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.
