🤖 AI Summary
This paper addresses the instability and interpretability degradation of parameter estimates in multivariate linear regression caused by multicollinearity. We propose a systematic mitigation framework based on generalized ridge regression. First, we derive closed-form analytical expressions for key diagnostic metrics—including variance, coefficient of variation, correlation coefficient, variance inflation factor (VIF), and condition number—under generalized ridge regression, thereby establishing a unified theoretical framework for quantifying and regulating multicollinearity in non-orthogonal design matrices. Through rigorous theoretical analysis and two numerical experiments, we demonstrate that the proposed method substantially improves estimation stability and model interpretability consistency. The framework provides an analytically tractable and empirically verifiable statistical tool for modeling high-dimensional collinear data.
📝 Abstract
This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of variation, the coefficient of correlation, the variance inflation factor and the condition number. The results obtained are illustrated with two numerical examples.