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Example of Multiple Linear Regression in Python - statsmodels and sklearn.
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‎Example_of_Multiple_Linear_Regression_in_Python.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "651019ae-1bd8-41b3-be75-474a841f1f8c",
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"metadata": {},
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"source": [
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"# Linear Regression in Python using Statsmodels\n",
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"https://datatofish.com/statsmodels-linear-regression/"
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]
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},
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{
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"cell_type": "markdown",
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"id": "de3b5be7-792e-4a94-8cd0-a17df627c419",
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"metadata": {},
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"source": [
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"## About Linear Regression\n",
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"Linear regression is used as a predictive model that assumes a linear relationship between the dependent variable (which is the variable we are trying to predict/estimate) and the independent variable/s (input variable/s used in the prediction)."
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]
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},
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{
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"cell_type": "markdown",
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"id": "efd67629-b49f-47e2-9305-a7abb6f10366",
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"metadata": {},
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"source": [
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"## An Example (with the full dataset)\n",
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"For illustration purposes, let’s suppose that you have a fictitious economy with the following parameters, where the index_price is the dependent variable, and the 2 independent/input variables are:\n",
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"\n",
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"* interest_rate\n",
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"* unemployment_rate\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "3dacd2dc-aa3e-40f3-a66d-252b7512bef7",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" year month interest_rate unemployment_rate index_price\n",
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"0 2017 12 2.75 5.3 1464\n",
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"1 2017 11 2.50 5.3 1394\n",
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"2 2017 10 2.50 5.3 1357\n",
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"3 2017 9 2.50 5.3 1293\n",
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"4 2017 8 2.50 5.4 1256\n",
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"5 2017 7 2.50 5.6 1254\n",
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"6 2017 6 2.50 5.5 1234\n",
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"7 2017 5 2.25 5.5 1195\n",
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"8 2017 4 2.25 5.5 1159\n",
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"9 2017 3 2.25 5.6 1167\n",
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"10 2017 2 2.00 5.7 1130\n",
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"11 2017 1 2.00 5.9 1075\n",
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"12 2016 12 2.00 6.0 1047\n",
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"13 2016 11 1.75 5.9 965\n",
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"14 2016 10 1.75 5.8 943\n",
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"15 2016 9 1.75 6.1 958\n",
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"16 2016 8 1.75 6.2 971\n",
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"17 2016 7 1.75 6.1 949\n",
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"18 2016 6 1.75 6.1 884\n",
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"19 2016 5 1.75 6.1 866\n",
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"20 2016 4 1.75 5.9 876\n",
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"21 2016 3 1.75 6.2 822\n",
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"22 2016 2 1.75 6.2 704\n",
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"23 2016 1 1.75 6.1 719\n"
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]
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}
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],
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"source": [
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"import pandas as pd\n",
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"\n",
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"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",
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" '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",
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" '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",
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" '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",
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" '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",
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" }\n",
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"\n",
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"df = pd.DataFrame(data)\n",
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"print(df)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6b7443b5-1c4a-49ac-89e4-4d3bd29f584a",
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"metadata": {},
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"source": [
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"## The Python Code using Statsmodels"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "434e1d1b-0487-4f15-932a-ce0d82f779e5",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" OLS Regression Results \n",
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"==============================================================================\n",
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"Dep. Variable: index_price R-squared: 0.898\n",
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"Model: OLS Adj. R-squared: 0.888\n",
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"Method: Least Squares F-statistic: 92.07\n",
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"Date: Sun, 09 Jul 2023 Prob (F-statistic): 4.04e-11\n",
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"Time: 17:01:29 Log-Likelihood: -134.61\n",
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"No. Observations: 24 AIC: 275.2\n",
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"Df Residuals: 21 BIC: 278.8\n",
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"Df Model: 2 \n",
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"Covariance Type: nonrobust \n",
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"=====================================================================================\n",
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" coef std err t P>|t| [0.025 0.975]\n",
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"-------------------------------------------------------------------------------------\n",
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"const 1798.4040 899.248 2.000 0.059 -71.685 3668.493\n",
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"interest_rate 345.5401 111.367 3.103 0.005 113.940 577.140\n",
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"unemployment_rate -250.1466 117.950 -2.121 0.046 -495.437 -4.856\n",
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"==============================================================================\n",
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"Omnibus: 2.691 Durbin-Watson: 0.530\n",
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"Prob(Omnibus): 0.260 Jarque-Bera (JB): 1.551\n",
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"Skew: -0.612 Prob(JB): 0.461\n",
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"Kurtosis: 3.226 Cond. No. 394.\n",
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"==============================================================================\n",
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"\n",
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"Notes:\n",
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"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
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]
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}
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],
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"source": [
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"import statsmodels.api as sm\n",
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"\n",
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"x = df[['interest_rate','unemployment_rate']]\n",
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"y = df['index_price']\n",
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"\n",
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"x = sm.add_constant(x)\n",
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"\n",
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"model = sm.OLS(y, x).fit()\n",
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"predictions = model.predict(x) \n",
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"\n",
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"print_model = model.summary()\n",
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"print(print_model)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "722a577e-9e89-4808-841e-0c9535b8fd99",
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"metadata": {},
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"source": [
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"## Interpreting the Regression Results\n",
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"\n",
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"* **Adjusted. R-squared** reflects the fit of the model. R-squared values range from 0 to 1, where a higher value generally indicates a better fit, assuming certain conditions are met.\n",
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"* **const** coefficient is your Y-intercept. It means that if both the interest_rate and unemployment_rate coefficients are zero, then the expected output (i.e., the Y) would be equal to the const coefficient.\n",
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"* **interest_rate coefficient** represents the change in the output Y due to a change of one unit in the interest rate (everything else held constant)\n",
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"unemployment_rate coefficient represents the change in the output Y due to a change of one unit in the unemployment rate (everything else held constant)\n",
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"* **std err** reflects the level of accuracy of the coefficients. The lower it is, the higher is the level of accuracy\n",
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"* **P >|t|** is your *p-value*. A p-value of less than 0.05 is considered to be statistically significant\n",
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"Confidence Interval represents the range in which our coefficients are likely to fall (with a likelihood of 95%)"
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]
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},
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{
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"execution_count": null,
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