This book provides a holistic view of linear models as the foundation for many statistical and machine learning methods. It covers the theory of the standard linear model, then explores extensions of that model and the use of linear predictors in a broad range of more computationally demanding modeling techniques. Optimization procedures that underlie this evolutionary tree of models are also covered, while highlighting the central role of the linear model in statistics, machine learning, and data science. The early chapters cover linear model formulation, matrix algebra, distribution theory, and estimation and inference for the standard linear model. Following an overview of optimization techniques, the later chapters cover models for correlated responses, regularization, models for non-normal responses, predictive models, and models for inherently nonlinear relationships. Throughout, the emphasis is on the interrelated ideas connecting these many methods that collectively address a wide range of modeling situations.

While the book emphasizes theoretical foundations, it also recognizes that implementation is essential for understanding why and how the methods work. Numerous data analysis examples illustrate modeling principles and the corresponding theory. Computing code and datasets are available from the book's GitHub repository and permanent Zenodo archive. Exercises provide hands-on training in applying the methods.

Designed as a graduate-level textbook for students in statistics, data science, and related fields, the book provides a concise and engaging treatment of linear models and their extensions. After studying this book, readers will have a comprehensive understanding of linear models and their connections to a broad range of methods employing linear predictors, providing a solid foundation for advanced study and research in data science.

Yili Hong is a Professor of Statistics and Cathie and Tom Woteki Data Science Faculty Fellow at Virginia Tech (VT). He is also a Co-Director of the VT Statistics and Artificial Intelligence Laboratory (VT-SAIL). His research interests include engineering statistics, machine learning and statistical computing, and biostatistics. He has authored over 100 publications in prestigious journals such as the Journal of the American Statistical Association, Annals of Applied Statistics, Technometrics, and Journal of Quality Technology. He has served as an associate editor for Technometrics and Journal of Quality Technology. He won the 2011 DuPont Young Professor Award and the 2016 Frank Wilcoxon Prize in Statistics. 

Xinwei Deng is a Professor of Statistics at Virginia Tech (VT). He is also a Cathie and Tom Woteki Data Science Faculty Fellow at VT and Co-Director of the VT Statistics and Artificial Intelligence Laboratory (VT-SAIL). His research interests include interface between experimental design and machine learning, statistical learning of complex data, and uncertainty quantification. He has authored over 100 publications in prestigious journals such as the Annals of Statistics, Journal of the American Statistical Association, Annals of Applied Statistics, and Technometrics. He has served as a department editor for IISE Transactions on Data Science, Quality and Reliability and an associate editor for Annals of Applied Statistics, Statistica Sinica, Technometrics, and International Statistical Review, among others.

John P. Morgan is a Professor of Statistics at Virginia Tech. His research interests include experimental design and linear models theory. He has numerous publications in flagship journals, including Annals of Statistics, Biometrika, Journal of the American Statistical Association, and Journal of the Royal Statistical Society, Series B. He has served as an associate editor for the Journal of the American Statistical Association, The American Statistician, and the Journal of Statistical Planning and Inference. He is founding director of the Academy of Integrated Science at Virginia Tech for leading the development of interdisciplinary, science-based degree programs.