A comprehensive review of regression models under heteroscedasticity: research review

Abstract

Heteroscedasticity is a common problem in linear regression analysis that can reduce the efficiency of ordinary least squares estimates, distort standard errors, and lead to unreliable statistical inference. This study aims to systematize the main approaches to detecting and correcting heteroscedasticity and to compare their effectiveness using simulated data. Ordinary Least Squares (OLS), Weighted Least Squares (WLS), Huber robust regression, and quantile regression were evaluated using original, logarithmically transformed, and Box–Cox-transformed data for sample sizes of 100, 200, and 500 observations. Heteroscedasticity was assessed using the Breusch–Pagan and White tests, while predictive performance was evaluated using Mean Squared Error (MSE). The results demonstrate that the Box–Cox transformation produced the lowest MSE values across all sample sizes. At n=100, it achieved formal homoscedasticity in all six regression models, whereas at n=200 both logarithmic and Box–Cox transformations achieved comparable results in five of six models. At n=500, the diagnostic tests remained highly sensitive to residual variance heterogeneity despite substantial reductions in prediction error. These findings indicate that the selection of an appropriate heteroscedasticity correction method should be based on the joint consideration of formal diagnostic tests and predictive-performance measures, particularly when large samples are analyzed.