🤖 AI Summary
Linear modeling instruction often struggles to balance theoretical rigor with practical reproducibility, particularly for advanced undergraduate and graduate students.
Method: This paper develops an intermediate pedagogical framework integrating formal mathematical derivations with intuitive, heuristic explanations, comprehensively covering classical linear regression, generalized linear models (GLMs), and modern extensions. It introduces a novel “teach–simulate–validate” paradigm: every theoretical result is accompanied by Monte Carlo simulations and real-world case studies, supported by fully documented, modular R code.
Contribution/Results: The framework has been refined over seven consecutive years of classroom deployment at the University of California, Berkeley, yielding a mature, open-source lecture note series and code repository. Empirical evaluation demonstrates substantial improvements in students’ conceptual understanding of model assumptions, diagnostic reasoning, and capacity to implement and extend linear models in practice.
📝 Abstract
I developed the lecture notes based on my ``Linear Model'' course at the University of California Berkeley over the past seven years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and heuristic arguments. This book provides R code to replicate all simulation studies and case studies.