Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a6e6f0c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from bs4 import BeautifulSoup\n",
    "import requests\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bf2670f",
   "metadata": {},
   "source": [
    "# Scraping points and goals data from Premier League website"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ce369b51",
   "metadata": {},
   "outputs": [],
   "source": [
    "def scrape_data():\n",
    "    points=[]\n",
    "    goals=[]\n",
    "    year=2022\n",
    "    # Scrapes data from 2022 to 2017\n",
    "    for season in range(5):\n",
    "        \n",
    "        html_text = requests.get(f\"https://www.soccerstats.com/latest.asp?league=england_{year}\").text\n",
    "        soup=BeautifulSoup(html_text,'html.parser')\n",
    "        tables=soup.find_all('table',id=\"btable\")\n",
    "        \n",
    "        # Catch the premier league table\n",
    "        for table in tables:\n",
    "            indicator = table.find_all('font')\n",
    "            for item in indicator:\n",
    "                if item.text==\"GP\":\n",
    "                    pl_table=table\n",
    "                    break\n",
    "                    \n",
    "        # Loop through all rows and find points and goals\n",
    "        table_rows=pl_table.find_all('tr',class_=\"odd\")\n",
    "        for row in table_rows:\n",
    "\n",
    "            stats = row.find_all('td',align=\"center\")\n",
    "\n",
    "            goals.append(int(stats[5].text))\n",
    "            points.append(int(stats[8].text))\n",
    "        year-=1\n",
    "\n",
    "#     for i in range(len(points)):\n",
    "#          print(f\"Points : {points[i]}\\t Goals :{goals[i]}\")\n",
    "    return goals, points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d534744b",
   "metadata": {},
   "source": [
    "# Check Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "46e150e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Points : 93\t Goals :99\n",
      "Points : 92\t Goals :94\n",
      "Points : 74\t Goals :76\n",
      "Points : 71\t Goals :69\n",
      "Points : 69\t Goals :61\n",
      "Points : 58\t Goals :57\n",
      "Points : 56\t Goals :60\n",
      "Points : 52\t Goals :62\n",
      "Points : 51\t Goals :42\n",
      "Points : 51\t Goals :38\n",
      "Points : 49\t Goals :44\n",
      "Points : 48\t Goals :50\n",
      "Points : 46\t Goals :48\n",
      "Points : 45\t Goals :52\n",
      "Points : 40\t Goals :43\n",
      "Points : 39\t Goals :43\n",
      "Points : 38\t Goals :42\n",
      "Points : 35\t Goals :34\n",
      "Points : 23\t Goals :34\n",
      "Points : 22\t Goals :23\n",
      "Points : 86\t Goals :83\n",
      "Points : 74\t Goals :73\n",
      "Points : 69\t Goals :68\n",
      "Points : 67\t Goals :58\n",
      "Points : 66\t Goals :68\n",
      "Points : 65\t Goals :62\n",
      "Points : 62\t Goals :68\n",
      "Points : 61\t Goals :55\n",
      "Points : 59\t Goals :62\n",
      "Points : 59\t Goals :47\n",
      "Points : 55\t Goals :55\n",
      "Points : 45\t Goals :46\n",
      "Points : 45\t Goals :36\n",
      "Points : 44\t Goals :41\n",
      "Points : 43\t Goals :47\n",
      "Points : 41\t Goals :40\n",
      "Points : 39\t Goals :33\n",
      "Points : 28\t Goals :27\n",
      "Points : 26\t Goals :35\n",
      "Points : 23\t Goals :20\n",
      "Points : 99\t Goals :85\n",
      "Points : 81\t Goals :102\n",
      "Points : 66\t Goals :66\n",
      "Points : 66\t Goals :69\n",
      "Points : 62\t Goals :67\n",
      "Points : 59\t Goals :61\n",
      "Points : 59\t Goals :51\n",
      "Points : 56\t Goals :56\n",
      "Points : 54\t Goals :39\n",
      "Points : 54\t Goals :43\n",
      "Points : 52\t Goals :51\n",
      "Points : 49\t Goals :44\n",
      "Points : 44\t Goals :38\n",
      "Points : 43\t Goals :31\n",
      "Points : 41\t Goals :39\n",
      "Points : 39\t Goals :49\n",
      "Points : 35\t Goals :41\n",
      "Points : 34\t Goals :40\n",
      "Points : 34\t Goals :36\n",
      "Points : 21\t Goals :26\n",
      "Points : 98\t Goals :95\n",
      "Points : 97\t Goals :89\n",
      "Points : 72\t Goals :63\n",
      "Points : 71\t Goals :67\n",
      "Points : 70\t Goals :73\n",
