32lfv36+XzvlpYWtbS0eO83NjaGc+gAAMBCgpqZWbp0qRwOR4+3AwcORGqshi1fvlxOp9N7y8nJMXtIAAAgQoKambn//vs1d+7cHq8ZPny4ofdyuVzau3dvp8eOHj3qfc7zn57HOl6Tlpbmd1ZGkh588EEtXrzYe7+xsZFAAwBAjAoqzGRmZiozMzMsH1xQUKDHHntMx44dU1ZWliRpy5YtSktLU35+vveaP/zhD51et2XLFhUUFPT43snJyUpOTg7LOAEAgLVFbANwbW2tysvLVVtbq7a2NpWXl6u8vFxffPGFJGnq1KnKz8/XLbfcovfff19/+tOf9NBDD2nBggXeIHLPPffoo48+0gMPPKADBw7oV7/6lV5++WUtWrQoUsMGAAA2E7Gj2XPnztULL7zQ7fEdO3ZowoQJkqSPP/5Y8+fP186dO3XWWWdpzpw5evzxx9WnzzcTRjt37tSiRYtUWVmpIUOGaNmyZQGXurriaDYAAPZj9Pc74nVmrIAwAwCA/Vi+zgwAAEA4EGYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICtEWYAAICt9TF7AHbV1u7W3pqTOvZ5s7JSUzQmN12JCQ6zhwUAQNwhzISgpKJORZsrVdfQ7H0s25miwhn5mj4q28SRAQAQf1hmClJJRZ3mF5d1CjKSVN/QrPnFZSqpqDNpZAAAxCfCTBDa2t0q2lwpt4/nPI8Vba5UW7uvKwAAQCQQZoKwt+ZktxmZjtyS6hqatbfmZPQGBQBAnCPMBOHY5/6DTCjXAQCA3iPMBCErNSWs1wEAgN4jzARhTG66sp0p8ncA26Ezp5rG5KZHc1gAAMQ1wkwQEhMcKpyRL0ndAo3nfuGMfOrNAAAQRYSZIE0fla1VN18ul7PzUpLLmaJVN19OnRkAAKKMonkhmD4qW1PyXVQABgDAAggzIUpMcKggL8PsYQAAEPdYZgIAALYWsTDz2GOPady4cerfv78GDBjQ7fn3339fN954o3JyctSvXz9deOGF+sUvftHpmp07d8rhcHS71dfXR2rYAADAZiK2zNTa2qobbrhBBQUFev7557s9v2/fPmVlZam4uFg5OTl69913dddddykxMVELFy7sdO3BgweVlpbmvZ+VlRWpYQMAAJuJWJgpKiqSJK1bt87n87fffnun+8OHD1dpaak2btzYLcxkZWX5nN0BAACw1J6ZhoYGpad3Lzh36aWXKjs7W1OmTNHu3bsDvk9LS4saGxs73QAAQGyyTJh59913tWHDBt11113ex7Kzs7V69Wq98soreuWVV5STk6MJEyaorKysx/davny5nE6n95aTkxPp4QMAAJMEFWaWLl3qc0Nux9uBAweCHkRFRYW+973vqbCwUFOnTvU+fsEFF+juu+/W6NGjNW7cOK1Zs0bjxo3TU0891eP7Pfjgg2poaPDePvnkk6DHBAAA7CGoPTP333+/5s6d2+M1w4cPD2oAlZWVuvbaa3XXXXfpoYceCnj9mDFjtGvXrh6vSU5OVnJyclDjAAAA9hRUmMnMzFRmZmbYPvyDDz7QpEmTNGfOHD322GOGXlNeXq7sbFoGAACAMyJ2mqm2tlYnT55UbW2t2traVF5eLkk677zzdPbZZ6uiokKTJk3StGnTtHjxYm/tmMTERG9gWrlypXJzczVy5Eg1Nzfrueee0/bt2/XWW28FNRa32y1JbAQGAMBGPL/bnt9xv9wRMmfOHLekbrcdO3a43W63u7Cw0OfzQ4cO9b7HihUr3Hl5ee6UlBR3enq6e8KECe7t27cHPZbq6mqfn8WNGzdu3Lhxs/7tk08+6fF33uF2B4o79nfq1Cmdc845qq2tldPpNHs4Ma2xsVE5OTn65JNPOhU6RPjxXUcP33V08X1Hj9W/a7fbrc8//1yDBw9WQoL/M0tx0WjS8wU4nU5L/pcVi9LS0viuo4TvOnr4rqOL7zt6rPxdG5mEsEydGQAAgFAQZgAAgK3FRZhJTk5WYWEhtWeigO86eviuo4fvOrr4vqMnVr7ruNgADAAAYldczMwAAIDYRZgBAAC2RpgBAAC2RpgBAAC2FndhZubMmTr33HOVkpKi7Oxs3XLLLTpy5IjZw4o5hw4d0h133KHc3Fz169dPeXl5KiwsVGtrq9lDi0mPPfaYxo0bp/79+2vAgAFmDyfmPPPMMxo2bJhSUlI0duxY7d271+whxaR33nlHM2bM0ODBg+VwOPTaa6+ZPaSYtHz5cl155ZVKTU1VVlaWZs2apYMHD5o9rF6JuzAzceJEvfzyyzp48KBeeeUVVVdX6/rrrzd7WDHnwIEDam9v17PPPqsPPvhATz31lFavXq2f/OQnZg8tJrW2tuqGG27Q/PnzzR5KzNmwYYMWL16swsJClZWV6ZJLLtG0adN07Ngxs4cWc5qamnTJJZfomWeeMXsoMe3tt9/WggULtGfPHm3ZskWnT5/W1KlT1dTUZPbQQhb3R7Nff/11zZo1Sy0tLerbt6/Zw4lpP/vZz7Rq1Sp99NFHZg8lZq1bt0733XefTp06ZfZQYsbYsWN15ZVX6umnn5Yktbe3KycnR/fee6+WLl1q8uhil8Ph0KuvvqpZs2aZPZSYd/z4cWVlZentt9/W+PHjzR5OSOJuZqajkydP6sUXX9S4ceMIMlHQ0NCg9PR0s4cBGNba2qp9+/Zp8uTJ3scSEhI0efJklZaWmjgyIHwaGhokydb/fI7LMLNkyRKdddZZysjIUG1trTZt2mT2kGJeVVWVfvnLX+ruu+82eyiAYZ999pna2to0aNCgTo8PGjRI9fX1Jo0KCJ/29nbdd999uvrqqzVq1CizhxOymAgzS5culcPh6PF24MAB7/U//vGP9Ze//EVvvfWWEhMTdeuttyrOV9sMC/a7lqTDhw9r+vTpuuGGGzRv3jyTRm4/oXzXABCMBQsWqKKiQi+99JLZQ+mVPmYPIBzuv/9+zZ07t8drhg8f7v3zwIEDNXDgQJ1//vm68MILlZOToz179qigoCDCI7W/YL/rI0eOaOLEiRo3bpx+/etfR3h0sSXY7xrhN3DgQCUmJuro0aOdHj969KhcLpdJowLCY+HChXrjjTf0zjvvaMiQIWYPp1diIsxkZmYqMzMzpNe2t7dLklpaWsI5pJgVzHd9+PBhTZw4UaNHj9batWuVkBATE4FR05v/XSM8kpKSNHr0aG3bts27EbW9vV3btm3TwoULzR0cECK32617771Xr776qnbu3Knc3Fyzh9RrMRFmjPrf//1fvffee7rmmmt0zjnnqLq6WsuWLVNeXh6zMmF2+PBhTZgwQUOHDtWTTz6p48ePe5/j32jDr7a2VidPnlRtba3a2tpUXl4uSTrvvPN09tlnmzs4m1u8eLHmzJmjK664QmPGjNHKlSvV1NSk2267zeyhxZwvvvhCVVVV3vs1NTUqLy9Xenq6zj33XBNHFlsWLFig9evXa9OmTUpNTfXu/3I6nerXr5/JowuRO47s37/fPXHiRHd6ero7OTnZPWzYMPc999zj/vTTT80eWsxZu3atW5LPG8Jvzpw5Pr/rHTt2mD20mPDLX/7Sfe6557qTkpLcY8aMce/Zs8fsIcWkHTt2+Pzf8Zw5c8weWkzx98/mtWvXmj20kMV9nRkAAGBvbGIAAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC2RpgBAAC29v8BAsU/1lWKpeMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Trainieren vom Model\n",
    "reg_model = LinearRegression()\n",
    "\n",
    "reg_model = reg_model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cn376qdlrQ4YMwVdffWV3SOfPP//En3/+afde4eHhuP322+vU3ppWrlyJhx9+GPPnz8fMmTMdfv/EiRPxwQcfIDs729TbsmTJEqSmpmLs2LGYMWMGDAYD5s6dizVr1uDKlSv43//+Z3feDRFRINIbRPRZsA2l2grcm78Nb25+w+KcpFeysCutv9M1nXwBdwBWwOnTp3H58mXceOONFq+1b98eX331ld1rtG7dGq1bt65zWy5fvgytVmt2TK1WWz3/oYcewvTp05GVleVUmJk+fTo++OADZGVlmcLMpEmTcPz4cSxatAgff/wxAKBHjx6YMWMG5s2bZ7aSioiIrjNusCfVG3PPuP/gYNPWgLYCy3cXoklkaJ2LVfo6hhkvc/HiRVkTY4ODgxEbG2v19VWrVmH8+PFmx+z1CsXHx+PcOed2noyPjwcAi/fPmzcPzz33HA4cOACVSoXOnTvjxRdfBAC0a9fOqXsREfm7U7rLkkGmVdoms+cvb/7N9Pe6FKv0dQwzLhQbG4vw8HD88ccfFq8dPnxY1jVee+01l8yZGTx4MLZs2SLrnkB10CkqKkJXJyupGofGpAJW48aN0adPH9PzrKwsNG/eHB06dHDqXkREfu0f/8CIt9+2OFw7yNRWpq1A6orcOhWr9FUMMy4UHByMwYMHY926dTh27JhpAvBvv/2Gb775RtY1Hn30UbMvfmukVgnVpNFooNFI/2M+ffq0RehYvHgxTp8+bbGL76FDhxAREWH6LDqdDqGhoQgNDTWdI4oi5s6dC6A6RNmyatUq/Pjjj3jttdcQFCA7UxIRySaxtLrXU8txMtL+nmCuKFbpqzgB2MX279+PXr16IS4uDk899RSuXr2Kt99+G02bNsX+/fud3tPFlSIiIvDAAw+gc+fOCAsLw65du/DZZ5/hlltuwe7duxEREWE6VxAE3HnnndixYwcAYMeOHRg9ejRGjx6Ntm3b4vLly1i7di12796NiRMnmu2p89133+Ff//oXBg0ahJiYGOTk5GDZsmUYOHAgNm7ciHr1mKWJiAAAlZWAREmZhGu9MY5+c3w64Ta7q6V8AScAK+Tmm2/GN998g2nTpmH27Nlo3rw5MjIyUFpaiv379yvdPADAww8/jD179mD16tWoqKhAy5YtMWPGDPzzn/80CzJSWrZsiTvuuANr165FWVkZgoKC0LFjRyxZsgQTJ040O/eGG25AcHAwFi1ahAsXLiAhIQFz587FtGnTGGSIiIxuuQWo/f1w443A779jca19ZuRyulilj2LPDBERkVKkduy9fNmsl0ZvEE0b7J25UGk26dca9swQERGRe504AVxbBWpGon+h5gZ7eoOID3cVurZYpR/gDEwiIiJPEgTLIDNhgqzdfI3FKoHrxSlNl732p0PFKv0Ee2aIiIg8xQWVro3FKmvPpVFf22dmYKIa2QVn7dZ98icMM0RERO72/fdA376Wx52ctmqtWOWWg2WmMghGgbCZHicAExERuZNUr8vChcDzz7v0NrULU5puf+1PX9xMjxOAiYiIlCYVZNzQh6A3iMjYeFByUnAgbKbHCcBERESu9s47HgsywPXClNaIAEq1Fdhb6Fz9PW/HnhkiIiJXkgoxW7YAAwa47ZZyN8nz1830GGaIiIhcQRQBqZpzHpiaGhdpWQqhLuf5Gg4zERER1dUDDygWZACgZ0I0NKowi71njARUr2ry1830GGaIiIjqQhCAzz83P1ZY6LEgA3AzPYYZIiLyWnqDiOyCs1ifV4zsgrPQG7xoN5HKSuuTfFu18nhzjJvpqVXmQ0lqVZhPLst2BOfMEBGRV8qUqBjtNRvARUYCFy9aHld46zZrm+n5a4+METfNIyIir+PVG8BJ9caUlwMREZ5vi5+T+/2t+DDTnDlzIAiC2aNDhw6m1ysqKjB58mTExMSgYcOGGDVqFE6ePKlgi4mIyJ3sbQAHVG8A54ohJ4eGsYqLrQ8rMcgoyiuGmW666SZkZWWZnterd71ZU6dOxebNm/HFF19ApVJhypQp+Nvf/obdu3cr0VQiInIzRzaAS2oT4/R9HBrGkgox99wDbN7s9P3JdbwizNSrVw9qtdriuFarxUcffYSVK1eif//+AIBly5ahY8eOyMnJwW233ebpphIRkZt5YgM4a8NYZdoKpK7INR/GckGla3IvxYeZAOCPP/5As2bN0Lp1azz88MM4duwYAGDfvn24cuUKBtTYNbFDhw5o0aIFsrOzrV6vsrISOp3O7EFERL7BVRvAWRtCkj2M9d331oeVGGS8iuI9M7169cLy5cvRvn17lJaWIiMjA3fccQfy8/NRVlaGkJAQNGrUyOw9TZs2RVlZmdVrzp8/HxkZGW5uORERuYNxA7gybYVk4BBQvdzY1gZwtoaQVOEhdoexsl+UKD2wYAEwY4b8D0Ieo3iYufvuu01/v/nmm9GrVy+0bNkSn3/+OcLDw5265gsvvIBp06aZnut0OsTHx9e5rURE5H7GDeBSV+RCAMwCjZwN4OwNIT12eyub9y9aMNTyoP8v/PVpXjHMVFOjRo3Qrl07HDlyBGq1GlVVVTh//rzZOSdPnpScY2MUGhqKqKgoswcREXm3msNCqvAQvPuQ4xvAyRlCWptXLPneR/dtZJDxUYr3zNR28eJFFBQU4JFHHkH37t1Rv359bN26FaNGjQIAHD58GMeOHUNSUpLCLSUiIlexNiw0a0hHNG4QKnsDODkroc6VX0F0gxD8VV5lCjhSIUb/zbcIHjTQ2Y9EHqR4z8xzzz2HnTt3oqioCHv27MG9996L4OBgjB49GiqVCo8//jimTZuG7du3Y9++fRg/fjySkpK4komIyE8Yh4Vqh5AybQUmr/wZ2stVGNHlBiS1ibG7k63cFU4juzQDUD1sJRVkMn8tYZDxIYr3zJw4cQKjR4/G2bNnERsbiz59+iAnJwexsbEAgDfffBNBQUEYNWoUKisrMXjwYPz3v/9VuNVEROQK9oaFBFSvLBqYqJa1Jb/clVADE9WY8q8JiP7JcmVs5q8lypdLIIewnAERESkmu+AsRn+QY/e8TyfcJmuDPL1BRJ8F2+yuhJJarZS7Ixe33NHF7+sY+RKfKWdARESBy9Ub5BlXQgHXVz4ZCQBCrlZJL7sWRXS7syuDjI9imCEiIsW4aoO8mlI6abB4jOVKqMIFQ3H49b9ZvsH/Byj8nuJzZoiIKHC5YoM8KSmdNBiYqMbewnM4daECI7o2tzzpwgWgYUOn2k3ehT0zRESkGHvDQoDtDfLsXTtJ0EoHGVFkkPEjDDNERKQoa8NC9jbIs0sQgDZtzI/FxnJYyQ9xmImIiBRXe1hIzgZ5NrHSdUBhmCEiIq8QHCTIWn5t0xdfAH//u+Vx9sb4NYYZIiLyD1K9LvffD3z+uefbQh7FMENERL5PKsiwNyZgcAIwERH5rtGjGWSIYYaIiHyUIACffWZ+7D//YZAJQBxmIiIi38PeGKqBYYaIiHyHtaXVDDIBjcNMRETkG6SCzI8/MsgQe2aIiMjLXboENGhgeZwhhq5hmCEiIu/FYSWSgcNMRETknaSCzF9/MciQBYYZIiLyLvn51lcrNWrk8eaQ9+MwExEReQ83DivpDaLrClmSV2GYISIit3A4PLix0nVmfikyNh5EqbbCdEyjCkP6sESkdNLU+fqkLIYZIiJyOYfCwwcfABMnWl7ERXNjMvNLkboiF7WvVqatQOqKXCwe042BxsdxzgwREbmUMTzUDDLA9fCQmV96/aAgWAaZrl1dFmT0BhEZGw9aBBkApmMZGw9Cb+CkYl/GMENERC7jUHiwNsk3N9dl7dlbeM4iVNVuU6m2AnsLz7nsnuR5DDNEROQycsLDvA9nIjhY4uvHDUuuT12w3hZnziPvxDBDREQuYy8UFC0Yiv5//mR+8JVX6hxk9AYR2QVnsT6vGNkFZ03DRnGRYbLeL/c88k6cAExERC5jKxQULRhqedAFvTG2JhsPTFRDowpDmbZCcuhLAKBWVa+0It/FnhkiInKZngnR0KjCUHM2TNGCoW4NMrYmG285WIb0YYkAgNozdIzP04clcr8ZH8cwQ0Tkh6wNu7hbcJBgFh6kQkzO/9a7bBM8OZONByaqsXhMN6hV5r1GalUYl2X7CQ4zERH5GaU3iEvppMH7f2uPgb1utGzbryUua4MjK5VSOmkwMFHNHYD9FMMMEZEf8YoN4gQBAyUO6/UGpLgwPDi6Uik4SEBSmxiX3Z+8B4eZiIj8hFdsECe1d8yZM4AourwXhCuVyEjxMDN//nzceuutiIyMRFxcHEaOHInDhw+bndOvXz8IgmD2mDRpkkItJiLyTopuEPfLL9Y3wYtxT2+I1GTjmgRUD69xpZL/UzzM7Ny5E5MnT0ZOTg62bNmCK1euYNCgQSgvLzc7b8KECSgtLTU9Fi5cqFCLiYi8k9xhl6yDZa69sSAAXbpYHnfDJng11Z5sbNaka39ypVJgUHzOTGZmptnz5cuXIy4uDvv27UPfvn1NxyMiIqBWqz3dPCIinyF3OOWj3UW4NSHaNXNnJHpj1uceR1xUOHoaXD+0VFtKJw0Wj+lmMeFZzYrYAUXxMFObVqsFAERHm3cLfvLJJ1ixYgXUajWGDRuGWbNmISIiQvIalZWVqKysND3X6XTuazARkZcwDrtY2yCupjkbDmBgotr5sPHOO8DTT1scbpW2CVj1CwDPraDiSiUSRNHN/YAOMBgMGD58OM6fP49du3aZjr///vto2bIlmjVrhv379yMtLQ09e/bEmjVrJK8zZ84cZGRkWBzXarWIiopyW/uJiJSWmV+KSSvkFWqcOqAdnhlguXzaLonemBNRceiTutT8tGt/ci8XcpZOp4NKpbL7/e1VYSY1NRVff/01du3ahebNm1s9b9u2bbjrrrtw5MgRtGnTxuJ1qZ6Z+Ph4hhki8nt6g4jOc77BpSq9rPOXOBo0JIJM0itZViceG8sF7Errz54ScpjcMKP4BGCjKVOmYNOmTdi+fbvNIAMAvXr1AgAcOXJE8vXQ0FBERUWZPYiIAsHewnOygwzgwFLtvn0lg0z2kTPKraAiukbxMCOKIqZMmYK1a9di27ZtSEhIsPuevLw8AIBGw25LIqKa5K5oMpIVNAQB+P5782P//Ccgig5vXEfkDopPAJ48eTJWrlyJ9evXIzIyEmVl1UsGVSoVwsPDUVBQgJUrV+Kee+5BTEwM9u/fj6lTp6Jv3764+eabFW49EZF3cWaDOJtBQ6I3Rq83mIaMuHEdeQPFe2YWL14MrVaLfv36QaPRmB6rVq0CAISEhCArKwuDBg1Chw4dMH36dIwaNQobN25UuOVERN7HuKLJEZJBQxAkg0yrtE3os2AbMvNLze7HjetISYr3zNibfxwfH4+dO3d6qDVERL4tOEjA8Fs0eO+7QrvnGifnWgQNiRDz8ANzsbtVFwCWdZ7ShyUidUUuBMBsSTg3riNPUbxnhoiIXEdvELHhl1LZ55sFjYsXrfbGGIMMYFnnybhxnbpWj5BaFcZl2eQRivfMEBGR69irz2QU3aA+Xrm38/WgIVVXCdc2wZNQc5VSUpsYblxHimKYISLyI3JXDc0aepPNIPP11l+Q+u1xh+4XHCQgqY17ikoS2cJhJiIiPyJ31ZA6KgzIzbVa6fp3Q7hL70fkTuyZISLyI/bqMxkn/Sa1bSJ9AVFEZn4p3sr63eZ9rE4eJlIAe2aIiPxIcJCA9GGJAGCxXNr4PPvFAZZvNBgAUYTeICJj40G7hSpFcJUSeQ+GGSIiP2NtddHU/RtRuGCo5RtE0TTcJHcC8dQBN3KVEnkNDjMREfmh2quLRnSVqHkXEQGUl5sdkjuBuFWTBq5oJpFLMMwQEfkp0+oiK5N8pbA8AfkihhkiIoXoDaJ792WxsneMtSADyJ9AzIm/5E0YZoiIFJCZX4qMjQfN5qc0Cq+P8be3wpT+N9Y91EgFmXHjgGXLbL7NOIGY5QnIlwiiveJIfkCn00GlUkGr1SIqKkrp5hBRgMvML0XqilyrK4YaRdTHq3/r7PwEWweGlayRClsaVRjShyVy4i95jNzvb4YZIiIP0htE9Fmwze6KIQFwvK6RE8NKtrh9GIzIDrnf3xxmIiLyoJyCs7KWPouoLuQ4MFEtL0BIBJm9r38A/Yh70dMgOhVCWJ6AfAXDDBGRh2Tml2Lm6l9ln1+zkKNVFy4AEr+xtkrbBJwC8EEOh4fI73HTPCLyWXqDiOyCs1ifV4zsgrPQG7x31Nw4T+b85SsOvc+474vkZxUE60GmhjJtBVJX5CIzv9T5D0DkxdgzQ0Q+yZcmqMotESAlLjJM8rMWSezkO2zmZ/hVbGhxXET1HByHhq2IfAh7ZojI5xh7OWrPPfHWHgi5JQJqElAdzv4qrzT7rN1O/CYZZLKPnJEMMkYirg9bEfkb9swQkU+x1cvhTT0QNVcC/XHygkPvNbZ61pBEvLz5+meVCjEAoNcbcGp/iaxrf30t6HFlEvkThhki8in2ejlq9kAotRJHaljIEeprw2Wq8BDTNaSCTMKMDRCFIHxaeE52eYH/yz6K/8s+6rVDckTOYJghIp8itxCi3PNczd6GeFIEANENQvDSkI5Qq8JNvSbr84rx0tYP8MRP6y3eU3OS76kLFRh6czObZQhqMw7JObqXDfeeIW/EMENEPsWbCyE6M9HXGAPm3dvJIlRIVrqG5WqlMxcqsWl/CR68NR5vZv1hUYZAijNDcr406ZoCC8MMEfkUby6E6MxEX7W1MCCxCV7tEAMAQQLw8ubfTM8bRdQHAJy/ZH8JuCNDctZ6nJzt4SFyJYYZIvIp3lIIUWq4Re7Q1pTktrixaUPpYRorJQkSJIIMANTeWkd7LcRMHdAOZ8sr8X/ZR+22x167fWXSNQUuLs0mIp+T0kmDxWO6Qa0yH0pSq8I80kOQmV+KPgu2YfQHOXjmszyM/iAHfRZsQ9GZclnvv71tE4zocgOS2sTYDzJ3343MX0ssPqu1zGAMHJ/9eAyDb1LLao+9ITlHJl0TKYE9M0Tkk1I6aTAwUV2nyajOTGa1NdzyZtYfaBRRH9pLVxwfArNR6ToFMPusZy5Umg0tWbwN1eHCYBBdMiTn7ZOuiRhmiMhn1aUQojOTWe0NtwBA1VWDaejF3hCY3iAiONhKB3mtStc1P+v6vGKbn83o6U9/xgO3Nsf73xXWaUjOmyddEwEcZiKiAOTsDsJyJvheqtIDsOxoqT0ElplfKhlk8hYttggytckNDecvX8H73xViYt+EOg3JGSddW4s8xt2KlZh0TQSwZ4aIAoyzk1n1BhG7j5yRfR/jxNzHb2+FAYlqsyGsLTm/IyWpvcV7EtI2AWeAxfmlNkOGvRVdtW34pRQ7n0/GvqN/OTUk5y2TromsYc8MEQUUuZNZl+8uNFXhNk74fWf7EYfuJQD4Kr/MPDgIAgZKBJlWaZtMISFj40GbFcCN4UIO4+fZd/QvJLWJkZ54LIPSk66JbGHPDBEFFLmTVF/e/Bs+3FWI4bdo8P53hU5VvLbYx0Vikm9S6jKURsVaf48VxnAxc/WvOH/Z/p4yrpic64pJ10Tu4DM9M++++y5atWqFsLAw9OrVC3v37lW6SUTkgxyZpFqmrcB7TgaZmsQtW6xuglczyNQkJ3ykdNLg3Ye6yWqDqybnGiciO9vDQ+QOPhFmVq1ahWnTpiE9PR25ubm45ZZbMHjwYJw6dUrpphGRj7E3mbWmuoYYoLpAZO/U0RbHpXbzrUlu+LitTQwn51LA84kw88Ybb2DChAkYP348EhMTsWTJEkRERGDp0qVKN42IfEzN+Sbu7lOQqnStv3IVSa9kuSx82Po8nJxLgcLrw0xVVRX27duHAQMGmI4FBQVhwIAByM7OlnxPZWUldDqd2YOIyMjaZNa6qBkV5n3zjmSQgSgiuF6w7PChN4jILjiL9XnFyC44a3VSMCfnUqDz+gnAZ86cgV6vR9OmTc2ON23aFIcOHZJ8z/z585GRkeGJ5hGRjzJOZl2+u9Dmbrq2GHfQnTUkES9vrt6ATzLEAGZ7xxjDR+1N+2oWnXR0Uz9OzqVAJoiind2ZFFZSUoIbbrgBe/bsQVJSkun4jBkzsHPnTvzwww8W76msrERlZaXpuU6nQ3x8PLRaLaKiojzSbiLyDXqDiD4Ltsnes8XIGBGMPR9Wd/O18b9Ya+UUrJVMqH1PIn+n0+mgUqnsfn97/TBTkyZNEBwcjJMnT5odP3nyJNRq6SJqoaGhiIqKMnsQEUmxN+dEAPBk3wRobA3hCILDQcZ479org+xt6ifC/j40RIHG68NMSEgIunfvjq1bt5qOGQwGbN261aynhojIWfbmnLxwTyJ2pfXHpxNuw78f7IJPJ9yGXWn9TUHGQv/+doOMNXJKJpRqK/DOtj+cuj6RP/L6OTMAMG3aNIwdOxY9evRAz5498dZbb6G8vBzjx49XumlE5CfszTmRLGppo9K1s+Rubvdm1h9or47kcBMRfCTMPPDAAzh9+jRmz56NsrIydOnSBZmZmRaTgomIrM1DkUN2FW6pEAMAolin+wOObW4nVUOKKBB5/QRgV5A7gYiIfJujK4CcIhVkVqwAHn7YJfc3Tki2N9Rk9OmE2+QFMCIf5DcTgImI5DCuAKodAsq0FUhdkYvM/NK63UCnsz6sdC3IuOL+jhSRBFxTc4nI1zHMEJHPs7cCCKjjCiBBAFQqiYuLbrl/SicNpg5oJ+tcV9VcIvJlDDNE5PPsrQCqWYnaYVK9MUePmk30dcf9p/RvC3VUqPVmgTWXiIwYZojI58kdaql5nt1SATt2WB9WatGizve3JzhIwJzhN5n2uqmJNZeIzPnEaiYiIlvkDrUYz5OaqBvdIARzR3TCPTdb2TsGQNIrWUjPL7WYzOvo/eWSU/aAiBhmiMgP9EyIhkYVZrUkgbGGUs+EaKulAs6VV+GplbkousWytlLCjA0QhSAI1ybz1i4n4Mj9jeQu4WbNJSL7GGaIyOcZVwClrsiFAJgFippDMgCsTtT957YPMeHHdRbHW6VtMv1dvHa92vu7yL2/8XxHl3DL3v+GKEBxzgwRuZ3d+SkuYK8kQUonjdWJukULhtoNMkbWJvPKuT/ggSXkRAGIPTNE5FYe2cjuGntDMlITcIsWWA4rSYWY2qSuZe/+9pZwS/X6EJF9DDNE5DbW5qeUWZl74gq2hmRqTsCVCjGAvCBT+1py7+/IEm4OKxHJx2EmInILt29k54SeCdGIbhAiGWRy4jvJCjJ12d/FHUu4iYg9M0TkJt7YCxEcJCB39iCL47VDTOOI+vjr0hVZk3kd4a4l3ESBjj0zROQW3tALUXPiMQRBcv+Y2kFGADD/b52xRMZkXkcZl3Bbi0Hc1ZfIOeyZISK3ULoXoubEY6lhpby5/8Zjhg5A+RXTsdoTk129v4ujS7iJSB6GGSJyC2c2knMV48TjBpWXUPTW3y1f/7UEKZ00+NHOxnXu2N+Fu/oSuR7DDBG5hVK9EMaJx4VWVislpG2CusbyZyVWDXFXXyLXEkRR9NxSAoXodDqoVCpotVpERUUp3RyigOLJfWYAILvgLJLaNrE4fvukpShWxZmefzrhNi5/JvJycr+/2TNDRG7l0V6IbduQdNddFoelllxz+TOR/2CYISK388hwjpVK19b2juHyZyL/wTBDRL5PIsi0eX499EHBlqfCfROPiUgZ3GeGiHzXhAmSQSbz1xIYgoIt9nPh8mci/8SeGSLySno7y6atDStBFJECcPkzUQBhmCEir2N3BZRUkKm1MDOlkwb9OzTF/7KLcPTcJbSMjsAjSa0QUo8d0kT+hmGGiBRXsxem6MwlvJX1u2Sl7ZTOzaQvILHDhFQg+nBXIXtmiPwQwwwRKUoqdEiR3ASvQwfgt98kr5m6IlcyEKWuyK1TfSUi8j4MM0Rkf36Km1gLHbVJ1VaS6o0Bru8ALPWqiOpJwBk1dgAmIt/HMEMU4Dy9Q6+RrdBhJBliAKz/+QRGWHnP3sJzNnt5RACl2grsLTzHHYCJ/ARnwhEFMGPPSO0vf+NwTGZ+qdvubS90SAWZlwamolXaJpsb3m05WCbr/twBmMh/sGeGKEApORyjN4jYfeS05GsNKy8hX6LStXEn38YR9a1ueKc3iFiXVyKrDdwBmMh/MMwQBSilhmNsTfi1NqxUsyTBX5euYMvBMskhsL2F53CuvMpuG6IbWA9EROR7GGaIApTcYRZXDsfYmvArFWT6TvwAxxqbhxZbPUZy23pvlxs4+ZfIjyg2Z6aoqAiPP/44EhISEB4ejjZt2iA9PR1VVVVm5wiCYPHIyclRqtlEfkPuMIurhmOsDWvdejxfMsi0SttkEWQA8x4jZ9s6IFEt6zwi8g2K9cwcOnQIBoMB7733Htq2bYv8/HxMmDAB5eXleO2118zOzcrKwk033WR6HhPDFQhEddUzIRoaVRjKtBWSPSWuLsgoNawlZ1jJGqleGE9/JiLyDoqFmZSUFKSkpJiet27dGocPH8bixYstwkxMTAzUav4mReRKwUEC0oclInVFLgTA7MvfHQUZa4cPqSDT+vn1MEhUupYi1Qvj6c9ERN7Bq5Zma7VaREdb/sY0fPhwxMXFoU+fPtiwYYPd61RWVkKn05k9iMhSSicNFo/pBrXKPBioVWEu3yXXGD5mbf3A6rCSISgY/7ynAxqF17d6HQHV++BY613x5GciIu8giKKVbTQ97MiRI+jevTtee+01TJgwAQBw5swZ/N///R9uv/12BAUFYfXq1Vi4cCHWrVuH4cOHW73WnDlzkJGRYXFcq9UiKirKbZ+ByFd5YgdgvUFEcLD070+t0jaZhoB2pfXHloNlSF2RC0C6d0VOKFFqV2Mich2dTgeVSmX3+9vlYWbmzJlYsGCBzXN+++03dOjQwfS8uLgYd955J/r164cPP/zQ5nsfffRRFBYW4vvvv7d6TmVlJSorK03PdTod4uPjGWaIlCRR6do4N0YqpCi1MzEReQ/Fwszp06dx9uxZm+e0bt0aISEhAICSkhL069cPt912G5YvX46gINsjX++++y7mzp2L0lL5O5PK/WEQkRuEhgJVlnu/1Jzkay2ksHeFKLDJ/f52+QTg2NhYxMbGyjq3uLgYycnJ6N69O5YtW2Y3yABAXl4eNBr+VkbkEyR6Y9ClC/T7cvGpjJASHCSwfhIR2aXYaqbi4mL069cPLVu2xGuvvYbTp69vbW5cufTxxx8jJCQEXbt2BQCsWbMGS5cutTsURUReQCrIXOsIDgaQ1CbG1POyaX+JZKhxZ88Me32I/IdiYWbLli04cuQIjhw5gubNm5u9VnPk6+WXX8bRo0dRr149dOjQAatWrcJ9993n6eYSkVxSIQYwBRkje3Ni3DlnhvNxiPyL16xmcifOmSFyL2MvR1LbJpYvLl0KjB9vdshaWQNjDJrYNwHvf1do9fW6LLG2d28u3ybyHnK/v71qnxki8j2Z+aW46+WvpIOMKFoEGXvVugHgg+8tg0zN1zM2HoTe4PjvYXLu7ey1iUg5DDNE5LTM/FKkdG6GHXMsN8FLSNuEzHzLVYdyqnXbyhK2ajPZ40ilcCLyHayaTURO0RtEpHRuZnH89klLUayKs1rd2lVVuJ25jhKVwonI/dgzQ0SO++UXyd18W6VtQrEqDoB5L4feICK74CzW5xXjzIVKi/c5w5lq3p6uFE5EnsGeGSJyjJXVStYqXWcdLMO0z/PMhneCBOtDScK1W9h63dnK16yqTeSf2DND5ENq9nBkF5z1/ERViSDT+vn1VoMMAHy0u8hinoqtoAIAE+5IqA41Vl53tvK1sap2zWu56tpEpBz2zBD5CEX3RnnrLWDqVIvDtkIMYLsHRup1dY3P07VFY4vPq3bB5zVW1XbHtYlIGdxnhsgHKLo3ioPDSo6aNaQjmkSGcgdgIrKgWG0mInIte3ujWFs15BISQWb9zyfwzGd5dt96Z7sm2Pn7GbvnNYkMxYguN0i+5s7aTKz7ROQ/OGeGyMvJ3Rtl+e5C182h6dbNam0luSt9+t4or+AsVw4RUV0xzBB5Obl7nry8+Tf0WbBNcqM6hwgC8PPP5sceeshUW8m4IshaH5AAIKZBCBqF10d0gxCb52m4coiIXIBhhsjLOdJzUaatQOqKXOcDjbVK1598Ynpqa0UQUN1TdLa8CtO/3I9z5VVWl0ADXDlERK7BMEPk5ez1hNTkdH0hQbAeZCQMTFTj2QHtoAqvL/8eNahVYSzoSEQuwwnARF7O2BOSuiIXAiDZ01FTzZ13ZU1wlQoxX34JjBolebrUEnFVeH1cNRhQXqm3epvoBvUxa+hNUEdx5RARuRZ7Zoh8gHFvFLVK/pCT3bk2ly9b742xEWRSV+RaTEjWXr5iM8gAwLnyK1BHhSGpTQyDDBG5FMMMkY9I6aTBrrT+mDWko6zzbc61EQQgIsLyuI1tp2wtEZeLBRyJyB0YZoh8SHCQgHG3J9hdTWRzlZBUb8yJEzaDDGB/ibgcXIZNRO7AMEPkY5yuL3TokPVhpRukN62rqS69KlyGTUTuxDBD5IOszaGxukpIEICOEsNTDlQzcbZXhcuwicjduJqJyEeldNJgYKLafn0hqd6Yq1eB4GCH7mdcIl6mrbC6d0yjiPoIrReEMl2l6TgLOBKRuzHMEPkwm/WFli8Hxo+3OLz+5xOIKzrv8PJoW0vEjVeZ/7fO8gIWEZELsWo2kZeqU1Vnid6Y8tAI3PTs56bnGid7TKT2mXH2WkREtsj9/maYIfJCdQoMEkEmIW2TxdCQ8SxnduKtU9AiIpJJ7vc3JwATeRlrG9PZrbs0fLhkkEl6JUtyjovTpQ9wfXhrRJcbuAkeESmOYYbIi9jamM5m+BAEYONG82P/+Aeyj5yxuTdMzdIHRES+ihOAibyIvY3pJOsu2SgQeSqvWNZ9uTMvEfkyhhkiLyI3VJy6UCEdYgCzvWPk7g3DnXmJyJdxmInIi8gNFSO6Nrc8uHmzxSZ4xr1hHCl9oDeIyC44i/V5xcguOOvwfBoiIk9jzwyRF7G3MV3o1Ss4/Pq9li9YWZQoZ2+Ymjvzctk1Efki9swQeRFbdZeKFgx1KMgYyS194PQqKiIihXGfGSIvVLuHpGjBUMuTSksBtVr2NW3tDaM3iOizYJvVyccCqsPPrrT+XIZNRB7jE/vMtGrVCoIgmD1effVVs3P279+PO+64A2FhYYiPj8fChQsVai2R56R00mBXWn+sSdFIBxlRdCjIALb3hnFkFRURkbdRfM7Mv/71L0yYMMH0PDIy0vR3nU6HQYMGYcCAAViyZAl+/fVXPPbYY2jUqBEmTpyoRHOJPCY4OAjdpF5wQ2eqQ6uoiIi8jOJhJjIyEmorv2F+8sknqKqqwtKlSxESEoKbbroJeXl5eOONNxhmyL9JLbvW64Eg93Smcgk3EfkyxScAv/rqq4iJiUHXrl2xaNEiXL161fRadnY2+vbti5CQENOxwYMH4/Dhw/jrr7+sXrOyshI6nc7sQeQTvv7a+iZ4bgoygHNLuImIvIWiYeYf//gHPvvsM2zfvh1PPvkkXnnlFcyYMcP0ellZGZo2bWr2HuPzsrIyq9edP38+VCqV6REfH++eD0DkSoIA3HOP+bG77nLLsFJttlZRSS3hJiLyJi4PMzNnzrSY1Fv7cejQIQDAtGnT0K9fP9x8882YNGkSXn/9dbz99tuorKysUxteeOEFaLVa0+P48eOu+GhE7mOtNyYry2NNkLuEm4jI27h8zsz06dMxbtw4m+e0bt1a8nivXr1w9epVFBUVoX379lCr1Th58qTZOcbn1ubZAEBoaChCQ0MdaziREmbOBBYssDyu0I4JKZ00GJiotrqEm4jIG7k8zMTGxiI2Ntap9+bl5SEoKAhxcXEAgKSkJPzzn//ElStXUL9+fQDAli1b0L59ezRu3NhlbSZShFRvzOuvA9Omeb4tNRiXcBMR+QrFVjNlZ2fjhx9+QHJyMiIjI5GdnY2pU6dizJgxpqDy0EMPISMjA48//jjS0tKQn5+Pf//733jzzTeVajaRa9iodE1ERI5RLMyEhobis88+w5w5c1BZWYmEhARMnToV02r8VqpSqfDtt99i8uTJ6N69O5o0aYLZs2dzWTb5rjvuAHbtsjzOIENE5DSWMyDyFKnemB9/BHr08HxbiIh8gNzvb8U3zSPye1euADX2SjLx/98jiIg8gmGGyJ2kemMABhkiIhdSfAdgIr8lFWTOnmWQISJyMYYZIlcrKbG+Wima5QCIiFyNw0xErsRhJSIij2PPDJGrWKt0zSBDRORWDDNEdbV9uyKVromIqBr/T0tUF4IA9O9vfmzUKPbGEBF5EOfMEDmLJQmIiLwCe2aIHDV/fp2DjN4gIrvgLNbnFSO74Cz0BoYgIiJnsWeGyAa9QcTewnM4daECcZFhSGrbxPKkxYuBSZNkXzMzvxQZGw+iVFthOqZRhSF9WCJSOmlc0WwiooDCMENkRe3QUbRgqOVJDg4rZeaXInVFLmq/q0xbgdQVuVg8phsDDRGRgxhmiCTUDB2rPklDrxMHLE9yMMjoDSIyNh60CDIAIAIQAGRsPIiBiWoEB1nZr4aIiCwwzBBdYxxSKtNexsubf4MI6d6YEY++gVMdbsYug+hQ6NhbeM5saKk2EUCptgJ7C88hqU2ME5+AiCgwMcxQwNMbRLyz7QiW7S7E+ctXAADBBj2KFo2wOLdV2qbqvzgROk5dsB5knDmPiIiqMcxQQMvML8XMNb/i/KUrpmM733sCLc+XWZxrCjLXOBo64iLDXHoeERFVY5ihgJWZX4pJK3LNjkkNK3V+dhUuhDawOO5o6OiZEA2NKgxl2grJeTMCALUqDD0TWIySiMgR3GeGApJxMq5RVMVFySDTKm2TRZARUL2U2tHQERwkIH1Youkata8JAOnDEjn5l4jIQQwzFJBqTsbd9v5E7P/3g2av52lutBhWAuoeOlI6abB4TDeoVea9OmpVGJdlExE5icNMFJCM812kemMSZmyAKEjnfLULNrdL6aTBwES12WZ8PROi2SNDROQkhhkKSC3OllgdVqotukF9zBp6E9RRrgsdwUECl18TEbkIwwwFHkFA11qHnr/7GXxx80DLUwG8cm9nDv8QEXkxhhkKLBIFIhPSNkmuLmocUR/z/8YgQ0Tk7TgBmALD1q2SQSbz1xKLybiNwutj6oAb8cOLA6AKD2FlayIiL8eeGfJ/EiEGu3YBt9+OFEByMu6Wg2W4c9F2VrYmIvIBgig6WC3PB+l0OqhUKmi1WkRFRSndHPIkqSBj55+8tcrWxitxCTURkWfI/f7mMBP5p3fecSrI2KtsDVRXtuaQExGR9+AwE/kfqRBz9CjQooXdt7KyNRGR72GYIf+h1wP1JP5JOzCSysrWRES+h8NM5B8ef9wyyPTo4VCQAVjZmojIF7Fnhnyf1LDSxYtAA8tK1/awsjURke9RrGdmx44dEARB8vHjjz8CAIqKiiRfz8nJUarZ5E10OuuTfJ0IMgArWxMR+SLFwkzv3r1RWlpq9njiiSeQkJCAHj16mJ2blZVldl737t0VajV5jfbtAZXK/NjTTzs8rCSFla2JiHyLYsNMISEhUKvVpudXrlzB+vXr8fTTT0Oo9dt2TEyM2bkU4KR6Y/R6IMh12ZyVrYmIfIfXzJnZsGEDzp49i/Hjx1u8Nnz4cFRUVKBdu3aYMWMGhg8fbvNalZWVqKysND3X6XQuby8p4MgR4MYbLY+7ad9HVrYmIvINXrOa6aOPPsLgwYPRvHlz07GGDRvi9ddfxxdffIHNmzejT58+GDlyJDZs2GDzWvPnz4dKpTI94uPj3d18cjdBsAwyH33ktiBDRES+w+XlDGbOnIkFCxbYPOe3335Dhw4dTM9PnDiBli1b4vPPP8eoUaNsvvfRRx9FYWEhvv/+e6vnSPXMxMfHs5yBD9IbRAQHS2RuhhgiIr8nt5yBy4eZpk+fjnHjxtk8p3Xr1mbPly1bhpiYGLvDRwDQq1cvbNmyxeY5oaGhCA0NtXst8m57PvsavUffY3E889cSpCjQHiIi8k4uDzOxsbGIjY2Vfb4oili2bBkeffRR1K9f3+75eXl50Gi4msTvCQJ61zp075jXkHdDB2BFLlcVERGRieITgLdt24bCwkI88cQTFq99/PHHCAkJQdeuXQEAa9aswdKlS/Hhhx96upnkSRKrlVqlbbr+MqqLPQ5MVHN1ERERKR9mPvroI/Tu3dtsDk1NL7/8Mo4ePYp69eqhQ4cOWLVqFe677z4Pt5I84osvgL//3ezQn42bof/E982OsdgjERHV5PIJwN5I7gQiUpBEb8ytk/8PpxtaLxvw7we7YESXG9zZKiIiUpBiE4CJHGIwAMHBFodrDitZw2KPREQEeNE+MxSAXn7ZMsiMGQO93gCNKsyiNpKRAEDDYo9ERHQNe2ZIGVIlCS5dAsLDEYzqYo6pK3IhAGbVq1nskYiIamPPDHlWebn1Stfh4aanLPZIRERysWeGXE5vEKULNN53H7B6tfnJCxYAM2ZIXofFHomISA6GGXKpzPxSZGw8iFJthemYRhWG7BcHWJ4so9I1iz0SEZE9DDPklJq9L00ahgIisPXQSSzdXWR2nlp3BtkLxllewP93BCAiIg9hmCGHSfW+SNnz33FoduGM2TH9mrUIvnekG1tHRESBhmGGHJKZX4rUFbmw169StGCoxbFWaZvw6c23Ick9TSMiogDF1Uwkm94gImPjQZtBpvXZE1aDDACcumC7N4eIiMhR7Jkh2fYWnrM5tLTt/Ylo/VeJ2bFBj72D32NbmZ5z114iInI1hhmSzVaviq3eGKB6szs1d+0lIiI34DATySbVq9L2zDGLILM2sZ9FkAG4ay8REbkHe2ZItp4J0dCowlCmrYAI4IPV/8LAI3vNzunyj5U4H25e2VStCkP6sETu2ktERG7BMEOyBQcJ1TWT/rcPXy3/BxJPFZq9XrvS9eO3t8KARDV37SUiIrdimCGHpERWoXDhMLNjT458Ed+07216rmFPDBEReRDDDMn3n/8AzzxjelrVVI2vN/+AR1UReFQEzpRXsn4SERF5HMMM2afXAxoNcPr09WPvvIOQyZMxQrlWERERAWCYIXsOHAA6dTI/dvQo0KKFMu0hIiKqhUuzybpZs8yDzK23AgYDgwwREXkV9syQpcpKIKzWnjKffQY88IAy7SEiIrKBYYbMZWcDvXubHzt9GmjSRJn2EBER2cFhJrpuwgTzIDNiBCCKDDJEROTV2DNDwIULQJT5rr3IzAQGD1amPURERA5gz0yg+/pryyBz4QKDDBER+QyGmUA2bBhwzz3Xn0+aVD2s1LChcm0iIiJyEIeZAtHp00BcnPmxnBygVy9l2kNERFQH7JkJNCtXWgaZigoGGSIi8lkMM4FCFIGuXYGHH75+LD29+nhoqHLtIiIiqiMOMwWCo0eBVq3Mjx04ACQmKtIcIiIiV2LPjL/7z3/Mg0yzZsDVqwwyRETkN9wWZubNm4fevXsjIiICjRo1kjzn2LFjGDJkCCIiIhAXF4fnn38eV69eNTtnx44d6NatG0JDQ9G2bVssX77cXU32L3p99dyYZ565fuydd4DiYiA4WLl2ERERuZjbwkxVVRXuv/9+pKamSr6u1+sxZMgQVFVVYc+ePfj444+xfPlyzJ4923ROYWEhhgwZguTkZOTl5eHZZ5/FE088gW+++cZdzfYPBw4A9epVr1oyOnoUmDxZuTYRERG5iSCKoujOGyxfvhzPPvsszp8/b3b866+/xtChQ1FSUoKmTZsCAJYsWYK0tDScPn0aISEhSEtLw+bNm5Gfn29634MPPojz588jMzNTdht0Oh1UKhW0Wi2iam8Q529mzQLmzr3+vEcPYO9eQBCUaxMREZET5H5/KzZnJjs7G507dzYFGQAYPHgwdDodDhw4YDpnwIABZu8bPHgwsrOzbV67srISOp3O7OH3KiurA0vNIPPpp8CPPzLIEBGRX1MszJSVlZkFGQCm52VlZTbP0el0uHz5stVrz58/HyqVyvSIj493ceu9TE4OEBZmfuz0aeDBB5VpDxERkQc5FGZmzpwJQRBsPg4dOuSutsr2wgsvQKvVmh7Hjx9XuknuM3EikJR0/fnw4ax0TUREAcWhfWamT5+OcePG2TyndevWsq6lVquxd+9es2MnT540vWb803is5jlRUVEIDw+3eu3Q0FCE+vtGcKx0TUREBMDBMBMbG4vY2FiX3DgpKQnz5s3DqVOnEHdte/0tW7YgKioKidf2QElKSsJXX31l9r4tW7YgqWZPRCDKzATuvtv82IULLBBJREQByW1zZo4dO4a8vDwcO3YMer0eeXl5yMvLw8WLFwEAgwYNQmJiIh555BH88ssv+Oabb/DSSy9h8uTJpl6VSZMm4c8//8SMGTNw6NAh/Pe//8Xnn3+OqVOnuqvZ3m/YMPMg8+STrHRNREQBzW1Ls8eNG4ePP/7Y4vj27dvRr18/AMDRo0eRmpqKHTt2oEGDBhg7dixeffVV1Kt3vcNox44dmDp1Kg4ePIjmzZtj1qxZdoe6avOLpdmsdE1ERAFG7ve32/eZ8QY+H2ZWrjQvEAlUV7r293lBREQU0Lx+nxmSQRSBbt1Y6ZqIiMgGVs32Vqx0TUREJAt7ZrzR22+bBxmNhpWuiYiIrGDPjDfR64FmzYBTp64fe/ttYMoU5dpERETk5RhmvMWBA0CnTubHjh4FWrRQpj1EREQ+gsNM3mDWLPMg06MHYDAwyBAREcnAnhklVVZaFohcuRIYPVqZ9hAREfkghhml5OSYF4gEqufKuKhcBBERUaDgMJMSnnxSutI1gwwREZHD2DPjSax0TURE5HLsmfGUzEzLIHPhAoMMERFRHTHMeAIrXRMREbkNh5ncSarSdXY2cNttyrSHiIjID7Fnxl0+/dQyyFRUMMgQERG5GMOMqxkrXT/00PVjs2ez0jUREZGbcJjJlVjpmoiIyOPYM+MqtStdq9WsdE1EROQB7JmpK1a6JiIiUhTDjJP0BhH7t/6AroNqlSRgpWsiIiKP4jCTEzLzS9FnwTaceeoZ07HfbmiHzP3FDDJEREQexp4ZB2XmlyJ1RS5EAGtu6o8Op49iUd9HsTHxTuCTn7F4jICUThqlm0lERBQwBFEURaUb4W46nQ4qlQparRZRtUsKOEBvENFnwTaUaiskXxcAqFVh2JXWH8FBgtP3ISIiIvnf3xxmcsDewnNWgwwAiABKtRXYW3jOc40iIiIKcAwzDjh1wXqQceY8IiIiqjuGGQfERYa59DwiIiKqO4YZB/RMiIZGFQZrs2EEABpVGHomRHuyWURERAGNYcYBwUEC0odV7+hbO9AYn6cPS+TkXyIiIg9imHFQSicNFo/pBrXKfChJrQrD4jHduCybiIjIw7jPjBNSOmkwMFGNvYXncOpCBeIiq4eW2CNDRETkeQwzTgoOEpDUJkbpZhAREQU8DjMRERGRT3NbmJk3bx569+6NiIgINGrUyOL1X375BaNHj0Z8fDzCw8PRsWNH/Pvf/zY7Z8eOHRAEweJRVlbmrmYTERGRj3HbMFNVVRXuv/9+JCUl4aOPPrJ4fd++fYiLi8OKFSsQHx+PPXv2YOLEiQgODsaUKVPMzj18+LDZNsZxcXHuajYRERH5GLeFmYyMDADA8uXLJV9/7LHHzJ63bt0a2dnZWLNmjUWYiYuLk+zdISIiIvKqOTNarRbR0ZYbznXp0gUajQYDBw7E7t277V6nsrISOp3O7EFERET+yWvCzJ49e7Bq1SpMnDjRdEyj0WDJkiVYvXo1Vq9ejfj4ePTr1w+5ubk2rzV//nyoVCrTIz4+3t3NJyIiIoU4FGZmzpwpOSG35uPQoUMONyI/Px8jRoxAeno6Bg0aZDrevn17PPnkk+jevTt69+6NpUuXonfv3njzzTdtXu+FF16AVqs1PY4fP+5wm4iIiMg3ODRnZvr06Rg3bpzNc1q3bu1QAw4ePIi77roLEydOxEsvvWT3/J49e2LXrl02zwkNDUVoaKhD7SAiIiLf5FCYiY2NRWxsrMtufuDAAfTv3x9jx47FvHnzZL0nLy8PGg1LBhAREVE1t61mOnbsGM6dO4djx45Br9cjLy8PANC2bVs0bNgQ+fn56N+/PwYPHoxp06aZ9o4JDg42Baa33noLCQkJuOmmm1BRUYEPP/wQ27Ztw7fffutQW0RRBABOBCYiIvIhxu9t4/e4VaKbjB07VgRg8di+fbsoiqKYnp4u+XrLli1N11iwYIHYpk0bMSwsTIyOjhb79esnbtu2zeG2FBQUSN6LDz744IMPPvjw/sfx48dtfs8Lomgv7vi+8+fPo3Hjxjh27BhUKpXSzfFrOp0O8fHxOH78uNlGh+R6/Fl7Dn/WnsWft+d4+89aFEVcuHABzZo1Q1CQ9TVLAVFo0vgDUKlUXvkfyx9FRUXxZ+0h/Fl7Dn/WnsWft+d4889aTieE1+wzQ0REROQMhhkiIiLyaQERZkJDQ5Gens69ZzyAP2vP4c/ac/iz9iz+vD3HX37WATEBmIiIiPxXQPTMEBERkf9imCEiIiKfxjBDREREPo1hhoiIiHxawIWZ4cOHo0WLFggLC4NGo8EjjzyCkpISpZvld4qKivD4448jISEB4eHhaNOmDdLT01FVVaV00/zSvHnz0Lt3b0RERKBRo0ZKN8fvvPvuu2jVqhXCwsLQq1cv7N27V+km+aXvvvsOw4YNQ7NmzSAIAtatW6d0k/zS/PnzceuttyIyMhJxcXEYOXIkDh8+rHSz6iTgwkxycjI+//xzHD58GKtXr0ZBQQHuu+8+pZvldw4dOgSDwYD33nsPBw4cwJtvvoklS5bgxRdfVLppfqmqqgr3338/UlNTlW6K31m1ahWmTZuG9PR05Obm4pZbbsHgwYNx6tQppZvmd8rLy3HLLbfg3XffVbopfm3nzp2YPHkycnJysGXLFly5cgWDBg1CeXm50k1zWsAvzd6wYQNGjhyJyspK1K9fX+nm+LVFixZh8eLF+PPPP5Vuit9avnw5nn32WZw/f17ppviNXr164dZbb8U777wDADAYDIiPj8fTTz+NmTNnKtw6/yUIAtauXYuRI0cq3RS/d/r0acTFxWHnzp3o27ev0s1xSsD1zNR07tw5fPLJJ+jduzeDjAdotVpER0cr3Qwi2aqqqrBv3z4MGDDAdCwoKAgDBgxAdna2gi0jch2tVgsAPv3/54AMM2lpaWjQoAFiYmJw7NgxrF+/Xukm+b0jR47g7bffxpNPPql0U4hkO3PmDPR6PZo2bWp2vGnTpigrK1OoVUSuYzAY8Oyzz+L2229Hp06dlG6O0/wizMycOROCINh8HDp0yHT+888/j59//hnffvstgoOD8eijjyLAR9tkc/RnDQDFxcVISUnB/fffjwkTJijUct/jzM+aiMgRkydPRn5+Pj777DOlm1In9ZRugCtMnz4d48aNs3lO69atTX9v0qQJmjRpgnbt2qFjx46Ij49HTk4OkpKS3NxS3+foz7qkpATJycno3bs33n//fTe3zr84+rMm12vSpAmCg4Nx8uRJs+MnT56EWq1WqFVErjFlyhRs2rQJ3333HZo3b650c+rEL8JMbGwsYmNjnXqvwWAAAFRWVrqySX7LkZ91cXExkpOT0b17dyxbtgxBQX7REegxdfl3Ta4REhKC7t27Y+vWraaJqAaDAVu3bsWUKVOUbRyRk0RRxNNPP421a9dix44dSEhIULpJdeYXYUauH374AT/++CP69OmDxo0bo6CgALNmzUKbNm3YK+NixcXF6NevH1q2bInXXnsNp0+fNr3G32hd79ixYzh37hyOHTsGvV6PvLw8AEDbtm3RsGFDZRvn46ZNm4axY8eiR48e6NmzJ9566y2Ul5dj/PjxSjfN71y8eBFHjhwxPS8sLEReXh6io6PRokULBVvmXyZPnoyVK1di/fr1iIyMNM3/UqlUCA8PV7h1ThIDyP79+8Xk5GQxOjpaDA0NFVu1aiVOmjRJPHHihNJN8zvLli0TAUg+yPXGjh0r+bPevn270k3zC2+//bbYokULMSQkROzZs6eYk5OjdJP80vbt2yX/HY8dO1bppvkVa/9vXrZsmdJNc1rA7zNDREREvo2TGIiIiMinMcwQERGRT2OYISIiIp/GMENEREQ+jWGGiIiIfBrDDBEREfk0hhkiIiLyaQwzRERE5NMYZoiIiMinMcwQERGRT2OYISIiIp/GMENEREQ+7f8BVY5wx88mx7QAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Darstellen vom Model inkl. der Koeffizienten\n",
    "plt.scatter(X_train, y_train)\n",
    "plt.plot(X_train, reg_model.predict(X_train), color='red')\n",
    "plt.text(0.05, 0.95, f'k = {reg_model.coef_[0]:.2f}', transform=plt.gca().transAxes, fontsize=12, verticalalignment='top')\n",
    "plt.text(0.05, 0.90, f'd = {reg_model.intercept_:.2f}', transform=plt.gca().transAxes, fontsize=12, verticalalignment='top')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prediction fürs Test-Set\n",
    "y_pred = reg_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.3264453 ],\n",
       "       [ 1.77652567],\n",
       "       [ 1.04075969],\n",
       "       [-0.29132783],\n",
       "       [-0.11666101],\n",
       "       [-0.18028931],\n",
       "       [-0.37273879],\n",
       "       [-1.80730815],\n",
       "       [ 1.05112845],\n",
       "       [ 1.17207851],\n",
       "       [ 1.2823485 ],\n",
       "       [ 0.53716248],\n",
       "       [-1.20774579],\n",
       "       [-0.44354384],\n",
       "       [-1.13050539],\n",
       "       [-0.38760574],\n",
       "       [ 1.22102688],\n",
       "       [ 0.40982897],\n",
       "       [ 0.95886478],\n",
       "       [ 0.55771432]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-58.66528327,  65.48743554,  36.04876271, -17.24928234,\n",
       "       -10.26070235, -12.80652919, -20.50660984, -77.90504757,\n",
       "        36.46362633,  41.30294944,  45.71495289,  15.89937588,\n",
       "       -53.91600662, -23.33958474, -50.82554729, -21.10145005,\n",
       "        43.26141852,  10.80464503,  32.7720721 ,  16.72167377])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Berechnen des MSE\n",
    "mse = mean_squared_error(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(104.20222653187018)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ist dieser Wert gut oder schlecht?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun mag man sich vielleicht fragen, warum verwendet man nicht einfach auch eine lineare Funktion wenn man eine Klassifikationsaufgabe vor sich hat? Sprich warum ist es nicht möglich, einfach zu eine lineare Funktion zu verwenden und im Anschluss zum Beispiel zu sagen\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\hat y = \\begin{cases}\n",
    "        1 & f(x)>0.5\\\\\n",
    "        0 & \\text{else},\n",
    "    \\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "wobei hier $\\hat y$ dann die Klassifikation Vorhersage des Models, sprich von $f(x)$ ist. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Classification_with_Regression](../resources/Linear_Classification.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Was passiert bei den Punkten $f(x)$ mit $x$ in etwa $0.5$?\n",
    "\n",
    "Obwohl die Daten bei $x=0.5$ einen großen Sprung (von Klasse 0 zu Klasse 1) \n",
    "machen, ist bei $f$ kein großer Unterschied zu sehen. Dies bedeutet, bei \n",
    "Werten bei ca. $0.5$ hat das Model fast gleiche Werte $f(x)$, jedoch ändert \n",
    "sich die Klassifizierung drastisch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir könnten nun eine andere Funktion verwenden (zum Beispiel Polynom vom \n",
