This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.

This book demonstrates the importance of computer-generated statistical analyses in behavioral science research, particularly those using the R software environment. Statistical methods are being increasingly developed and refined by computer scientists, with expertise in writing efficient and elegant computer code. Unfortunately, many researchers lack this programming background, leaving them to accept on faith the black-box output that emerges from the sophisticated statistical models they frequently use. Building on the author's previous volume, Linear Models in Matrix Form, this text bridges the gap between computer science and research application, providing easy-to-follow computer code for many statistical analyses using the R software environment. The text opens with a foundational section on linear algebra, then covers a variety of advanced topics, including robust regression, model selection based on bias and efficiency, nonlinear models and optimization routines, generalized linear models, and survival and time-series analysis. Each section concludes with a presentation of the computer code used to illuminate the analysis, as well as pointers to packages in R that can be used for similar analyses and nonstandard cases. The accessible code and breadth of topics make this book an ideal tool for graduate students or researchers in the behavioral sciences who are interested in performing advanced statistical analyses without having a sophisticated background in computer science and mathematics.