Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Linear Regression using Least square method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing required libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating dataset\n",
    "data = {'Y':[245, 312, 279, 308, 199, 219, 405, 324, 319, 255],\n",
    "        'X':[1400, 1600, 1700, 1875, 1100, 1550, 2350, 2450, 1425, 1700]}\n",
    "df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reshaping the dataset to fit in the model\n",
    "x = df.X\n",
    "y = df.Y\n",
    "x = np.array(x)\n",
    "y = np.array(y)\n",
    "y = y.reshape(-1,1)\n",
    "x = x.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scaling the independent variable\n",
    "scaler = StandardScaler()\n",
    "x_scaled = scaler.fit_transform(x)\n",
    "x_scaled = np.insert(x_scaled, 0, values=1,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns coefficient of the best fitting regression line\n",
    "# formula used:\n",
    "# beta= (x.(x^T))^(-1).(x^T).y\n",
    "def coefficients(x_scaled, y):\n",
    "    return (np.linalg.inv(x_scaled.T.dot(x_scaled))).dot(x_scaled.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept:[286.5]\n",
      "Slope:[43.5142905]\n"
     ]
    }
   ],
   "source": [
    "# regression line intercept and slope for the given dataset\n",
    "beta = coefficients(x_scaled, y)\n",
    "print('Intercept:{}\\nSlope:{}'.format(beta[0], beta[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 3000, y = [344.6484166]\n",
      "x = 2000, y = [274.87031668]\n",
      "x = 1500, y =[239.98126672]\n"
     ]
    }
   ],
   "source": [
    "# predictions\n",
    "x_pred = np.array([3000, 2000, 1500])\n",
    "x_pred=x_pred.reshape(-1,1)\n",
    "x_pred = scaler.fit_transform(x_pred)\n",
    "x_pred = np.insert(x_pred, 0, values=1,axis=1)\n",
    "y_predict = x_pred.dot(beta)\n",
    "print('x = 3000, y = {}\\nx = 2000, y = {}\\nx = 1500, y ={}'.format(*y_predict))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "# scatterplot and regression line\n",
    "plt.scatter(x, y)\n",
    "y_preds = [beta[0] + beta[1] *i for i in x_scaled[:, 1]]\n",
    "plt.plot(x, y_preds)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean square error: 1366.556522430798\n",
      "Root Mean Square error: 36.96696528565467\n",
      "R2 Score: 0.5808173118722725\n"
     ]
    }
   ],
   "source": [
    "# performance evaluation\n",
    "error = y - y_preds\n",
    "square_error = np.power(error,2)\n",
    "mse = sum(square_error)/len(y)\n",
    "rms = np.sqrt(mse)\n",
    "y_mean = np.mean(y)\n",
    "var = np.sum((y-y_mean)**2)\n",
    "r = 1 - sum(square_error)/var\n",
    "print('Mean square error: {}\\nRoot Mean Square error: {}\\nR2 Score: {}'.format(mse[0],rms[0],r[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple Linear Regression using Least Square Method "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "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>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Interest_Rate</th>\n",
       "      <th>Unemployment_Rate</th>\n",
       "      <th>Stock_Index_Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2017</td>\n",
       "      <td>12</td>\n",
       "      <td>2.75</td>\n",
       "      <td>5.3</td>\n",
       "      <td>1464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2017</td>\n",
       "      <td>11</td>\n",
       "      <td>2.50</td>\n",
       "      <td>5.3</td>\n",
       "      <td>1394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2017</td>\n",
       "      <td>10</td>\n",
       "      <td>2.50</td>\n",
       "      <td>5.3</td>\n",
       "      <td>1357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2017</td>\n",
       "      <td>9</td>\n",
       "      <td>2.50</td>\n",
       "      <td>5.3</td>\n",
       "      <td>1293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2017</td>\n",
       "      <td>8</td>\n",
       "      <td>2.50</td>\n",
       "      <td>5.4</td>\n",
       "      <td>1256</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year  Month  Interest_Rate  Unemployment_Rate  Stock_Index_Price\n",
       "0  2017     12           2.75                5.3               1464\n",
       "1  2017     11           2.50                5.3               1394\n",
       "2  2017     10           2.50                5.3               1357\n",
       "3  2017      9           2.50                5.3               1293\n",
       "4  2017      8           2.50                5.4               1256"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create dataset\n",
    "data = {'Year':[2017, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2016, 2016, 2016, 2016, 2016, 2016, 2016, 2016, 2016, 2016, 2016, 2016],\n",
