4_LineareRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lineare Regression\n",
    "----------\n",
    "Wir verwenden  die {\\it Galton families} - Daten, die von Sir Francis Galton im 19. Jahrhundert gesammelt wurden. Galton war ein sehr vielseitiger Forscher, der wichtige Beiträge zur Statistik geleistet hat, allerdings gilt er auch als einer der Begründer der Eugenik. Die acht Spalten der Daten sind\n",
    "\n",
    "- eine ID für die Familie (204 verschiedene Familien) (*family*);\n",
    "- die Größe des Vaters (in inch)  (*father*);\n",
    "- die Größe der Mutter (in inch)  (*mother*);\n",
    "- die mittlere Größe der Eltern: 0.5(Größe Vater + 1.08 Größe Mutter)  (*midparentHeight*);\n",
    "- Anzahl Kinder in der Familie  (*children*);\n",
    "- Nummer des Kindes in der Familie (geordnet nach Junge und Mädchen, jeweils das größte Kind zuerst)  (*childNum*);\n",
    "- Geschlecht des Kindes  (*gender*);\n",
    "- Größe des Kindes (in inch)  (*childHeight*).\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import os\n",
    "\n",
    "os.chdir('C:\\\\Users\\\\Priwitzer\\\\Documents\\\\StatistikfIng\\\\Python\\\\4_LineareRegression')\n",
    "\n",
    "GaltonData=pd.read_table('GaltonFamilies.csv',delimiter=',')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zeichnen Sie ein Streudiagramm für die beiden Variable *midparentHeight* und *ChildHeight*  und berechnen Sie die Korrelation der beiden Variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'numpy' has no attribute 'corcoeff'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-4-da7731a4d83c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     15\u001b[0m \u001b[1;31m#plt.ylabel('')\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m \u001b[1;31m#Korrelationskoeffizient\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcorcoeff\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: module 'numpy' has no attribute 'corcoeff'"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "plt.plot()\n",
    "plt.title('')\n",
    "plt.xlabel('')\n",
    "plt.ylabel('')\n",
    "#Korrelationskoeffizient\n",
    "np.corcoeff()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bilden Sie ein lineares Modell mit der Variable *midparentHeight*  als unabhängige Variable und *Child Height* als abhängige Variable. Schreiben Sie die Gleichung für das lineare Modell auf. Welchen Wert für *Child Height* sagt das Modell voraus, wenn *midparentHeight* den Wert 70 hat?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "#Package, um statistische Modelle zu bilden\n",
    "\n",
    "#Lineares Modell OLS = ordinary least square\n",
    "model=sm.OLS.from_formula(\" ~ \", data=GaltonData ) #hier die Variablen vor und nach ~ eintragen\n",
    "#~ bedeutet \"in Abhaengigkeit von\"\n",
    "\n",
    "\n",
    "result=model.fit()  #Berechnung der wichtigen Werte für das Modell\n",
    "\n",
    "print(result.params) #Regressionkoeffizienten\n",
    "\n",
    "\n",
    "\n",
    "#Vorhersage für MidParentHeight \n",
    "\n",
    "result.predict(exog=dict(midparentHeight=[ ])) #exog = unabhängige Variable\n",
    "\n",
    "# aus der Beschreibung von statsmodels\n",
    "#If a formula was used, then exog is processed in the same way as the original data. \n",
    "#This transformation needs to have key access to the same variable names, \n",
    "#and can be a pandas DataFrame or a dict like object that contains numpy arrays.\n",
    "\n",
    "#Das bedeutet:\n",
    "# der Name der unabhängigen Variable muss erscheinen\n",
    "# die Zuordnung erfolgt entweder als ein DataFrame oder mit dict\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zeichnen Sie jetzt das Streudiagramm mit Regressionsgerade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot()\n",
    "plt.title('')\n",
    "plt.xlabel('')\n",
    "plt.ylabel('')\n",
    "\n",
    "\n",
    "plt.plot(,'r')\n",
    "plt.legend(['Modell','Daten'],loc='upper left')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotten Sie den Residualplot. Was können Sie daran erkennen?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Residualplot\n",
    "plt.figure()\n",
    "plt.scatter() #Residualplot\n",
    "plt.plot([np.min(),np.max()],[0,0],':r') #Nulllinie\n",
    "plt.xlabel('')\n",
    "plt.ylabel('')\n",
    "plt.title('')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}