Transforming to Normality in Regression Analysis with Exponentially Residuals

Abstract

In this article, a simulated study is introduced, focusing on the use of power transformation to estimate a nonlinear regression model in the presence of residuals following an exponential distribution. Four criteria were employed to estimate the power parameter: the p-value of Shapiro-Wilk test statistics for both the transformed and backtransformed data's normality, maximum likelihood estimation, and coefficient of determination. The findings of the study indicate that while it is possible to identify a range of viable solutions to select the optimal power parameter, finding a single optimal value that satisfies all estimation and decision methods is not feasible.