1 - A Brief Overview of Linear Models

Abstract

Generalized linear regression models are the global framework of this book, but we shall only introduce them. Chapter 1 is dedicated to (standard and Gaussian) linear regression models. Despite just being a special case of generalized linear models, linear models need to be discussed separately for a few reasons. Performing linear regression in a Gaussian setting always leads to specific distributions (e.g. for the test statistics), regardless of sample size. By contrast, when working with generalized linear models, test statistics and confidence intervals are constructed by asymptotic arguments. Furthermore, generalized linear models are an extremely general approach to expressing the relationship between a response variable and a set of explanatory variables. It is easier to appreciate the benefits of these tools by considering the special case of Gaussian linear models before introducing the general formalism.