{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dff037b7-7d71-49c2-8a47-48017c073f81",
   "metadata": {},
   "source": [
    "$R^2$ für ein polynomielles Modell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "8b1ff6ff-f80e-4cc3-b266-0ad417911d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "# plotting settings\n",
    "pd.plotting.register_matplotlib_converters()\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "from tqdm.notebook import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f698283d-7346-4618-9b87-60a3de061a98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Suburb', 'Address', 'Rooms', 'Type', 'Price', 'Method', 'SellerG',\n",
       "       'Date', 'Distance', 'Postcode', 'Bedroom2', 'Bathroom', 'Car',\n",
       "       'Landsize', 'BuildingArea', 'YearBuilt', 'CouncilArea', 'Lattitude',\n",
       "       'Longtitude', 'Regionname', 'Propertycount'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "melbourne_file_path = 'data/melb_data.csv'\n",
    "melbourne_data = pd.read_csv(melbourne_file_path)\n",
    "melbourne_data = melbourne_data.dropna(axis=0)  # entfernen von Daten mit fehlenden Werten\n",
    "melbourne_data.columns  # Spaltennamen der Tabelle (potentielle Features)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "dac65c52-f2ce-47b6-ba65-3c6bd915dfe8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/plex/.pyenv/versions/ki/lib/python3.12/site-packages/pandas/core/nanops.py:1016: RuntimeWarning: invalid value encountered in subtract\n",
      "  sqr = _ensure_numeric((avg - values) ** 2)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Rooms</th>\n",
       "      <th>BuildingArea</th>\n",
       "      <th>Lattitude</th>\n",
       "      <th>Price</th>\n",
       "      <th>price_per_area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>79.0</td>\n",
       "      <td>-37.8079</td>\n",
       "      <td>1035000.0</td>\n",
       "      <td>6634.615385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>150.0</td>\n",
       "      <td>-37.8093</td>\n",
       "      <td>1465000.0</td>\n",
       "      <td>10932.835821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>142.0</td>\n",
       "      <td>-37.8072</td>\n",
       "      <td>1600000.0</td>\n",
       "      <td>13333.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>210.0</td>\n",
       "      <td>-37.8024</td>\n",
       "      <td>1876000.0</td>\n",
       "      <td>7657.142857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>107.0</td>\n",
       "      <td>-37.8060</td>\n",
       "      <td>1636000.0</td>\n",
       "      <td>6390.625000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Rooms  BuildingArea  Lattitude      Price  price_per_area\n",
       "1      2          79.0   -37.8079  1035000.0     6634.615385\n",
       "2      3         150.0   -37.8093  1465000.0    10932.835821\n",
       "4      4         142.0   -37.8072  1600000.0    13333.333333\n",
       "6      3         210.0   -37.8024  1876000.0     7657.142857\n",
       "7      2         107.0   -37.8060  1636000.0     6390.625000"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#features = ['BuildingArea', Rooms', 'Bathroom', 'Landsize', 'Lattitude', 'Longtitude', 'YearBuilt', 'Distance']\n",
    "features = ['Rooms', 'BuildingArea', 'Lattitude']\n",
    "data = melbourne_data[features + ['Price']]\n",
    "data = data.assign(price_per_area = melbourne_data['Price'] / melbourne_data[\"Landsize\"])\n",
    "data.describe()\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "afe5a08a-abec-4164-85c4-1d3ac8398a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "def h(x, w):\n",
    "    \"\"\"x und w sind numpy arrays; x kann auch die komplette Feature-Matrix sein\"\"\"\n",
    "    # Diese Form erlaubt es für x eine ganze (Feature-)Matrix zu übergeben. Die Matrix enthält\n",
    "    # zeilenweise je einen Datenpunkt, für den h berechnet werden soll.\n",
    "    # w @ x.T ist dann ein Vektor mit je einem Ergebnis in den Komponenten des Vektors pro Zeile\n",
    "    # der übergebenen (Feature-)Matrix.\n",
    "    return x @ w\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "c2e256a3-3575-45c4-a99c-d41c3c56e1c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition der Kostenfunktion\n",
    "def J(w, X, y):\n",
    "    \"\"\"\n",
    "    w, X, y müssen numpy arrays sein\n",
    "    X: Feature-Matrix aller Trainingsdaten inkl. Spalte mit 1; Dimension: n x (d+1)\n",
    "    y: Vektor aller Targets zu X\n",
    "    \"\"\"\n",
    "    errors = y - h(x=X, w=w)\n",
    "    mse = 1.0/(2.0*len(y)) * ( errors @ errors )\n",
    "    return mse\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b41b9c03-0c1d-4a6b-80e8-d7e8775b69c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def feature_matrix_from_data(data):\n",
    "    # hier erzeugen wir die Matrix mit unseren Input-Daten (Features) inklusive der Spalte mit \"1\"\n",
    "    return np.hstack((np.ones((len(data),1)), data.to_numpy(copy=True)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "2c631e17-eb36-43d0-97b1-59add1c93dd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# hier erzeugen wir die Matrix mit unseren Input-Daten (Features) inklusive der Spalte mit \"1\"\n",
    "#X = np.hstack((np.ones((len(data),1)), data[features].to_numpy(copy=True)))\n",
    "X = feature_matrix_from_data(data[features])\n",
    "# und ausserdem den Vektor der Targets\n",
    "y = data.Price.to_numpy(copy=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "8301eb74-9aae-446c-ad46-924811b99777",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Die 4 Parameter der linearen Regression:\n",
      "[-6.97461781e+07  2.41559504e+05  2.31456611e+03 -1.84562537e+06]\n",
      "Kostenfunktion J(w_ana): 137899453867.5851\n",
      "CPU times: user 495 μs, sys: 39 μs, total: 534 μs\n",
      "Wall time: 553 μs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "w_ana = np.linalg.solve(X.T @ X, X.T @ y)\n",
    "print('Die {} Parameter der linearen Regression:\\n{}'.format(len(w_ana), w_ana))\n",
    "J_ana = J(w=w_ana, X=X, y=y)\n",
    "print('Kostenfunktion J(w_ana): {}'.format(J_ana))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "a89c591c-4ebd-4a3d-958b-915738d7361a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1     6634.615385\n",
      "2    10932.835821\n",
      "4    13333.333333\n",
      "6     7657.142857\n",
      "7     6390.625000\n",
      "Name: price_per_area, dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='BuildingArea', ylabel='Price'>"
      ]
     },
     "execution_count": 91,
     "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": [
    "ax = sns.scatterplot(x=data['BuildingArea'], y=data['Price'])\n",
    "\n",
    "xplot = data['price_per_area']\n",
    "yplot = data['price_per_area'][0:len(xplot)]\n",
    "print(yplot.head())\n",
    "sns.lineplot(x=xplot, y=yplot, ax=ax)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "e4fc1d51-3435-415d-875f-db85dfda39e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     6634.615385\n",
       "2    10932.835821\n",
       "4    13333.333333\n",
       "6     7657.142857\n",
       "7     6390.625000\n",
       "Name: price_per_area, dtype: float64"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['price_per_area'].head()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (ki)",
   "language": "python",
   "name": "myenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}