Overlap of OLS Regression and Principal Loading Analysis

Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. Potentially, principal loading analysis and ordinary least squares regression coincide by construction. We contribute conditions under which both methods intersect. Further, we provide bounds for the cut-off value in principal loading analysis for the case of intersection. This gives a choice for such a threshold based on the perturbation matrices.