Regression tests.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "502e9f8a",
   "metadata": {},
   "source": [
    "# Regressziós tesztek"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0136ea95",
   "metadata": {},
   "source": [
    "Az alábbi Notebook a BME-VIK Önálló labor (AUT) tárgyához készült és beosztástervezések igazságosságával foglalkozik.\n",
    "\n",
    "Készítette: Seben Domonkos, 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "476c5b14",
   "metadata": {},
   "source": [
    "**Az alkalmazás célja:** Felépíteni egy keretrendszert, mely képes valamilyen egyszerűen előállítható inputokat (valamilyen kész beosztás) kiértékelni azok igazságossága szerint. Fontos tulajdonsága a problémának, hogy többdimenziós regressziót kell alkalmaznunk.\n",
    "\n",
    "A program az alábbi dimenziókat fogja figyelembe venni:\n",
    "- betöltött szerep (*vizsgáztató, bizottsági tag*)\n",
    "- ráeső hallgatók száma\n",
    "- oktatott tárgyak száma\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05db98f7",
   "metadata": {},
   "source": [
    "### Ismerkedés a sklearn regressziós keretrendszerével\n",
    "\n",
    "Egy [Realpython tutorial](https://realpython.com/linear-regression-in-python/) alapján. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d95775c5",
   "metadata": {},
   "source": [
    "#### Egydimenziós lineáris regresszió:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "53cc48f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52bdfa7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([5, 15, 25, 35, 45, 55]).reshape((-1, 1))\n",
    "y = np.array([5, 20, 14, 32, 22, 38])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "674646b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "77e873a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.33333333, 13.73333333, 19.13333333, 24.53333333, 29.93333333,\n",
       "       35.33333333])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "87a3a3ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.715875613747954"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9fbe161d",
   "metadata": {},
   "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.scatter(x, y)\n",
    "plt.plot(x, y_pred, 'r')\n",
    "plt.ylabel('some numbers')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "915fc321",
   "metadata": {},
   "source": [
    "#### Többdimenziós lineáris regresszió:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1aa0473",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [[0, 1], [5, 1], [15, 2], [25, 5], [35, 11], [45, 15], [55, 34], [60, 35]]\n",
    "y = [4, 5, 20, 14, 32, 22, 38, 43]\n",
    "x, y = np.array(x), np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fc55b96f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:  [[ 0  1]\n",
      " [ 5  1]\n",
      " [15  2]\n",
      " [25  5]\n",
      " [35 11]\n",
      " [45 15]\n",
      " [55 34]\n",
      " [60 35]]\n",
      "y:  [ 4  5 20 14 32 22 38 43]\n"
     ]
    }
   ],
   "source": [
    "print('x: ', x)\n",
    "print('y: ', y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3df11518",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8615939258756775"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression().fit(x, y)\n",
    "r_sq = model.score(x, y)\n",
    "r_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "99ed62ca",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.77760476,  8.012953  , 12.73867497, 17.9744479 , 23.97529728,\n",
       "       29.4660957 , 38.78227633, 41.27265006])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edc4f19d",
   "metadata": {},
   "source": [
    "#### Többdimenziós, polinomiális regresszió"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a189b9bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "fe679a4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [[0, 1], [5, 1], [15, 2], [25, 5], [35, 11], [45, 15], [55, 34], [60, 35]]\n",
    "y = [4, 5, 20, 14, 32, 22, 38, 43]\n",
    "x, y = np.array(x), np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d57535a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.000e+00, 1.000e+00, 0.000e+00, 0.000e+00, 1.000e+00],\n",
       "       [5.000e+00, 1.000e+00, 2.500e+01, 5.000e+00, 1.000e+00],\n",
       "       [1.500e+01, 2.000e+00, 2.250e+02, 3.000e+01, 4.000e+00],\n",
       "       [2.500e+01, 5.000e+00, 6.250e+02, 1.250e+02, 2.500e+01],\n",
       "       [3.500e+01, 1.100e+01, 1.225e+03, 3.850e+02, 1.210e+02],\n",
       "       [4.500e+01, 1.500e+01, 2.025e+03, 6.750e+02, 2.250e+02],\n",
       "       [5.500e+01, 3.400e+01, 3.025e+03, 1.870e+03, 1.156e+03],\n",
       "       [6.000e+01, 3.500e+01, 3.600e+03, 2.100e+03, 1.225e+03]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_ = PolynomialFeatures(degree=2, include_bias=False).fit_transform(x)\n",
    "x_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f120c949",
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x_, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d4ed78b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determinációs együttható:  0.9453701449127822\n"
     ]
    }
   ],
   "source": [
    "r_sq = model.score(x_, y)\n",
    "intercept, coefficients = model.intercept_, model.coef_\n",
    "print('Determinációs együttható: ', r_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "61893b33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.54047408, 11.36340283, 16.07809622, 15.79139   , 29.73858619,\n",
       "       23.50834636, 39.05631386, 41.92339046])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = model.predict(x_)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "444b824a",
   "metadata": {},
   "source": [
    "> A jövőben hasznos lehet egyéb modelleket is kipróbálni. Ld. [Scikit regressziós modellek](https://scikit-learn.org/stable/modules/linear_model.html)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}