Article

Geometric Residual Projection in Linear Regression: Rank-Aware Operators and a Geometric Multicollinearity Index

2026-01-28

Abstract excerpt

Residuals play a central role in linear regression, but their geometric structure is often obscured by formulas built from matrix inverses and pseudoinverses. This paper develops a rank-aware geometric framework for residual projection that makes the underlying orthogonality explicit. When the design matrix has codimension-one, the unexplained part of the response lies on a single unit normal to the predictor spac...

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Literature Corpus work: ac4d77cd-a248-5d24-a96b-14934a9004c0
DOI: 10.20944/preprints202601.2172.v1

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