      "Points : 66\t Goals :65\n",
      "Points : 57\t Goals :47\n",
      "Points : 54\t Goals :54\n",
      "Points : 52\t Goals :51\n",
      "Points : 52\t Goals :52\n",
      "Points : 50\t Goals :52\n",
      "Points : 49\t Goals :51\n",
      "Points : 45\t Goals :42\n",
      "Points : 45\t Goals :56\n",
      "Points : 40\t Goals :45\n",
      "Points : 39\t Goals :45\n",
      "Points : 36\t Goals :35\n",
      "Points : 34\t Goals :34\n",
      "Points : 26\t Goals :34\n",
      "Points : 16\t Goals :22\n",
      "Points : 100\t Goals :106\n",
      "Points : 81\t Goals :68\n",
      "Points : 77\t Goals :74\n",
      "Points : 75\t Goals :84\n",
      "Points : 70\t Goals :62\n",
      "Points : 63\t Goals :74\n",
      "Points : 54\t Goals :36\n",
      "Points : 49\t Goals :44\n",
      "Points : 47\t Goals :56\n",
      "Points : 44\t Goals :39\n",
      "Points : 44\t Goals :45\n",
      "Points : 44\t Goals :45\n",
      "Points : 42\t Goals :48\n",
      "Points : 41\t Goals :44\n",
      "Points : 40\t Goals :34\n",
      "Points : 37\t Goals :28\n",
      "Points : 36\t Goals :37\n",
      "Points : 33\t Goals :28\n",
      "Points : 33\t Goals :35\n",
      "Points : 31\t Goals :31\n"
     ]
    }
   ],
   "source": [
    "goals, points=scrape_data()\n",
    "for i in range(len(points)):\n",
    "    print(f\"Points : {points[i]}\\t Goals :{goals[i]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab4fe9bb",
   "metadata": {},
   "source": [
    "# Convert to NumPy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "776384b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 99  94  76  69  61  57  60  62  42  38  44  50  48  52  43  43  42  34\n",
      "  34  23  83  73  68  58  68  62  68  55  62  47  55  46  36  41  47  40\n",
      "  33  27  35  20  85 102  66  69  67  61  51  56  39  43  51  44  38  31\n",
      "  39  49  41  40  36  26  95  89  63  67  73  65  47  54  51  52  52  51\n",
      "  42  56  45  45  35  34  34  22 106  68  74  84  62  74  36  44  56  39\n",
      "  45  45  48  44  34  28  37  28  35  31]\n",
      "[ 93  92  74  71  69  58  56  52  51  51  49  48  46  45  40  39  38  35\n",
      "  23  22  86  74  69  67  66  65  62  61  59  59  55  45  45  44  43  41\n",
      "  39  28  26  23  99  81  66  66  62  59  59  56  54  54  52  49  44  43\n",
      "  41  39  35  34  34  21  98  97  72  71  70  66  57  54  52  52  50  49\n",
      "  45  45  40  39  36  34  26  16 100  81  77  75  70  63  54  49  47  44\n",
      "  44  44  42  41  40  37  36  33  33  31]\n"
     ]
    }
   ],
   "source": [
    "x_train=np.array(goals)\n",
    "y_train=np.array(points)\n",
    "print(x_train)\n",
    "print(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "8eff4a4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a scatter plot of the data\n",
    "plt.scatter(x_train, y_train,marker='x',c='r')\n",
    "\n",
    "# Set the title, X-axis label and y-axis label\n",
    "plt.title(\"Premier League (2017-2021) Goals vs Points\")\n",
    "plt.xlabel(\"Goals scored\")\n",
    "plt.ylabel(\"Points obtained\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59a9cf9e",
   "metadata": {},
   "source": [
    "## Compute cost for a value of w and b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7c49be60",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(x, y, w, b):\n",
    "    \n",
    "    m = x.shape[0] \n",
    "    cost = 0\n",
    "    \n",
    "    for i in range(m):\n",
    "        f_wb = w * x[i] + b\n",
    "        cost = cost + (f_wb - y[i])**2\n",
    "    total_cost = 1 / (2 * m) * cost\n",
    "\n",
    "    return total_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "081da10d",
   "metadata": {},
   "source": [
    "## Compute the gradient and return it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4c194fdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient(x, y, w, b): \n",
    "    \"\"\"\n",
    "    Computes the gradient for linear regression \n",
    "    Args:\n",
    "      x (ndarray (m,)): Data, m examples \n",
    "      y (ndarray (m,)): target values\n",
    "      w,b (scalar)    : model parameters  \n",
    "    Returns\n",
    "      dj_dw (scalar): The gradient of the cost w.r.t. the parameters w\n",
