Analyzing the Relationship Between Multicollinearity and Model Interpretability in Multiple Regression Analysis

Posted: Jun 28, 2024

• Mason Anderson
• Samuel Smith
• Grace Wilson

Abstract

Multiple regression analysis stands as one of the most widely employed statistical techniques across scientific disciplines, serving as a fundamental tool for understanding relationships between variables and making predictions. The interpretability of regression models represents a critical concern for researchers seeking not only to predict outcomes but to comprehend the underlying mechanisms driving observed phenomena. Traditional statistical education has consistently emphasized multicollinearity as a problematic condition that compromises regression analysis by inflating coefficient variances and creating instability in parameter estimates. This conventional perspective has led to widespread application of variance inflation factor thresholds and correlation matrices as diagnostic tools, with researchers typically seeking to eliminate or reduce multicollinearity whenever detected. However, this universally negative view of multicollinearity fails to account for the complex interplay between statistical properties and substantive interpretability in real-world research contexts. In many applied settings, particularly in social sciences, healthcare, and environmental studies, variables naturally exhibit correlations that reflect genuine underlying relationships in the phenomena being studied. The forced orthogonalization of such variables through statistical manipulation may produce mathematically elegant models that nonetheless lack contextual meaning and practical interpretability. This research challenges the orthodox position by proposing that multicollinearity exists on a continuum of effects rather than representing a binary problem.