Regression Models

Abstract

In Chap. 3, we have introduced the linear model

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

(8.1)

where Y denotes a (n × 1) random vector of observations of the response variable, $\mathcal{X}$ is the (n × r) design matrix containing the corresponding values of the explanatory variables, β is a (r × 1) vector of unknown parameters and $\varepsilon$ is a (n × 1) random vector such that $\mathop{\mathrm{\mathsf{E}}}\nolimits \varepsilon = 0_{n}$ and $\mathop{\mathrm{\mathsf{Var}}}\nolimits \varepsilon =\sigma ^{2}\mathcal{I}_{n}$.