Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c44c2554",
   "metadata": {},
   "source": [
    "# Logistic Regression Project\n",
    "\n",
    "This is a model that will predict whether a team will be able to finish top 4 in the premier league or not with a given number of points, based on sample data of previous 5 seasons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3fdb48b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "0f1da149",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.092 0.093 0.074 0.071 0.069 0.058 0.069 0.067 0.066 0.065 0.081 0.066\n",
      " 0.062 0.059 0.072 0.071 0.07  0.066 0.077 0.075 0.07  0.063 0.054 0.076\n",
      " 0.075 0.069 0.061 0.054 0.056 0.062]\n",
      "[1. 1. 1. 1. 0. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 1. 0. 0. 0. 1.\n",
      " 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "# Sample data collected manually, X= number of points, Y= top 4 or not\n",
    "X_train=np.array([92.,93.,74.,71.,69.,58.,69.,67.,66.,65.,81.,66.,62.,59.,72.,71.,70.,66.,77.,75.,70.,63.,54.,76.,75.,69.,61.,54.,56.,62.])\n",
    "Y_train=np.array([1.,1.,1.,1.,0.,0.,1.,1.,0.,0.,1.,1.,0.,0.,1.,1.,0.,0.,1.,1.,0.,0.,0.,1.,0.,0.,0.,0.,0.,0.])\n",
    "\n",
    "print(X_train)\n",
    "print(Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "02c12db9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shape of X_train is: (30,)\n",
      "The shape of y_train is: (30,)\n",
      "We have m = 30 training examples\n"
     ]
    }
   ],
   "source": [
    "# Checking the dimension of data\n",
    "print ('The shape of X_train is: ' + str(X_train.shape))\n",
    "print ('The shape of y_train is: ' + str(Y_train.shape))\n",
    "print ('We have m = %d training examples' % (len(Y_train)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "7f6271e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the data\n",
    "plt.scatter(X_train,Y_train)\n",
    "plt.xlabel(\"Points obtained\")\n",
    "\n",
    "m =X_train.shape[0]\n",
    "col =[]\n",
    "  \n",
    "for i in range(0, len(Y_train)):\n",
    "    if Y_train[i]==1:\n",
    "        col.append('green')  \n",
    "    else:\n",
    "        col.append('red') \n",
    "  \n",
    "for i in range(m):\n",
    "      \n",
    "    # plotting the corresponding x with y \n",
    "    # and respective color\n",
    "    plt.scatter(X_train[i], Y_train[i], c = col[i])\n",
    "    \n",
    "#plt.legend([\"Didn't finish top 4\", \"Finished top 4\"], loc =\"center right\",labelcolor=[\"red\",\"green\"])\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5df5f1f1",
   "metadata": {},
   "source": [
    "### Sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "24c6fada",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    \n",
    "    g = 1/(1+np.exp(-z))\n",
    "    return g\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cdceae1",
   "metadata": {},
   "source": [
    "### Cost function for logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "fca28548",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def compute_cost(X,y,w,b):\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    total_loss=0\n",
    "    epsilon = 1e-7\n",
    "    for i in range(m):\n",
    "        \n",
    "        z_wb= w*X[i]+b  \n",
    "        f_wb=sigmoid(z_wb)\n",
    "        #print(f_wb)\n",
    "        loss =  -y[i] * np.log(f_wb) - (1 - y[i]) * np.log(1 - f_wb+epsilon)\n",
    "        total_loss=total_loss+loss\n",
    "        \n",
    "    total_cost = (1 / m) * total_loss\n",
    "    \n",
    "    ### END CODE HERE ### \n",
    "\n",
    "    return total_cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "9b13fe09",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at w=1 is 5.665465215248766\n"
     ]
    }
   ],
   "source": [
    "m=X_train.shape[0]\n",
    "\n",
    "# Compute and display cost with w initialized to zeroes\n",
    "initial_w = 0.\n",
    "initial_b = 10\n",
    "cost = compute_cost(X_train, Y_train, initial_w, initial_b)\n",
    "print(f\"Cost at w=0 is {cost}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf4a8774",
   "metadata": {},
   "source": [
    "### Gradient function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "13fddcde",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient(X, y, w, b): \n",
    "\n",
    "    m=X.shape[0]\n",
    "    dj_dw = 0.\n",
    "    dj_db = 0.\n",
