Diagnosing and correcting violations of normality and constant variance assumptions in multiple linear regression analysis

This study showcased the significance of correcting for Non-normality and Nonconstant variance of residuals in ‎linear regression modelling. The concept was demonstrated by using two different hypothetical, Data M (the Initial Dataset) ‎and Data N (the Initial Dataset). The diagnosis of non-normality and nonconstant variance was performed using the ‎Anderson-Darling test (or D’Agostino Omnibus test) and White test, respectively, revealing their presence in the models for ‎the initial datasets, while the assumptions of no multicollinearity and no autocorrelation were met. The model established for ‎Data M (the Initial Dataset) was statistically significant with an R-square value of 0.538, an AIC value of 1071.424, an SBC ‎value of 1083.787, and an RMSE value of 9774.849. Similarly, the model established for Data N (the Initial Dataset) was ‎statistically significant with an R-square value of 0.865, an AIC value of 768.443, an SBC value of 776.427, an RMSE ‎value of 584.946. Data M (the Initial Dataset) and Data N (the Initial Dataset) were transformed using the Semi-Logarithm ‎transformation method, generating new sets of data, Data M (Non-normality and Nonconstant Variance Corrected) and Data ‎N (Non-normality and Nonconstant Variance Corrected). After the correction was made, the datasets complied with all the ‎linear assumptions necessary for regression analysis. The multiple linear regression model estimated for Data M (Non-‎normality and Nonconstant Variance Corrected) was found to be statistically significant, achieving an R-square value of ‎‎0.748, an AIC value of -81.061, an SBC value of -61.699, and an RMSE value of 0.473; and the model established for Data ‎N (Non-normality and Nonconstant Variance Corrected) was statistically significant with an R-square value of 0.871, an ‎AIC value of -145.907, an SBC value of -137.529, an RMSE value of 0.287. Based on the R-squares, AIC, SBC, and ‎RMSE values for both initial and transformed models, it was concluded that the estimated regression model for Data M ‎‎(Non-normality and Nonconstant Variance Corrected) and Data N (Non-normality and Nonconstant Variance Corrected) ‎demonstrated superior model performance when compared to the regression models for Data M (the Initial Dataset) and ‎Data N (the Initial Dataset)‎.