Regression Model Diagnostic, Test and Robustification in the Presence of Multicollinear Covariates: A Review

Regression techniques has so many applications in the fields of science, social science and engineering. This article contributes to the theoretical and empirical literature related to the use of regression techniques and methods in experimental and non experimental subjects. We attempt to review the basic pedagogic concepts of classical linear regression model with respect to the necessary assumptions, optimality conditions, and its applications in quantitative analysis, environmental science and engineering. We address some mechanics of regression model robustification with an algebraic exposition of the ordinary least squares regression coefficients. Finally, we point out the peculiarity of the presence of multicollinear covariates as revealed in our empirical results using statistical software packages like STATA and SPSS.