Dimensionality-Prediction Dilemma: The Dual Effects of PCA in Housing Price Regression Modeling

This study evaluates the practical dimensionality reduction efficacy of Principal Component Analysis (PCA) and its consequential impacts on regression-based housing price prediction by comparing three modelsmultiple linear regression, ridge regression, and LASSO regressionapplied to California housing data, while preliminarily exploring the underlying mechanisms. The research first establishes a spatial-economic-social framework influencing housing prices through data dimensionality reduction. This process initiates with KMO-Bartlett validation of the dataset, followed by variable screening conducted under comprehensive consideration of variables practical significance, and subsequently implements Kaiser criterion-guided PCA to derive three primary factors governing housing prices within this spatiotemporal context: Spatial Distribution & Density, Geographic Location, and Economic Status, thereby yielding interpretable components reflecting spatial, geographic, and economic dimensions. Further findings reveal that all models exhibit quantitatively comparable declines in predictive performance post-PCA implementation, with ridge and LASSO regression demonstrating nearly equivalent performance to ordinary linear regression, suggesting limited benefits of regularization in this scenario. These results challenge the presumed utility of PCA in regression workflows, highlighting that simplistic PCA dimensionality reduction may discard inherent latent predictive signals within housing datasets. These insights advocate for circumspect adoption of PCA in real estate analytics and emphasize the necessity for domain-specific regularization strategies to balance interpretability with predictive fidelity.