Honors Linear Regression Models

This high-level course in linear regression delves deeply into the theoretical and geometric aspects of regression analysis, offering a comprehensive exploration of its foundational principles and advanced topics. Students will study regression within vector space contexts, emphasizing the role of inner products and orthogonal projections. The analysis of projection matrices will include their properties, such as idempotence and symmetry, and their implications for regression diagnostics and metrics. Students will explore why various test statistics follow t- and F-distributions, with careful attention to degrees of freedom and their derivations. As the course progresses, it will address the complexities of high dimensional regression scenarios.