    "\tGrad 5). Hier sieht das Ergebnis dann so aus:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Classification_with_Polynomial](../resources/Classification_Polynomial.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da auch das nicht ganz ideal ist, zeigen wir nun, wie man das Problem lösen kann. Dies führt nun zur sogenannten *Logistische Regression*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistische Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die logistische Regression verwenden wir die sogenannte *Sigmoid Funktion*.\n",
    "\t\n",
    "Sie ist folgendermaßen definiert.\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\sigma(x) = \\frac{1}{1+e^{-x}}.\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Sigmoid_Funktion](../resources/Sigmoid.png)\n",
    "\n",
    "(von https://de.wikipedia.org/wiki/Sigmoidfunktion)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Welche Eigenschaften fallen uns bei dieser Funktion auf?\n",
    "* Alle Funktionswerte liegen zwischen $0$ und $1$\n",
    "* Die Funktion ist monoton wachsend\n",
    "* Die Funktion ist leicht zu differenzieren und erfüllt $\\sigma'(x) = \\sigma(x)\\cdot (1-\\sigma(x))$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir verwenden nun als Argument dieser Funktion unsere bisherige Funktion (also zum Beispiel $kx+d$) und erhalten dann\n",
    "\\begin{equation*}\n",
    "    g(x) = \\sigma(f(x)) = \\sigma(k\\cdot x + d).\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dies sieht dann so aus\n",
    "\n",
    "![Regression_vs_Linear_Regression](../resources/Logistic_Regression_vs_Linear_Regression.png)\n",
    "\n",
    "(von https://www.saedsayad.com/logistic_regression.htm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "bzw. mit expliziten Datenpunkten:\n",
    "\n",
    "![Logistic_Regression_with_Points](../resources/Logistic_Regression_with_Points.png)\n",
    "\n",
    "(von https://medium.com/analytics-vidhya/the-math-behind-logistic-regression-c2f04ca27bca)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Was ist nun ein großer **Nachteil**? Es is nur mehr die Klassifikation von binären Klassen (binary classification), sprich wenn es nur 2 verschiedene Labels gibt, möglich. Außerdem können wir die optimale Lösung **nicht** mehr analytisch finden (also *keine* **Closed-Form-Solution**). Der Grund dafür ist, dass wir nun nicht mehr den MSE minimieren, sondern wir optimieren jetzt nach einer anderen Funktion, genannt *Log-Likelihood*.\n",
    "\n",
    "Nun müssen wir tatsächlich die Lösung (sprich in diesem Fall unsere Parameter der Funktion, also zum Beispiel $k$ und $d$) numerisch bestimmen. Das können (und werden) wir mit Python ganz einfach machen.\n",
    "\n",
    "Wir haben nun alle Grundlagen für die logistische Regression gelernt und können nun mit Hilfe von Python versuchen, bei verschiedenen Datasets eine Regression und eine Klassifikation zu machen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dummy Dataset für Klassifikation\n",
    "X, y = make_classification(n_samples=1000, n_features=1, n_classes=2, random_state=42, n_informative=1, n_redundant=0, n_clusters_per_class=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [-1.33033222],\n",
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       "       [-0.34125884],\n",
       "       [-1.05041267],\n",
       "       [ 2.0754617 ],\n",
       "       [ 0.84334183],\n",
       "       [-0.427216  ],\n",
       "       [ 1.05886674],\n",
       "       [ 2.11390178],\n",
       "       [ 0.13929414],\n",
       "       [ 0.93151923],\n",
       "       [-1.491106  ],\n",
       "       [-0.28781918],\n",
       "       [ 0.65200827],\n",
       "       [ 0.98543356],\n",
       "       [ 0.93492453],\n",
       "       [ 1.05549156],\n",
       "       [ 1.45138288],\n",
       "       [ 0.79459474],\n",
       "       [ 0.07644283],\n",
       "       [ 0.78879947],\n",
       "       [ 0.70647397],\n",
       "       [-0.66286513],\n",
       "       [ 1.57506685],\n",
       "       [-1.03030686],\n",
       "       [-0.60138301],\n",
       "       [-0.1146026 ],\n",
       "       [-0.92767071],\n",
       "       [ 0.42601707],\n",
       "       [-0.7936618 ]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train und Test set erzeugen\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardisieren der Features (optional; welche anderen Methoden gibt es?)\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Auswahl und Training von Model\n",
    "class_model = LogisticRegression()\n",
    "class_model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prediction vom Testset\n",
    "y_pred = class_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.91\n"
     ]
    }
   ],
   "source": [
    "# Metriken berechnen\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "print(f'Accuracy: {accuracy:.2f}')\n",
    "# print('Classification Report:\\n', classification_report(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisierung der Ergebnisse\n",
    "X_plot = np.linspace(X.min(), X.max(), 300).reshape(-1, 1)\n",
    "X_plot_scaled = scaler.transform(X_plot)\n",
    "y_prob = class_model.predict_proba(X_plot_scaled)[:, 1]\n",
    "\n",
    "\n",
    "plt.scatter(X_test, y_test, color='blue', label='True labels')\n",
    "plt.plot(X_plot, y_prob, color='red', label='Decision Boundary')\n",
    "plt.axhline(0.5, color='black', linestyle='--')\n",
    "plt.xlabel('Feature')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Logistic Regression Decision Boundary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Wichtig:** Auch wenn die **logistische Regression** für Klassifikationsaufgaben verwendet wird, ist es rein technisch **keine Klassifikation**. Wir werden aber trotzdem von Klassifikation sprechen, wenn wir von logistischer Regression sprechen, auch wenn es genau genommen nicht ganz korrekt ist."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aufgabe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Verwende nun die folgenden Datasets und versuche die bestmögliche Performance zu erreichen.\n",
    "* Lade dazu das Dataset mit den bekannten Methoden (Laden mit Hilfe von `pd.read_csv`)\n",
    "* Überlege, wie du bei schlechter Performance diese verbessern kannst. Zum Beipsiel: Normalisieren, Ausreißer entfernen etc.\n",
    "* Müssen wir ggf. Features entfernen?\n",
    "* Gehören ggf. Features mit einem Ordinal-Encoder oder mit einem Onehot-Encoder encodiert?\n",
    "* Verwende für jedes Dataset eigene Code-Zellen und dokumentiere für die verschiedenen Durchläufe die Ergebnisse (zBsp. Accuracy, Confusion Matrix oder den MSE)\n",
    "\n",
    "**Datasets:**\n",
    "* Breast Cancer `breast_cancer.csv` (verwendet von https://archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic)\n",
    "* Diabetes `diabetes.csv` (verwendet von https://www.kaggle.com/uciml/pima-indians-diabetes-database)\n",
    "* Stroke Prediction `stroke.csv` (verwendet von https://www.kaggle.com/datasets/fedesoriano/stroke-prediction-dataset)\n",
    "* Cars `cars.csv` (verwendet von https://www.kaggle.com/datasets/hellbuoy/car-price-prediction)\n",
    "\n",