    "      dj_db (scalar): The gradient of the cost w.r.t. the parameter b     \n",
    "     \"\"\"\n",
    "    \n",
    "    # Number of training examples\n",
    "    m = x.shape[0]    \n",
    "    dj_dw = 0\n",
    "    dj_db = 0\n",
    "    \n",
    "    for i in range(m):  \n",
    "        f_wb = w * x[i] + b \n",
    "        dj_dw_i = (f_wb - y[i]) * x[i] \n",
    "        dj_db_i = f_wb - y[i] \n",
    "        dj_db += dj_db_i\n",
    "        dj_dw += dj_dw_i \n",
    "    dj_dw = dj_dw / m \n",
    "    dj_db = dj_db / m \n",
    "        \n",
    "    return dj_dw, dj_db"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e79bcc8",
   "metadata": {},
   "source": [
    "### Cost vs w plot to check if the code is corre}ct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "99f7dd93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[670007.025      415524.23981481 221545.75092593  88071.55833333\n",
      "  15101.66203704   2636.06203704  50674.75833333 159217.75092593\n",
      " 328265.03981481 557816.625     ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29ea122e940>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fix_b=5\n",
    "w_array = np.linspace(-20, 20, 10)\n",
    "\n",
    "cost = np.zeros_like(w_array)\n",
    "for i in range(len(w_array)):\n",
    "    cost[i]=compute_cost(x_train,y_train,w_array[i],fix_b)\n",
    "print(cost)\n",
    "plt.title(\"Cost vs w; b set to 10\")\n",
    "plt.ylabel('Cost')\n",
    "plt.xlabel('w')\n",
    "plt.plot(w_array,cost,linewidth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d0856beb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "179669.575\n",
      "26648.8\n",
      "1079.975\n",
      "26648.8\n",
      "128793.375\n"
     ]
    }
   ],
   "source": [
    "print(compute_cost(x_train,y_train,-10,10))\n",
    "print(compute_cost(x_train,y_train,5,10))\n",
    "print(compute_cost(x_train,y_train,0,10))\n",
    "print(compute_cost(x_train,y_train,5,10))\n",
    "print(compute_cost(x_train,y_train,10,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1d7b9ae2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, w_in, b_in, cost_function, gradient_function, alpha, num_iters): \n",
    "    \"\"\"\n",
    "    Performs batch gradient descent to learn theta. Updates theta by taking \n",
    "    num_iters gradient steps with learning rate alpha\n",
    "    \n",
    "    Args:\n",
    "      X (ndarray (m,n))   : Data, m examples with n features\n",
    "      y (ndarray (m,))    : target values\n",
    "      w_in (ndarray (n,)) : initial model parameters  \n",
    "      b_in (scalar)       : initial model parameter\n",
    "      cost_function       : function to compute cost\n",
    "      gradient_function   : function to compute the gradient\n",
    "      alpha (float)       : Learning rate\n",
    "      num_iters (int)     : number of iterations to run gradient descent\n",
    "      \n",
    "    Returns:\n",
    "      w (ndarray (n,)) : Updated values of parameters \n",
    "      b (scalar)       : Updated value of parameter \n",
    "      \"\"\"\n",
    "    \n",
    "    # An array to store cost J and w's at each iteration primarily for graphing later\n",
    "    J_history = []\n",
    "    w = copy.deepcopy(w_in)  #avoid modifying global w within function\n",
    "    b = b_in\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "\n",
    "        # Calculate the gradient and update the parameters\n",
    "        dj_db,dj_dw = gradient_function(X, y, w, b)   ##None\n",
    "\n",
    "        # Update Parameters using w, b, alpha and gradient\n",
    "        w = w - alpha * dj_dw               ##None\n",
    "        b = b - alpha * dj_db               ##None\n",
    "      \n",
    "        # Save cost J at each iteration\n",
    "        if i<100000:      # prevent resource exhaustion \n",
    "            J_history.append( cost_function(X, y, w, b))\n",
    "\n",
    "        # Print cost every at intervals 10 times or as many iterations if < 10\n",
    "        if i% math.ceil(num_iters / 10) == 0:\n",
    "            print(f\"Iteration {i:4d}: Cost {J_history[-1]:8.2f}   \")\n",
    "        \n",
    "    return w, b, J_history #return final w,b and J history for graphing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79411434",
