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Linear Models in Matrix Form

A Hands-On Approach for the Behavioral Sciences

  • Jonathon D.¬†Brown

Table of contents

  1. Front Matter
    Pages i-xix
  2. Jonathon D. Brown
    Pages 1-37
  3. Jonathon D. Brown
    Pages 39-67
  4. Jonathon D. Brown
    Pages 69-104
  5. Jonathon D. Brown
    Pages 105-145
  6. Jonathon D. Brown
    Pages 147-184
  7. Jonathon D. Brown
    Pages 185-226
  8. Jonathon D. Brown
    Pages 227-260
  9. Jonathon D. Brown
    Pages 303-340
  10. Jonathon D. Brown
    Pages 341-375
  11. Jonathon D. Brown
    Pages 377-408
  12. Jonathon D. Brown
    Pages 409-441
  13. Jonathon D. Brown
    Pages 443-467
  14. Jonathon D. Brown
    Pages 469-492
  15. Jonathon D. Brown
    Pages 493-527
  16. Back Matter
    Pages 529-536

About this book

Introduction

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.

Keywords

Computational Statistics Linear Equations Linear Model Linear Model in Matrix Form Matrix Algebra Political Science Modeling Psychometrics

Authors and affiliations

  • Jonathon D.¬†Brown
    • 1
  1. 1.Department of PsychologyUniversity of WashingtonSeattleUSA

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