Performing legitimate parametric regression analysis without knowing the true underlying random mechanisms

Real data are rarely normally distributed. Nonetheless, regression analysis is routinely done under the assumption of normality. Such a practice generally results in invalid statistical inferences once normality is false. This article shows how one could carry out corrected normal regression and gamma regression analysis, which provides asymptotically valid inferences without the knowledge of the true underlying distributions. No additional programming is necessary in order to implement the proposed novel regression method. Outputs provided by existing statistical software suffice.