    "*Hinweis:* Überlege dir stets, welchen Problemtyp du verwendest und verwende dementsprechend das richtige Model! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   car_ID  symboling                   CarName fueltype aspiration doornumber  \\\n",
      "0       1          3        alfa-romero giulia      gas        std        two   \n",
      "1       2          3       alfa-romero stelvio      gas        std        two   \n",
      "2       3          1  alfa-romero Quadrifoglio      gas        std        two   \n",
      "3       4          2               audi 100 ls      gas        std       four   \n",
      "4       5          2                audi 100ls      gas        std       four   \n",
      "\n",
      "       carbody drivewheel enginelocation  wheelbase  ...  enginesize  \\\n",
      "0  convertible        rwd          front       88.6  ...         130   \n",
      "1  convertible        rwd          front       88.6  ...         130   \n",
      "2    hatchback        rwd          front       94.5  ...         152   \n",
      "3        sedan        fwd          front       99.8  ...         109   \n",
      "4        sedan        4wd          front       99.4  ...         136   \n",
      "\n",
      "   fuelsystem  boreratio  stroke compressionratio horsepower  peakrpm citympg  \\\n",
      "0        mpfi       3.47    2.68              9.0        111     5000      21   \n",
      "1        mpfi       3.47    2.68              9.0        111     5000      21   \n",
      "2        mpfi       2.68    3.47              9.0        154     5000      19   \n",
      "3        mpfi       3.19    3.40             10.0        102     5500      24   \n",
      "4        mpfi       3.19    3.40              8.0        115     5500      18   \n",
      "\n",
      "   highwaympg    price  \n",
      "0          27  13495.0  \n",
      "1          27  16500.0  \n",
      "2          26  16500.0  \n",
      "3          30  13950.0  \n",
      "4          22  17450.0  \n",
      "\n",
      "[5 rows x 26 columns]\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import os\n",
    "\n",
    "# Lade das cars dataset\n",
    "cars = pd.read_csv(\"../../_data/cars.csv\") # ggf. etwas anders als unser bisheriges Dataset\n",
    "print(cars.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f628a1fcdc0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars.highwaympg, cars.price)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = cars.drop('price', axis=1)\n",
    "x = x.select_dtypes(include=[np.number])\n",
    "y = cars.price\n",
    "X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.microsoft.datawrangler.viewer.v0+json": {
       "columns": [
        {
         "name": "index",
         "rawType": "int64",
         "type": "integer"
        },
        {
         "name": "car_ID",
         "rawType": "int64",
         "type": "integer"
        },
        {
         "name": "symboling",
         "rawType": "int64",
         "type": "integer"
        },
        {
         "name": "wheelbase",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "carlength",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "carwidth",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "carheight",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "curbweight",
         "rawType": "int64",
         "type": "integer"
        },
        {
         "name": "enginesize",
         "rawType": "int64",
         "type": "integer"
        },
        {
         "name": "boreratio",
         "rawType": "float64",
         "type": "float"
        },
        {
         "name": "stroke",
         "rawType": "float64",
         "type": "float"
        },
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       "      <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>106</th>\n",
       "      <td>107</td>\n",
       "      <td>1</td>\n",
       "      <td>99.2</td>\n",
       "      <td>178.5</td>\n",
       "      <td>67.9</td>\n",
       "      <td>49.7</td>\n",
       "      <td>3139</td>\n",
       "      <td>181</td>\n",
       "      <td>3.43</td>\n",
       "      <td>3.27</td>\n",
       "      <td>9.0</td>\n",
       "      <td>160</td>\n",
       "      <td>5200</td>\n",
       "      <td>19</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>103.5</td>\n",
       "      <td>189.0</td>\n",
       "      <td>66.9</td>\n",
       "      <td>55.7</td>\n",
       "      <td>3055</td>\n",
       "      <td>164</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.19</td>\n",
       "      <td>9.0</td>\n",
       "      <td>121</td>\n",
       "      <td>4250</td>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>93</td>\n",
       "      <td>1</td>\n",
       "      <td>94.5</td>\n",
       "      <td>165.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>54.5</td>\n",
       "      <td>1938</td>\n",
       "      <td>97</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.29</td>\n",
       "      <td>9.4</td>\n",
       "      <td>69</td>\n",
       "      <td>5200</td>\n",
       "      <td>31</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>180</td>\n",
       "      <td>3</td>\n",
       "      <td>102.9</td>\n",
       "      <td>183.5</td>\n",
       "      <td>67.7</td>\n",
       "      <td>52.0</td>\n",
       "      <td>3016</td>\n",
       "      <td>171</td>\n",
       "      <td>3.27</td>\n",
       "      <td>3.35</td>\n",
       "      <td>9.3</td>\n",
       "      <td>161</td>\n",
       "      <td>5200</td>\n",
       "      <td>19</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>103</td>\n",
       "      <td>0</td>\n",
       "      <td>100.4</td>\n",
       "      <td>184.6</td>\n",
       "      <td>66.5</td>\n",
       "      <td>56.1</td>\n",
       "      <td>3296</td>\n",
       "      <td>181</td>\n",
       "      <td>3.43</td>\n",
       "      <td>3.27</td>\n",
       "      <td>9.0</td>\n",
       "      <td>152</td>\n",
       "      <td>5200</td>\n",
       "      <td>17</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>164 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     car_ID  symboling  wheelbase  carlength  carwidth  carheight  curbweight  \\\n",
       "66       67          0      104.9      175.0      66.1       54.4        2700   \n",
       "111     112          0      107.9      186.7      68.4       56.7        3075   \n",
       "153     154          0       95.7      169.7      63.6       59.1        2280   \n",
       "96       97          1       94.5      165.3      63.8       54.5        1971   \n",
       "38       39          0       96.5      167.5      65.2       53.3        2289   \n",
       "..      ...        ...        ...        ...       ...        ...         ...   \n",
       "106     107          1       99.2      178.5      67.9       49.7        3139   \n",
       "14       15          1      103.5      189.0      66.9       55.7        3055   \n",
       "92       93          1       94.5      165.3      63.8       54.5        1938   \n",
       "179     180          3      102.9      183.5      67.7       52.0        3016   \n",
       "102     103          0      100.4      184.6      66.5       56.1        3296   \n",
       "\n",
       "     enginesize  boreratio  stroke  compressionratio  horsepower  peakrpm  \\\n",
       "66          134       3.43    3.64              22.0          72     4200   \n",
