Using a logarithmically weighted exponential regression model to address data heterogeneity

Abstract

Among various regression techniques, exponential regression is widely used to model growth and decay phenomena in economics, biology, epidemiology, and engineering. However, the classical exponential regression model often fails when applied to heteroscedastic data with non-constant variance and skewed distributions. Logarithmically weighted exponential regression addresses these issues by incorporating logarithmic weights into the estimation process. This study presents the mathematical framework of log-weighted exponential regression, including estimation procedures such as weighted least squares and weighted maximum likelihood, along with computational considerations for implementing the model in Python and R (Altun, 2021).
Case studies from economics, epidemiology, engineering, and environmental sciences illustrate the practical application of the model. Comparative analyses of linear and traditional exponential regression demonstrate the superior performance and robustness of the log-weighted model in real-world datasets. The study also outlines its advantages, limitations, and potential avenues for future extensions (Greene, 2018; Wooldridge, 2020).