Estimating Optimal Parameter of Box-Cox Transformation in Multiple Regression with Non-normal Data

Abstract

Normally distributed data are needed in many statistical analyses including multiple regression (MR). When data is not normally distributed, reme- dial actions in making the data normal are necessary. In this study, the violation of this assumption is overcome by using the Box-Cox transformation (BCT). 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 (100, 500 and 1000) are carried out. Hence, the simulation studies are implemented to estimate optimal lambda in the BCT based on two scenarios: (i) response variable (Y) follows several non-normal distributions and (ii) errors from several non-normal distributions. The results show that lambda = 0.30, 0.40 and 0.50 are the optimal lambdas produced for Exponential, Gamma and Beta Distributions. Therefore, BCT with optimal lambda value improves analyses in MRs when data are not normal. The performance of BCT method is also illustrated using the real-life data.