    "\n",
    "\n",
    "    for i in range(m):\n",
    "       \n",
    "        z_wb= w*X[i]+b  \n",
    "        f_wb=sigmoid(z_wb)\n",
    "        \n",
    "        dj_db_i = f_wb - y[i]\n",
    "        dj_db += dj_db_i\n",
    "        \n",
    "        dj_dw_i = (f_wb - y[i])* X[i]\n",
    "        dj_dw += dj_dw_i\n",
    "            \n",
    "    dj_dw = dj_dw/m\n",
    "    dj_db = dj_db/m\n",
    "\n",
    "\n",
    "        \n",
    "    return dj_db, dj_dw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "b233e3e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dj_db at initial w (zeros):0.2977252452966716\n",
      "dj_dw at initial w (zeros):17.47246159045667\n"
     ]
    }
   ],
   "source": [
    "# Compute and display gradient with w initialized to zeroes\n",
    "initial_w = 0.\n",
    "initial_b = 1.\n",
    "\n",
    "dj_db, dj_dw = compute_gradient(X_train, Y_train, initial_w, initial_b)\n",
    "print(f'dj_db at initial w (zeros):{dj_db}' )\n",
    "print(f'dj_dw at initial w (zeros):{dj_dw}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfb62814",
   "metadata": {},
   "source": [
    "### Learning parameters using gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "6cd686c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, w_in, b_in, cost_function, gradient_function, alpha, num_iters): \n",
    "    \n",
    "   \n",
    "    # number of training examples\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    # An array to store cost J and w's at each iteration primarily for graphing later\n",
    "    J_history = []\n",
    "    w_history = []\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_in, b_in)   \n",
    "\n",
    "        # Update Parameters using w, b, alpha and gradient\n",
    "        w_in = w_in - alpha * dj_dw               \n",
    "        b_in = b_in - alpha * dj_db              \n",
    "       \n",
    "        # Save cost J at each iteration\n",
    "        if i<100000:      # prevent resource exhaustion \n",
    "            cost =  cost_function(X, y, w_in, b_in)\n",
    "            J_history.append(cost)\n",
    "\n",
    "        # Print cost every at intervals 10 times or as many iterations if < 10\n",
    "        if i% math.ceil(num_iters/10) == 0 or i == (num_iters-1):\n",
    "            w_history.append(w_in)\n",
    "            print(f\"Iteration {i:4}: Cost {float(J_history[-1]):8.2f}   \")\n",
    "        \n",
    "    return w_in, b_in, J_history, w_history #return w and J,w history for graphing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "c6376a92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    0: Cost     2.71   \n",
      "Iteration 2000: Cost     0.96   \n",
      "Iteration 4000: Cost     0.96   \n",
      "Iteration 6000: Cost     0.96   \n",
      "Iteration 8000: Cost     0.96   \n",
      "Iteration 10000: Cost     0.96   \n",
      "Iteration 12000: Cost     0.96   \n",
      "Iteration 14000: Cost     0.96   \n",
      "Iteration 16000: Cost     0.96   \n",
      "Iteration 18000: Cost     0.96   \n",
      "Iteration 19999: Cost     0.96   \n"
     ]
    }
   ],
   "source": [
    "\n",
    "intial_w = 1.\n",
    "initial_b = 5.\n",
    "\n",
    "\n",
    "# Some gradient descent settings\n",
    "iterations = 20000\n",
    "alpha = 0.0001\n",
    "\n",
    "w,b, J_history,_ = gradient_descent(X_train ,Y_train, initial_w, initial_b, \n",
    "                                   compute_cost, compute_gradient, alpha, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34cda924",
   "metadata": {},
   "source": [
    "## PREDICTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "c943610d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the number of points: 69\n",
      "The team is expected to finish top 4 and qualify for the champions league\n"
     ]
    }
   ],
   "source": [
    "\n",
    "points= int(input(\"Enter the number of points: \"))\n",
    "result = sigmoid(w*points+b)\n",
    "if(result<0.5):\n",
    "    print(\"The team is expected to finish top 4 and qualify for the champions league\")\n",
    "else:\n",
    "    print(\"The team is not expected to finish top 4.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "cd0b1dfa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d739cf24",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80e6dcbf",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}