       "111         120       3.46    2.19               8.4          95     5000   \n",
       "153          92       3.05    3.03               9.0          62     4800   \n",
       "96           97       3.15    3.29               9.4          69     5200   \n",
       "38          110       3.15    3.58               9.0          86     5800   \n",
       "..          ...        ...     ...               ...         ...      ...   \n",
       "106         181       3.43    3.27               9.0         160     5200   \n",
       "14          164       3.31    3.19               9.0         121     4250   \n",
       "92           97       3.15    3.29               9.4          69     5200   \n",
       "179         171       3.27    3.35               9.3         161     5200   \n",
       "102         181       3.43    3.27               9.0         152     5200   \n",
       "\n",
       "     citympg  highwaympg  \n",
       "66        31          39  \n",
       "111       19          24  \n",
       "153       31          37  \n",
       "96        31          37  \n",
       "38        27          33  \n",
       "..       ...         ...  \n",
       "106       19          25  \n",
       "14        20          25  \n",
       "92        31          37  \n",
       "179       19          24  \n",
       "102       17          22  \n",
       "\n",
       "[164 rows x 15 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
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         "3.78",
         "3.15",
         "9.5",
         "114",
         "5400",
         "23",
         "28"
        ],
        [
         "117",
         "118",
         "0",
         "108.0",
         "186.7",
         "68.3",
         "56.0",
         "3130",
         "134",
         "3.61",
         "3.21",
         "7.0",
         "142",
         "5600",
         "18",
         "24"
        ],
        [
         "2",
         "3",
         "1",
         "94.5",
         "171.2",
         "65.5",
         "52.4",
         "2823",
         "152",
         "2.68",
         "3.47",
         "9.0",
         "154",
         "5000",
         "19",
         "26"
        ],
        [
         "77",
         "78",
         "2",
         "93.7",
         "157.3",
         "64.4",
         "50.8",
         "1944",
         "92",
         "2.97",
         "3.23",
         "9.4",
         "68",
         "5500",
         "31",
         "38"
        ],
        [
         "46",
         "47",
         "2",
         "96.0",
         "172.6",
         "65.2",
         "51.4",
         "2734",
         "119",
         "3.43",
         "3.23",
         "9.2",
         "90",
         "5000",
         "24",
         "29"
        ],
        [
         "122",
         "123",
         "1",
         "93.7",
         "167.3",
         "63.8",
         "50.8",
         "2191",
         "98",
         "2.97",
         "3.23",
         "9.4",
         "68",
         "5500",
         "31",
         "38"
        ],
        [
         "127",
         "128",
         "3",
         "89.5",
         "168.9",
         "65.0",
         "51.6",
         "2756",
         "194",
         "3.74",
         "2.9",
         "9.5",
         "207",
         "5900",
         "17",
         "25"
        ],
        [
         "85",
         "86",
         "1",
         "96.3",
         "172.4",
         "65.4",
         "51.6",
         "2365",
         "122",
         "3.35",
         "3.46",
         "8.5",
         "88",
         "5000",
         "25",
         "32"
        ],
        [
         "138",
         "139",
         "2",
         "93.7",
         "156.9",
         "63.4",
         "53.7",
         "2050",
         "97",
         "3.62",
         "2.36",
         "9.0",
         "69",
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         "31",
         "36"
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       "shape": {
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        "rows": 164
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      "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",
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       "        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>car_ID</th>\n",
       "      <th>symboling</th>\n",
       "      <th>wheelbase</th>\n",
       "      <th>carlength</th>\n",
       "      <th>carwidth</th>\n",
       "      <th>carheight</th>\n",
       "      <th>curbweight</th>\n",
       "      <th>enginesize</th>\n",
       "      <th>boreratio</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compressionratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peakrpm</th>\n",
       "      <th>citympg</th>\n",
       "      <th>highwaympg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "      <td>104.9</td>\n",
       "      <td>175.0</td>\n",
       "      <td>66.1</td>\n",
       "      <td>54.4</td>\n",
       "      <td>2700</td>\n",
       "      <td>134</td>\n",
       "      <td>3.43</td>\n",
       "      <td>3.64</td>\n",
       "      <td>22.0</td>\n",
       "      <td>72</td>\n",
       "      <td>4200</td>\n",
       "      <td>31</td>\n",
       "      <td>39</td>\n",
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       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>112</td>\n",
       "      <td>0</td>\n",
       "      <td>107.9</td>\n",
       "      <td>186.7</td>\n",
       "      <td>68.4</td>\n",
       "      <td>56.7</td>\n",
       "      <td>3075</td>\n",
       "      <td>120</td>\n",
       "      <td>3.46</td>\n",
       "      <td>2.19</td>\n",
       "      <td>8.4</td>\n",
       "      <td>95</td>\n",
       "      <td>5000</td>\n",
       "      <td>19</td>\n",
       "      <td>24</td>\n",
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       "      <th>153</th>\n",
       "      <td>154</td>\n",
       "      <td>0</td>\n",
       "      <td>95.7</td>\n",
       "      <td>169.7</td>\n",
       "      <td>63.6</td>\n",
       "      <td>59.1</td>\n",
       "      <td>2280</td>\n",
       "      <td>92</td>\n",
       "      <td>3.05</td>\n",
       "      <td>3.03</td>\n",
       "      <td>9.0</td>\n",
       "      <td>62</td>\n",
       "      <td>4800</td>\n",
       "      <td>31</td>\n",
       "      <td>37</td>\n",
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       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>97</td>\n",
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       "      <td>94.5</td>\n",
       "      <td>165.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>54.5</td>\n",
       "      <td>1971</td>\n",
       "      <td>97</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.29</td>\n",
       "      <td>9.4</td>\n",
       "      <td>69</td>\n",
       "      <td>5200</td>\n",
       "      <td>31</td>\n",
       "      <td>37</td>\n",
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       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>96.5</td>\n",
       "      <td>167.5</td>\n",
       "      <td>65.2</td>\n",
       "      <td>53.3</td>\n",
       "      <td>2289</td>\n",
       "      <td>110</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.58</td>\n",
       "      <td>9.0</td>\n",
       "      <td>86</td>\n",
       "      <td>5800</td>\n",
       "      <td>27</td>\n",