    "        'Month':[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],\n",
    "        'Interest_Rate':[2.75, 2.5, 2.5, 2.5, 2.5, 2.5,2.5, 2.25, 2.25, 2.25, 2, 2, 2, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75],\n",
    "        'Unemployment_Rate': [5.3, 5.3, 5.3, 5.3, 5.4, 5.6, 5.5, 5.5, 5.5, 5.6, 5.7, 5.9, 6, 5.9, 5.8, 6.1, 6.2, 6.1,6.1,6.1,5.9,6.2,6.2,6.1],\n",
    "        'Stock_Index_Price':[1464, 1394,1357,1293,1256,1254,1234,1195,1159,1167,1130,1075,1047,965,943,958,971,949,884,866,876,822,704,719]\n",
    "        \n",
    "       }\n",
    "df = pd.DataFrame(data)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  1.        ,  1.59325501,  1.97880334, -1.47026414],\n",
       "       [ 1.        ,  1.        ,  1.30357228,  1.24816826, -1.47026414],\n",
       "       [ 1.        ,  1.        ,  1.01388955,  1.24816826, -1.47026414],\n",
       "       [ 1.        ,  1.        ,  0.72420682,  1.24816826, -1.47026414],\n",
       "       [ 1.        ,  1.        ,  0.43452409,  1.24816826, -1.16073485],\n",
       "       [ 1.        ,  1.        ,  0.14484136,  1.24816826, -0.54167626],\n",
       "       [ 1.        ,  1.        , -0.14484136,  1.24816826, -0.85120556],\n",
       "       [ 1.        ,  1.        , -0.43452409,  0.51753318, -0.85120556],\n",
       "       [ 1.        ,  1.        , -0.72420682,  0.51753318, -0.85120556],\n",
       "       [ 1.        ,  1.        , -1.01388955,  0.51753318, -0.54167626],\n",
       "       [ 1.        ,  1.        , -1.30357228, -0.2131019 , -0.23214697],\n",
       "       [ 1.        ,  1.        , -1.59325501, -0.2131019 ,  0.38691162],\n",
       "       [ 1.        , -1.        ,  1.59325501, -0.2131019 ,  0.69644091],\n",
       "       [ 1.        , -1.        ,  1.30357228, -0.94373698,  0.38691162],\n",
       "       [ 1.        , -1.        ,  1.01388955, -0.94373698,  0.07738232],\n",
       "       [ 1.        , -1.        ,  0.72420682, -0.94373698,  1.0059702 ],\n",
       "       [ 1.        , -1.        ,  0.43452409, -0.94373698,  1.3154995 ],\n",
       "       [ 1.        , -1.        ,  0.14484136, -0.94373698,  1.0059702 ],\n",
       "       [ 1.        , -1.        , -0.14484136, -0.94373698,  1.0059702 ],\n",
       "       [ 1.        , -1.        , -0.43452409, -0.94373698,  1.0059702 ],\n",
       "       [ 1.        , -1.        , -0.72420682, -0.94373698,  0.38691162],\n",
       "       [ 1.        , -1.        , -1.01388955, -0.94373698,  1.3154995 ],\n",
       "       [ 1.        , -1.        , -1.30357228, -0.94373698,  1.3154995 ],\n",
       "       [ 1.        , -1.        , -1.59325501, -0.94373698,  1.0059702 ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scaling and transforming\n",
    "x = df.iloc[:,:-1]\n",
    "x = np.array(x)\n",
    "x_scaled = scaler.fit_transform(x)\n",
    "x_scaled = np.insert(x_scaled, 0, values=1,axis=1)\n",
    "x_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df.Stock_Index_Price\n",
    "y = np.array(y)\n",
    "y = y.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta 1: [1070.08333333]\n",
      "beta 2: [169.13407143]\n",
      "beta 3: [96.04977006]\n",
      "beta 4: [24.60949865]\n",
      "beta 5: [14.56927777]\n"
     ]
    }
   ],
   "source": [
    "# regression coefficients for the dataset\n",
    "beta = coefficients(x_scaled, y)\n",
    "\n",
    "print('beta 1: {}'.format(beta[0]))\n",
    "print('beta 2: {}'.format(beta[1]))\n",
    "print('beta 3: {}'.format(beta[2]))\n",
    "print('beta 4: {}'.format(beta[3]))\n",
    "print('beta 5: {}'.format(beta[4]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y is [1191.49939239] for interest rate 1.5 and unemplyment rate 5.8\n"
     ]
    }
   ],
   "source": [
    "# prediction \n",
    "\n",
    "y_pred = beta[0] + beta[-1]*5.8 + beta[-2]*1.5\n",
    "print('y is {} for interest rate 1.5 and unemplyment rate 5.8'.format(y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean square error: 923.6388149319869\n",
      "Root Mean Square error: 30.39142666825608\n",
      "R2 Score: 0.9782974467058868\n"
     ]
    }
   ],
   "source": [
    "# performance evaluation\n",
    "beta=np.array(beta).reshape(-1,1)\n",
    "y_preds=x_scaled.dot(beta)\n",
    "error = y - y_preds\n",
    "square_error = np.power(error,2)\n",
    "mse = sum(square_error)/len(y)\n",
    "rms = np.sqrt(mse)\n",
    "y_mean = np.mean(y)\n",
    "var = np.sum((y-y_mean)**2)\n",
    "r = 1 - sum(square_error)/var\n",
    "print('Mean square error: {}\\nRoot Mean Square error: {}\\nR2 Score: {}'.format(mse[0],rms[0],r[0]))"
   ]
  }
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