Irregular errors such as heteroscedasticity and nonnormality remain major challenges in linear modeling. These issues often lead to biased inference and unreliable measures of uncertainty. Traditional remedies, such as log transformations, robust standard errors, or weighted least squares, only partially address the problem and may fail when heteroscedasticity interacts with skewness or nonlinear mean patterns. To address this, we propose a two-stage cumulative distribution function-based beta regression framework. The response is first transformed using an empirical distribution function and modeled with a flexible beta distribution, then mapped back to the original scale via the empirical quantile function. Because the beta distribution links variance directly to its mean and precision, heteroscedasticity and nonnormality are handled naturally, without requiring ad hoc variance assumptions or weighting schemes. A comprehensive Monte Carlo simulation study evaluates the proposed method against other methods such as weighted least squares. The results show that the cumulative distribution function-based beta method outperforms traditional competitors. By directly modeling the full conditional distribution, it offers reliable inference, calibrated prediction even under extreme assumption violations, and meaningful interpretation of effects through percentile shifts.

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