Bootstrapping Two-step Least Squares Approach for Solving Heteroscedasticity Problem in Linear Regression Analysis

Abstract

In this study, the problem of heteroscedasticity which is referred to as unequal variability in linear regression analysis is considered. Bootstrapping Two Step Least Squares (BWLS) for controlling heteroscedasticity in linear regression analysis was proposed. This method was compared with other existing methods (Ordinary Least Squares, Weighted Least Squares, Two Step Least Squares, Bootstrap Weighted Least) based on the Root Mean Square Error (RMSE) of the regression coefficient and the Euclidean norm was used to measure the accuracy across all coefficients. Simulated data was used in the comparison. The results show that the proposed bootstrap method performed better than the other methods in performing regression analysis in the presence of heteroscedasticity across all the sample sizes and at various levels of heteroscedasticity considered from the analysis. Real life data was used to demonstrate the results, which corresponds with result obtain from the simulation studies.