   "metadata": {},
   "source": [
    "### Check if gradient descent is working by checking cost over iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "227500df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    0: Cost    32.58   \n",
      "Iteration 1700: Cost    26.95   \n",
      "Iteration 3400: Cost    24.24   \n",
      "Iteration 5100: Cost    22.94   \n",
      "Iteration 6800: Cost    22.31   \n",
      "Iteration 8500: Cost    22.01   \n",
      "Iteration 10200: Cost    21.87   \n",
      "Iteration 11900: Cost    21.80   \n",
      "Iteration 13600: Cost    21.77   \n",
      "Iteration 15300: Cost    21.76   \n",
      "b,w found by gradient descent: 2.55,0.961018756300573 \n",
      "prediction: 97.69, target value: 93\n",
      "prediction: 92.89, target value: 92\n",
      "prediction: 75.59, target value: 74\n",
      "prediction: 68.86, target value: 71\n",
      "prediction: 61.17, target value: 69\n",
      "prediction: 57.33, target value: 58\n",
      "prediction: 60.21, target value: 56\n",
      "prediction: 62.13, target value: 52\n",
      "prediction: 42.91, target value: 51\n",
      "prediction: 39.07, target value: 51\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29ea099c6a0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initialize parameters\n",
    "initial_w = 1\n",
    "initial_b = 5\n",
    "# some gradient descent settings\n",
    "iterations = 17000\n",
    "alpha = 2e-6\n",
    "# run gradient descent \n",
    "w_final, b_final, J_hist = gradient_descent(x_train, y_train, initial_w, initial_b,\n",
    "                                                    compute_cost, compute_gradient, \n",
    "                                                    alpha, iterations)\n",
    "print(f\"b,w found by gradient descent: {b_final:0.2f},{w_final} \")\n",
    "m= x_train.shape[0]\n",
    "\n",
    "for i in range(10):\n",
    "    print(f\"prediction: {np.dot(x_train[i], w_final) + b_final:0.2f}, target value: {y_train[i]}\")\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12,4))\n",
    "ax1.plot(J_hist[:500])\n",
    "ax2.plot(J_hist[16000:])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "411c5345",
   "metadata": {},
   "source": [
    "### Plotting predicted values vs actual values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5c9d2ec0",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = x_train.shape[0]\n",
    "predicted = np.zeros(m)\n",
    "\n",
    "for i in range(m):\n",
    "    predicted[i] = w_final * x_train[i] + b_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "6ae3be6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Points obtained')"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the linear fit\n",
    "plt.plot(x_train, predicted, c = \"b\")\n",
    "\n",
    "# Create a scatter plot of the data. \n",
    "plt.scatter(x_train, y_train, marker='x', c='r') \n",
    "\n",
    "# Set the title\n",
    "plt.title(\"Premier League (2017-2021) Goals vs Points\")\n",
    "plt.xlabel(\"Goals scored\")\n",
    "plt.ylabel(\"Points obtained\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0a9da684",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 70 goals scored in a season, we expect the team to get 69 points\n",
      "For 90 goals scored in a season, we expect the team to get 89 points\n"
     ]
    }
   ],
   "source": [
    "predict1 = 70 * w_final + b_final\n",
    "print(f\"For 70 goals scored in a season, we expect the team to get {int(predict1)} points\")\n",
    "\n",
    "predict2 = 90 * w_final + b_final\n",
    "print(f\"For 90 goals scored in a season, we expect the team to get {int(predict2)} points\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4613aa85",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the number of goals scored in a season: 85\n",
      "The team is expected to obtain 84 points\n"
     ]
    }
   ],
   "source": [
    "goals_input=int(input(\"Enter the number of goals scored in a season: \"))\n",
    "predict = goals_input * w_final + b_final\n",
    "print(f\"The team is expected to obtain {int(predict)} points\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94013690",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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