The Exponentiated Normal Regression Model with Application

Abstract This paper introduces a novel regression model based on the Exponentiated Normal (Exp-N) distribution and compares its performance with traditional Normal regression. Using the maximum likelihood method, parameters for both the regression structure and the underlying distributions were estimated. The Exp-N regression model was thoroughly investigated, with several new statistical properties derived and validated. Applied to a real-world dataset of testosterone hormone levels, the model demonstrated superior goodness-of-fit over the conventional Normal regression, offering a more flexible and accurate framework for data analysis in medical and biological research.