       "      <td>33</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>107</td>\n",
       "      <td>1</td>\n",
       "      <td>99.2</td>\n",
       "      <td>178.5</td>\n",
       "      <td>67.9</td>\n",
       "      <td>49.7</td>\n",
       "      <td>3139</td>\n",
       "      <td>181</td>\n",
       "      <td>3.43</td>\n",
       "      <td>3.27</td>\n",
       "      <td>9.0</td>\n",
       "      <td>160</td>\n",
       "      <td>5200</td>\n",
       "      <td>19</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>103.5</td>\n",
       "      <td>189.0</td>\n",
       "      <td>66.9</td>\n",
       "      <td>55.7</td>\n",
       "      <td>3055</td>\n",
       "      <td>164</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.19</td>\n",
       "      <td>9.0</td>\n",
       "      <td>121</td>\n",
       "      <td>4250</td>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
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       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>93</td>\n",
       "      <td>1</td>\n",
       "      <td>94.5</td>\n",
       "      <td>165.3</td>\n",
       "      <td>63.8</td>\n",
       "      <td>54.5</td>\n",
       "      <td>1938</td>\n",
       "      <td>97</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.29</td>\n",
       "      <td>9.4</td>\n",
       "      <td>69</td>\n",
       "      <td>5200</td>\n",
       "      <td>31</td>\n",
       "      <td>37</td>\n",
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       "      <th>179</th>\n",
       "      <td>180</td>\n",
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       "      <td>102.9</td>\n",
       "      <td>183.5</td>\n",
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       "      <td>52.0</td>\n",
       "      <td>3016</td>\n",
       "      <td>171</td>\n",
       "      <td>3.27</td>\n",
       "      <td>3.35</td>\n",
       "      <td>9.3</td>\n",
       "      <td>161</td>\n",
       "      <td>5200</td>\n",
       "      <td>19</td>\n",
       "      <td>24</td>\n",
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       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>103</td>\n",
       "      <td>0</td>\n",
       "      <td>100.4</td>\n",
       "      <td>184.6</td>\n",
       "      <td>66.5</td>\n",
       "      <td>56.1</td>\n",
       "      <td>3296</td>\n",
       "      <td>181</td>\n",
       "      <td>3.43</td>\n",
       "      <td>3.27</td>\n",
       "      <td>9.0</td>\n",
       "      <td>152</td>\n",
       "      <td>5200</td>\n",
       "      <td>17</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>164 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     car_ID  symboling  wheelbase  carlength  carwidth  carheight  curbweight  \\\n",
       "66       67          0      104.9      175.0      66.1       54.4        2700   \n",
       "111     112          0      107.9      186.7      68.4       56.7        3075   \n",
       "153     154          0       95.7      169.7      63.6       59.1        2280   \n",
       "96       97          1       94.5      165.3      63.8       54.5        1971   \n",
       "38       39          0       96.5      167.5      65.2       53.3        2289   \n",
       "..      ...        ...        ...        ...       ...        ...         ...   \n",
       "106     107          1       99.2      178.5      67.9       49.7        3139   \n",
       "14       15          1      103.5      189.0      66.9       55.7        3055   \n",
       "92       93          1       94.5      165.3      63.8       54.5        1938   \n",
       "179     180          3      102.9      183.5      67.7       52.0        3016   \n",
       "102     103          0      100.4      184.6      66.5       56.1        3296   \n",
       "\n",
       "     enginesize  boreratio  stroke  compressionratio  horsepower  peakrpm  \\\n",
       "66          134       3.43    3.64              22.0          72     4200   \n",
       "111         120       3.46    2.19               8.4          95     5000   \n",
       "153          92       3.05    3.03               9.0          62     4800   \n",
       "96           97       3.15    3.29               9.4          69     5200   \n",
       "38          110       3.15    3.58               9.0          86     5800   \n",
       "..          ...        ...     ...               ...         ...      ...   \n",
       "106         181       3.43    3.27               9.0         160     5200   \n",
       "14          164       3.31    3.19               9.0         121     4250   \n",
       "92           97       3.15    3.29               9.4          69     5200   \n",
       "179         171       3.27    3.35               9.3         161     5200   \n",
       "102         181       3.43    3.27               9.0         152     5200   \n",
       "\n",
       "     citympg  highwaympg  \n",
       "66        31          39  \n",
       "111       19          24  \n",
       "153       31          37  \n",
       "96        31          37  \n",
       "38        27          33  \n",
       "..       ...         ...  \n",
       "106       19          25  \n",
       "14        20          25  \n",
       "92        31          37  \n",
       "179       19          24  \n",
       "102       17          22  \n",
       "\n",
       "[164 rows x 15 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Trainieren vom Model\n",
    "reg_model = LinearRegression()\n",
    "\n",
    "reg_model = reg_model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Darstellen vom Model inkl. der Koeffizienten\n",
    "plt.scatter(X_train.horsepower, y_train)\n",
    "plt.plot(X_train.horsepower, reg_model.predict(X_train), color='red')\n",
    "plt.text(0.05, 0.95, f'k = {reg_model.coef_[0]:.2f}', transform=plt.gca().transAxes, fontsize=12, verticalalignment='top')\n",
    "plt.text(0.05, 0.90, f'd = {reg_model.intercept_:.2f}', transform=plt.gca().transAxes, fontsize=12, verticalalignment='top')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "y_pred = reg_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28136.61662501, 17897.05420754, 10501.64869541, 14894.10445051,\n",
       "       25867.1892059 ,  6173.84364331,  8980.28750149,  5919.21217674,\n",
       "       11392.64574211,  9460.45070261, 14560.47727625,  5262.80065897,\n",
       "       17528.77959034,  7491.46641038, 40299.85379014,  5336.56626822,\n",
       "       -1096.23360087, 15347.30470178, 10145.97735703, 11163.54831384,\n",
       "       11083.28073461, 22416.79275323,  6592.9098689 ,   938.10218382,\n",
       "        6895.75103695, 27936.87659594, 12978.79601747, 16477.60756576,\n",
       "        5956.53671362, 15851.60074806, 25165.44825207,  5672.24625495,\n",
       "        6140.96330188, 23125.61626048,  8083.42458411, 24748.61143859,\n",
       "       10938.04831201,  9709.93935657,  5425.3770443 , 15389.31688372,\n",
       "        9064.98801667])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse = mean_squared_error(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(11710105.07880735)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dsai",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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