Box-Cox Optimal Parameter Estimation for Multiple Regressions with Homoscedasticity

Abstract

Many real data do not conform to the assumption of homoscedasticity. In multiple regressions, the violation of the homoscedasticity assumption can be a complicating factor in estimating parameters, hypothesis testing and model selection. In this study, the violation of this assumption can be overcome by using the Box-Cox transformation. An investigation using simulation designs with data generated from three skewed sample data of non-normal distributions namely Exponential, Gamma and Beta distributions based on the various sample sizes (n = 100, 500 and 1000) are carried out. Hence, the simulation studies are implemented to estimate optimal lambda in the Box-Cox transformation based on data sets with different variances with errors that follow a normal distribution with a mean (µ = 0) and different variances (r 2 = 50, 100). Results show that lambda = 0.30* and lambda = 0.40* are the most often optimal lambda produced for these three distributions. As such, Box-Cox transformation with optimal lambda value improves analyses in multiple regressions particularly in the presence of homoscedasticity.