Assessment of the Effects of Influential Observations on Heteroscedasticity Detection in Multiple Linear Regression

Abstract

Influential observations can substantially affect regression diagnostics and lead to misleading conclusions about the presence of heteroscedasticity. This study investigated the effects of bad leverage points (BLPs) and vertical outliers (VOs) on heteroscedasticity detection in multiple linear regression using the classical White test (WT) and robust White test (RWT). Four numerical examples and Monte Carlo simulation experiments involving 2,000 replications were employed to evaluate the behaviour of both tests under different contamination conditions. The simulation experiments considered sample sizes ranging from 20 to 250 and contamination levels of 5% and 10%. Results indicated that introducing BLPs into initially homoscedastic datasets increased the tendency of the classical White test to reject the homoscedasticity hypothesis, while the robust White test generally retained the expected decision. Conversely, introducing VOs into heteroscedastic datasets reduced the ability of the classical White test to detect heteroscedasticity, whereas the robust test continued to reject the null hypothesis. These findings suggest that influential observations can either enhance or mask evidence of heteroscedasticity in conventional regression diagnostics. The study highlights the importance of robust diagnostic procedures when analysing contaminated regression datasets and recommends further evaluation of their empirical rejection rates and statistical properties under alternative contamination mechanisms.