Classical regression approaches, including ordinary least squares, rely on strong assumptions such as constant variance and normality of residuals, which are often violated in real-world data. Although log-transformation is commonly used to stabilise variance, it may introduce re-transformation bias and fail to address heteroscedasticity and asymmetric dependence structures adequately. To overcome these limitations, this study proposes a copula-based regression framework for modelling data in the presence of heteroscedastic error structures. The proposed approach explicitly accounts for heteroscedasticity without requiring restrictive distributional assumptions. A comprehensive simulation study is conducted under varying dependence levels and heteroscedastic scenarios to compare the performance of the proposed method with usual regression models and log-linear models. The simulation results demonstrated that the proposed copula-based model consistently outperformed conventional approaches, achieving an average mean absolute percentage error of 0.21, compared with 0.27 and 0.36 for the linear and log-linear models, respectively. Across all simulation settings, the copula-based model reduced prediction errors by approximately 6%-33% relative to the linear model and 24%-57% relative to the log-linear model. A real-data application using the Wages dataset from the ISLR package in R further confirmed these findings, where conventional log-linear models failed to adequately capture heteroscedasticity. In contrast, the proposed copula-based regression framework produced more accurate predictions, demonstrating its effectiveness for modelling heteroscedastic data. Overall, the results demonstrate that copula-based regression represents a viable modelling alternative in the presence of heteroscedasticity and complex dependence structures.
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