linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression From Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 739,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 740,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "\n",
    "num_rooms = np.random.randint(1, 8, 100)\n",
    "\n",
    "area = np.random.uniform(500, 4000, 100)  # area in square feet\n",
    "\n",
    "# Generate price based on the number of rooms and area with noise\n",
    "price = 50 * area + 20000 * num_rooms + np.random.normal(0, 4000, 100)\n",
    "\n",
    "total_datapoints = price.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 741,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2400x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the features vs target\n",
    "# Set the font size for the plots\n",
    "font_size = 16\n",
    "\n",
    "# Create subplots\n",
    "fig, ax = plt.subplots(1, 2, figsize=(24, 8))\n",
    "\n",
    "# Plotting scatter plot for number of rooms vs price\n",
    "ax[0].scatter(num_rooms, price, color='green', label='Data points')\n",
    "ax[0].set_title('Number of Rooms vs House Price', fontsize=20)\n",
    "ax[0].set_xlabel('Number of Rooms', fontsize=font_size)\n",
    "ax[0].set_ylabel('Price (USD)', fontsize=font_size)\n",
    "ax[0].grid(True)\n",
    "ax[0].tick_params(axis='both', which='major', labelsize=font_size)\n",
    "\n",
    "# Plotting scatter plot for area vs price\n",
    "ax[1].scatter(area, price, color='blue', label='Data points')\n",
    "ax[1].set_title('House Area vs Price', fontsize=20)\n",
    "ax[1].set_xlabel('Area of house (sq ft)', fontsize=font_size)\n",
    "ax[1].set_ylabel('Price (USD)', fontsize=font_size)\n",
    "ax[1].grid(True)\n",
    "ax[1].tick_params(axis='both', which='major', labelsize=font_size)\n",
    "\n",
    "# Adjust layout to prevent overlap\n",
    "plt.tight_layout()\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 742,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of feature matrix X: 2 x 100. (2 features and 100 data points)\n"
     ]
    }
   ],
   "source": [
    "# Preparing feature matrix\n",
    "num_rooms = num_rooms.reshape(1, total_datapoints)\n",
    "area = area.reshape(1, total_datapoints)\n",
    "X = np.concatenate([num_rooms, area])\n",
    "rows_X, columns_X = X.shape\n",
    "print(f'Dimension of feature matrix X: {rows_X} x {columns_X}. ({rows_X} features and {columns_X} data points)')\n",
    "total_features = rows_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 743,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of target vector y: 1 x 100. (1 target variable(s) and 100 data points)\n"
     ]
    }
   ],
   "source": [
    "# Preparing target vector\n",
    "y = price.reshape(1, total_datapoints)\n",
    "rows_y, columns_y = y.shape\n",
    "print(f'Dimension of target vector y: {rows_y} x {columns_y}. ({rows_y} target variable(s) and {columns_y} data points)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 744,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Splitting dataset into train and test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X.transpose(), y.transpose(), test_size=0.2, random_state=20)\n",
    "y_train = y_train.transpose()\n",
    "y_test = y_test.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 745,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalizing the feature matrix\n",
    "mm = MinMaxScaler()\n",
    "mm.fit(X_train)\n",
    "X_train = mm.transform(X_train).transpose()\n",
    "X_test = mm.transform(X_test).transpose()\n",
    "total_training_datapoints = X_train.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 746,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train shape (features x examples): (2, 80)\n",
      "X_test shape (features x examples): (2, 20)\n",
      "y_train shape (target variables x examples): (1, 80)\n",
      "y_test shape(target variables x examples): (1, 20)\n"
     ]
    }
   ],
   "source": [
    "print('X_train shape (features x examples):', X_train.shape)\n",
    "print('X_test shape (features x examples):', X_test.shape)\n",
    "print(\"y_train shape (target variables x examples):\", y_train.shape)\n",
    "print(\"y_test shape(target variables x examples):\", y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 747,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of transposed weight vector wT: 1 x 2. (1 target variable(s) and 2 features)\n"
     ]
    }
   ],
   "source": [
    "# Initializing Weight Vector and Bias\n",
    "wT = np.random.randn(1, total_features)\n",
    "b = 0\n",
    "rows_wT, columns_wT = wT.shape\n",
    "print(f'Dimension of transposed weight vector wT: {rows_wT} x {columns_wT}. ({rows_wT} target variable(s) and {columns_wT} features)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reinitializing Weight Vector and Bias\n",
    "wT = np.random.randn(1, total_features)\n",
    "b =  0\n",
    "inv_total_training_data_points = 1/total_training_datapoints\n",
    "dJ_by_dwT = np.zeros((1, total_features))\n",
    "dJ_by_db = 0\n",
    "alpha = 0.1\n",
    "J_history = []\n",
    "iteration = 0\n",
    "total_iterations = 500\n",
    "while iteration < total_iterations:\n",
    "    iteration +=1 \n",
    "    y_hat = np.matmul(wT, X_train) + b\n",
    "    diff = y_hat - y_train\n",
    "    diff_sq = np.square(diff)\n",
    "    J = np.sum(diff_sq, axis=1)[0]\n",
    "    J *= inv_total_training_data_points/2\n",
    "    print(f'Iteration #{iteration}')\n",
    "    print(f'Cost: {J}\\n')\n",
    "    J_history.append(J)\n",
    "    diff_X_train = np.multiply(diff, X_train)\n",
    "    dJ_by_dwT = inv_total_training_data_points * np.sum(diff_X_train, axis=1)\n",
    "    dJ_by_db = inv_total_training_data_points * np.sum(diff, axis=1)\n",
    "    # Updation\n",
    "    wT -= alpha * dJ_by_dwT\n",
    "    b -= alpha * dJ_by_db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 766,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iterations = np.arange(1, len(J_history)+1)\n",
    "plt.figure(figsize=(9, 6))\n",
    "plt.plot(iterations, J_history, linewidth=2)\n",
    "plt.title('Cost vs Iterations', fontsize=20)\n",
    "plt.xlabel('Iteration', fontsize=16)\n",
    "plt.ylabel('Cost', fontsize=16)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 767,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat_test = np.matmul(wT, X_test) + b\n",
    "x = np.arange(1, X_test.shape[1]+1)\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(x, y_hat_test, color='red', label='Estimated Values')\n",
    "plt.scatter(x, y_test, color='blue', label='Actual Values')\n",
    "plt.title('Test Set Actual vs Estimated Target Values', fontsize=20)\n",
    "plt.xlabel('Example', fontsize=16)\n",
    "plt.ylabel('Price (USD)', fontsize=16)\n",
    "plt.legend(fontsize=16)\n",
    "plt.xticks(ticks=x, fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.tight_layout()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 765,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Percentage Error (MAPE) for Test Set: 1.90%\n"
     ]
    }
   ],
   "source": [
    "mape = np.mean(np.abs((y_test - y_hat_test) / y_test)) * 100\n",
    "print(f\"Mean Absolute Percentage Error (MAPE) for Test Set: {mape:.2f}%\")"
   ]
  }
 ],
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