Regression Models

Abstract

The aim of regression models is to model the variation of a quantitative response variable y in terms of the variation of one or several explanatory variables (x ₁,…,x _p )^⊤. We have already introduced such models in Chapters 3 and 7 where linear models were written in (3.50) as

$$y={\mathcal{X}} \beta + \varepsilon,$$

where y(n×1) is the vector of observation for the response variable, ${\mathcal{X}} (n\times p)$ is the data matrix of the p explanatory variables and ε are the errors. Linear models are not restricted to handle only linear relationships between y and x. Curvature is allowed by including appropriate higher order terms in the design matrix ${\mathcal{X}}$.