Transforming to Normality in Regression Analysis with Exponentially Residuals

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 back-transformed 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.