MML-14-02: Geometric Projection View of OLS vs. Probabilistic MLE View – Practice Quiz

35 worked single-select and multiselect questions on Geometric Projection View of OLS vs. Probabilistic MLE View. Cognitive level: Tier 1–4. Prerequisites: QS 14.1, Part 03, Part 10.

Develop conceptual understanding, step-by-step computations, ML diagnostics and the assigned theoretical derivations. Each explanation analyzes every choice by its content.

Learning objectives: Interpret fitted values as an orthogonal column-space projection. Derive hat-matrix identities and residual geometry. Calculate small projections, leverages and residuals. Build Gaussian conditional likelihoods with explicit noise assumptions. Prove OLS-MLE equivalence and distinguish coefficient and variance estimation. Analyze weighted errors, rank deficiency and changes of basis. Connect geometric degrees of freedom to probabilistic uncertainty.

Study references: Deisenroth, Faisal & Ong, Mathematics for Machine Learning, Sections 9.1–9.2.1; Deisenroth, Faisal & Ong, Mathematics for Machine Learning, Section 9.3, equations 9.43–9.61.