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7.3.1 Applications with Examples - I

Introduction

  • Objective: This session illustrates the application of multiple linear regression (MLR) using real-world data to determine factors influencing household debt.
  • Context: Manjula Nayak from 99acres is analyzing a dataset from a household survey in Bengaluru to understand the determinants of household debt, specifically looking at household income and monthly payments.

Data Overview

  • Dataset: Consists of approximately 500 observations from a household survey in Bengaluru.
  • Variables: Includes household size, residential location, monthly income, and monthly payments.
  • Goal: To identify if household income and monthly payments significantly determine household debt.

Methodology

  • Regression Analysis Setup:
  • Dependent Variable (Y): Household debt.
  • Independent Variables (X1 and X2): First income and monthly payments, respectively.
  • Data Columns: Debt (Column K), first income (Column H), and monthly payments (Column I).

Analytical Tools

  • Tool Used: Analysis tool pack in Excel.
  • Procedure: Conduct regression analysis with household debt as the dependent variable and first income and monthly payments as independent variables.

Statistical Analysis

  • Residuals and Standardization:
  • Calculation of residuals and standardized residuals to assess model fit and assumptions.
  • Creation of plots for visual inspection of residual distribution and anomalies.

Results and Interpretation

  • R-Squared Value: Increased from 0.31 (with only first income) to 0.45 in the MLR model, indicating an improvement in model fit with the addition of monthly payments.
  • Adjusted R-Squared: Close to the R-squared value at approximately 0.448, indicating that the model adequately adjusts for the number of predictors.
  • Standard Error: Decreased compared to the individual regression models, suggesting better precision with the inclusion of two independent variables.

ANOVA and Regression Output

  • SSR and SSE: Noted significant sums of squares for regression and error, with SSR increasing in the MLR model compared to single-variable models.
  • F-Statistic: Indicates the overall significance of the regression model with a very low p-value, leading to rejection of the null hypothesis that both beta coefficients are zero.

Coefficient Analysis

  • Interpretation of Coefficients:
  • B1 (First Income): A unit increase in first income, holding monthly payments constant, increases debt by 0.025.
  • B2 (Monthly Payments): A unit increase in monthly payments, holding first income constant, increases debt by 2.09.
  • Significance Tests: Both coefficients are significant with very low p-values, confirming their influence on household debt.

Conclusion

  • Implications: The analysis demonstrates a significant relationship between household debt and both first income and monthly payments.
  • Further Analysis: Suggests conducting further MLR with additional variables like utilities to explore other potential influences on debt.
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