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 Chaps. 3 and 7 where linear models were written in (3.50) as

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

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 $\varepsilon$ are the errors.