Simple Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordinary Least Square Method :\n",
    "\n",
    "*Predecting Brain Weight (Dependent variable) based on Head Size (Independent variable). For Goodness of fit R Squared Error method is used.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Necessary Libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(237, 4)\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>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0       1          1             4512                 1530\n",
       "1       1          1             3738                 1297\n",
       "2       1          1             4261                 1335\n",
       "3       1          1             3777                 1282\n",
       "4       1          1             4177                 1590"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reading Data\n",
    "data = pd.read_csv('headbrain.csv')\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collecting X and Y\n",
    "X = data['Head Size(cm^3)'].values\n",
    "Y = data['Brain Weight(grams)'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "325.57342104944223 0.26342933948939945\n"
     ]
    }
   ],
   "source": [
    "# Mean X and Y\n",
    "mean_x = np.mean(X)\n",
    "mean_y = np.mean(Y)\n",
    "\n",
    "# Total number of values\n",
    "m = len(X)\n",
    "\n",
    "# Using the formula to calculate b0 and b1\n",
    "numer = 0\n",
    "denom = 0\n",
    "for i in range(m):\n",
    "    numer += (X[i] - mean_x) * (Y[i] - mean_y)\n",
    "    denom += (X[i] - mean_x) ** 2\n",
    "b1 = numer / denom\n",
    "b0 = mean_y - (b1 * mean_x)\n",
    "\n",
    "# Print coefficients\n",
    "print(b0, b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "# Plotting Values and Regression Line\n",
    "\n",
    "max_x = np.max(X) + 100\n",
    "min_x = np.min(X) - 100\n",
    "\n",
    "# Calculating line values x and y\n",
    "x = np.linspace(min_x, max_x, 1000)\n",
    "y = b0 + b1 * x\n",
    "\n",
    "# Ploting Scatter Points\n",
    "plt.scatter(X, Y, color = \"m\", label='Scatter Plot')\n",
    "# Ploting Line\n",
    "plt.plot(x, y, color = 'g', label='Regression Line')\n",
    "\n",
    "plt.xlabel('Head Size in cm3')\n",
    "plt.ylabel('Brain Weight in grams')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "# Calculating Root Mean Squares Error\n",
    "rmse = 0\n",
    "for i in range(m):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    rmse += (Y[i] - y_pred) ** 2\n",
    "rmse = np.sqrt(rmse/m)\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6393117199570003\n"
     ]
    }
   ],
   "source": [
    "# R Square Method – Goodness of Fit\n",
    "sumofsquares = 0\n",
    "sumofresiduals = 0\n",
    "for i in range(m):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    sumofsquares += (Y[i] - mean_y) ** 2\n",
    "    sumofresiduals += (Y[i] - y_pred) ** 2\n",
    "r2 = 1 - (sumofresiduals/sumofsquares)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.639311719957\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    " \n",
    "# Cannot use Rank 1 matrix in scikit learn\n",
    "X = np.array(data['Head Size(cm^3)']).reshape(-1, 1) \n",
    "# Creating Model\n",
    "reg = LinearRegression()\n",
    "# Fitting training data\n",
    "reg = reg.fit(X, Y)\n",
    "# Y Prediction\n",
    "Y_pd = reg.predict(X)\n",
    " \n",
    "# Calculating R2 Score\n",
    "r2_score = reg.score(X, Y)\n",
    " \n",
    "print(r2_score)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}