Simultaneous raise regression: a novel approach to combating collinearity in linear regression models

The effect of multicollinearity deems the estimation and interpretation of regression coefficients by the method of Ordinary Least Squares (OLS) as burdensome. Even if there are alternate techniques like Ridge Regression (RR) and Liu Regression (LR) for providing a model, the statistical inference is impaired. In this study, we present the Simultaneous Raise Regression (SRR) approach, which is based on QR decomposition and reduces multicollinearity while preserving statistical inference. In contrast to the classical raise approach, the proposed strategy attains the number of variables to be raised and their corresponding raise parameter with a single step. We have designed Sequential Variation Inflation Factor for this purpose (SVIF). The performance of SRR has been compared with OLS, Ridge Regression and Liu Regression through Predictive Root Mean Square Error (PRMSE), Predictive Mean Absolute Error (PMAE) and Standard Error of the coefficients. To validate the suggested approach, a simulation study and a real-life example are presented; both outcomes imply that our proposed method outperforms the competition.