Multicollinearity in Regression Models and Its Geometric Solutions

Multicollinearity is a pervasive challenge in regression analysis that inflates variance estimates and obscures the interpretation of predictor effects. This study develops intuitive geometric approaches for addressing multicollinearity within an observation-axes framework. We examine the structure of multicollinearity and introduce three complementary geometric approaches. First, we present a simple and effective method for resolving multicollinearity when the causal ordering among predictors is known. Second, we refine and extend the geometric interpretation of Principal Component Analysis (PCA) proposed by Wickens (2014) by incorporating angular information between predictor variables. Third, motivated by Partial Least Squares (PLS) regression, we develop a geometry-based method that identifies directions jointly determined by predictor variance and alignment with the response. Together, these solutions demonstrate that geometric reasoning provides richer and more intuitive insights into variable relationships, offering substantial pedagogical and methodological value as a resource for beginners and as a foundation for future research in regression analysis.