{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 500px; float: left;\"> \n",
    "        <h1>Ingenieurinformatik – Übung</h1>\n",
    "        Lehrstuhl <b>Computational Civil Engineering</b><br>\n",
    "        Kontakt: <a href = \"mailto: cce-inginf@uni-wuppertal.de\">Email senden</a> | Individuelle Kontakte siehe Webseite des Lehrstuhls<br>\n",
    "        Links: \n",
    "        <a href=\"cce.uni-wuppertal.de/inginf\">Vorlesungsskript</a> | \n",
    "        <a href=\"cce.uni-wuppertal.de/\">Webseite des Lehrstuhls</a>\n",
    "    </div>\n",
    "    <div style=\"float:right;\"> \n",
    "        <img src=\"logo_cce_combined.png\" style=\"width:150px;\"/>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modellierung"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lineare Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lineare Regression zu Fuß\n",
    "\n",
    "Gegeben sind zwei numpy Arrays. Die Daten Zeigen das Verhähltnis zwischen Lernzeit und Note für 10 Studentinnen.\n",
    "\n",
    "`Lernzeit = np.array([2,7,11,17,20,22,30,35,39,41])`\n",
    "\n",
    "`Note = np.array([5,5,4,3.7,3,3.7,2.7,2,2.3,1])`\n",
    "\n",
    "I. Plotten Sie die Daten auf ein Scatter Plot, wobei die Lernzeit auf der X-Achse und der Note auf der Y-Achse aufgetragen werden sollen.\n",
    "\n",
    "II. Eine lineare Regression sucht die Gerade, die den quadratischen Abstand aller Messwerte zu jener Gerade minimiert. Folgend sind die beiden Formeln für die Steigung $m$ und den y-Achsenabschnitt $b$ der gesuchten Gerade. $n$ ist die Anzahl der Datenpunkte.\n",
    "\n",
    "$$\n",
    "m &= \\frac{(n \\cdot \\sum xy) - (\\sum x \\cdot \\sum y)}{(n \\cdot \\sum x^2) - ((\\sum x)^2)}\\\\\n",
    "b &= \\frac{\\sum y - (m \\cdot \\sum x)}{n}\n",
    "$$\n",
    "\n",
    "Berechnen Sie mit den gegebenen Daten und mithilfe der beiden Formeln die Gerade.\n",
    "\n",
    "III. Speichern Sie die berechnete Gerade in einer Funktion und bennenen Sie diese. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-ourput"
    ]
   },
   "outputs": [
    {
     "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Lernzeit = np.array([2,7,11,17,20,22,30,35,39,41])\n",
    "Note = np.array([5,5,4,3.7,3,3.7,2.7,2,2.3,1])\n",
    "\n",
    "plt.scatter(Lernzeit,Note)\n",
    "plt.xlabel('Lernzeit / St')\n",
    "plt.ylabel('Note')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung II"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.09101666264187402\n",
      "5.278773243177978\n"
     ]
    }
   ],
   "source": [
    "#Steigung\n",
    "\n",
    "x_summe = np.sum(Lernzeit)\n",
    "y_summe = np.sum(Note)\n",
    "xy_summe = np.sum(Lernzeit*Note)\n",
    "xx_summe = np.sum(Lernzeit**2)\n",
    "\n",
    "m = ((10*xy_summe)-(x_summe*y_summe))/((10*xx_summe)-(x_summe**2))\n",
    "print(m)\n",
    "\n",
    "#Achsenabschnitt\n",
    "\n",
    "b = (y_summe-m*x_summe)/10\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung III"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# y = m*x + b\n",
    "\n",
    "def zufuss(Stunden):\n",
    "    return -0.091*Stunden + 5.278"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lineare Regression mit `np.polyfit()`\n",
    "\n",
    "Berechnen Sie die Koeffizienten $m$ und $b$ mithilfe `np.polyfit()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.09101666,  5.27877324])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polyline = np.polyfit(Lernzeit,Note,1)\n",
    "polyline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vergleichen der Lösungswege\n",
    "\n",
    "Plotten Sie die Datenpunkte, und beide berechnete Linien mit matplotlib."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [
    {
     "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": [
    "plt.plot(Lernzeit, polyline[0]*Lernzeit + polyline[1], 'r', label='np.polyfit')\n",
    "plt.plot(Lernzeit, zufuss(Lernzeit), '--y', label='Zufuß')\n",
    "plt.scatter(Lernzeit, Note, label='Datenpunkte')\n",
    "plt.xlabel('Lernzeit / St')\n",
    "plt.ylabel('Note')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Schätzung\n",
    "\n",
    "Eine Regression erlaubt es, Erwartungswerte für Punkte zu erhalten, für die man keine Daten hat.\\\n",
    "Was wäre die erwartete Note einer Studentin, die 25 Stunden gelernt hat? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0029999999999997\n"
     ]
    },
    {
     "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": [
    "print(zufuss(25))\n",
    "\n",
    "plt.scatter(25, zufuss(25), c='g', label='Prediction')\n",
    "\n",
    "plt.plot(Lernzeit, polyline[0]*Lernzeit + polyline[1], 'r', label='np.polyfit')\n",
    "plt.plot(Lernzeit, zufuss(Lernzeit), '--y', label='Zufuß')\n",
    "plt.scatter(Lernzeit, Note, label='Datenpunkte')\n",
    "plt.xlabel('Lernzeit / St')\n",
    "plt.ylabel('Note')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}