# Chapter 2: Linear Regression Models

• Peter K. Dunn
• Gordon K. Smyth
Chapter
Part of the Springer Texts in Statistics book series (STS)

## Abstract

The most common of all regression models is the linear regression model, introduced in this chapter. This chapter also introduces the notation and language used in this book so a common foundation is laid for all readers for the upcoming study of generalized linear models: linear regression models are a special case of generalized linear models. We first define linear regression models and introduce the relevant notation and assumptions. We then describe least-squares estimation for simple linear regression models and multiple regression models. The use of the R functions to fit linear regression models is explained, followed by a discussion of the interpretation of linear regression models. Inference procedures are developed for the regression coefficients, followed by analysis of variance methods. We then discuss methods for comparing nested models, and for comparing non-nested models. Tools to assist in model selection are then described.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

## Authors and Affiliations

• Peter K. Dunn
• 1
• Gordon K. Smyth
• 2
1. 1.Faculty of Science, Health, Education and EngineeringSchool of Health of Sport Science, University of the Sunshine CoastQueenslandAustralia
2. 2.Bioinformatics DivisionWalter and Eliza Hall Institute of Medical ResearchParkvilleAustralia