LinearRegressionPractice.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basic Tutorial from https://datatofish.com/multiple-linear-regression-python/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    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\n",
      "5   2017      7           2.50                5.6               1254\n",
      "6   2017      6           2.50                5.5               1234\n",
      "7   2017      5           2.25                5.5               1195\n",
      "8   2017      4           2.25                5.5               1159\n",
      "9   2017      3           2.25                5.6               1167\n",
      "10  2017      2           2.00                5.7               1130\n",
      "11  2017      1           2.00                5.9               1075\n",
      "12  2016     12           2.00                6.0               1047\n",
      "13  2016     11           1.75                5.9                965\n",
      "14  2016     10           1.75                5.8                943\n",
      "15  2016      9           1.75                6.1                958\n",
      "16  2016      8           1.75                6.2                971\n",
      "17  2016      7           1.75                6.1                949\n",
      "18  2016      6           1.75                6.1                884\n",
      "19  2016      5           1.75                6.1                866\n",
      "20  2016      4           1.75                5.9                876\n",
      "21  2016      3           1.75                6.2                822\n",
      "22  2016      2           1.75                6.2                704\n",
      "23  2016      1           1.75                6.1                719\n"
     ]
    }
   ],
   "source": [
    "# create dataframe\n",
    "\n",
    "Stock_Market = {'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(Stock_Market,columns=['Year','Month','Interest_Rate','Unemployment_Rate','Stock_Index_Price']) \n",
    "\n",
    "print (df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check Linearity\n",
    "plt.scatter(df['Interest_Rate'], df['Stock_Index_Price'], color='red')\n",
    "plt.title('Stock Index Price Vs Interest Rate', fontsize=14)\n",
    "plt.xlabel('Interest Rate', fontsize=12)\n",
    "plt.ylabel('Stock Index Price', fontsize=12)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, linear relationship exists between the Stock_Index_Price and the Interest_Rate."
   ]
  },
  {
   "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": [
    "plt.scatter(df['Unemployment_Rate'], df['Stock_Index_Price'], color='green')\n",
    "plt.title('Stock Index Price Vs Unemployment Rate', fontsize=14)\n",
    "plt.xlabel('Unemployment Rate', fontsize=14)\n",
    "plt.ylabel('Stock Index Price', fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that a linear relationship also exists between the Stock_Index_Price and the Unemployment_Rate – but with a negative slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# here we have 2 variables for multiple regression. \n",
    "# If you just want to use one variable for simple linear regression, then use X = df['Interest_Rate'] for example.\n",
    "# Alternatively, you may add additional variables within the brackets\n",
    "X = df[['Interest_Rate','Unemployment_Rate']] \n",
    "Y = df['Stock_Index_Price']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: \n",
      " 1798.4039776258546\n",
      "Coefficients: \n",
      " [ 345.54008701 -250.14657137]\n"
     ]
    }
   ],
   "source": [
    "# with sklearn\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X, Y)\n",
    "print('Intercept: \\n', regr.intercept_)\n",
    "print('Coefficients: \\n', regr.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Stock Index Price: \n",
      " [1422.86238865]\n"
     ]
    }
   ],
   "source": [
    "# prediction with sklearn\n",
    "New_Interest_Rate = 2.75\n",
    "New_Unemployment_Rate = 5.3\n",
    "print ('Predicted Stock Index Price: \\n', regr.predict([[New_Interest_Rate ,New_Unemployment_Rate]]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:      Stock_Index_Price   R-squared:                       0.898\n",
      "Model:                            OLS   Adj. R-squared:                  0.888\n",
      "Method:                 Least Squares   F-statistic:                     92.07\n",
      "Date:                Thu, 27 Aug 2020   Prob (F-statistic):           4.04e-11\n",
      "Time:                        19:20:21   Log-Likelihood:                -134.61\n",
      "No. Observations:                  24   AIC:                             275.2\n",
      "Df Residuals:                      21   BIC:                             278.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const              1798.4040    899.248      2.000      0.059     -71.685    3668.493\n",
      "Interest_Rate       345.5401    111.367      3.103      0.005     113.940     577.140\n",
      "Unemployment_Rate  -250.1466    117.950     -2.121      0.046    -495.437      -4.856\n",
      "==============================================================================\n",
      "Omnibus:                        2.691   Durbin-Watson:                   0.530\n",
      "Prob(Omnibus):                  0.260   Jarque-Bera (JB):                1.551\n",
      "Skew:                          -0.612   Prob(JB):                        0.461\n",
      "Kurtosis:                       3.226   Cond. No.                         394.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# with statsmodels\n",
    "X = sm.add_constant(X) # adding a constant\n",
    " \n",
    "model = sm.OLS(Y, X).fit()\n",
    "predictions = model.predict(X) \n",
    " \n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output includes the intercept and coefficients. Using this information, the multiple linear regression equation can be built as follows:\n",
    "\n",
    "Stock_Index_Price = (Intercept) + (Interest_Rate coef)*X1 + (Unemployment_Rate coef)*X2\n",
    "\n",
    "Stock_Index_Price = (1798.4040) + (345.5401)*(X1) + (-250.1466)*(X2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Stock Index Price: \n",
      " 1422.862295\n"
     ]
    }
   ],
   "source": [
    "# prediction with statsmodels\n",
    "# Using model we get\n",
    "New_Interest_Rate = 2.75\n",
    "New_Unemployment_Rate = 5.3\n",
    "print ('Predicted Stock Index Price: \\n', (1798.4040) + (345.5401*New_Interest_Rate) + (-250.1466*New_Unemployment_Rate))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that the values obtained by prediction by statsmodels are same as those predicted by sklearn. Hurray!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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