Theoretical Statistics pp 269-299 | Cite as

# General Linear Model

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## Abstract

The general linear model incorporates many of the most popular and useful models that arise in applied statistics, including models for multiple regression and the analysis of variance. The basic model can be written succinctly in matrix form as
where

$$Y = X\beta + \epsilon,$$

(14.1)

*Y*, our observed data, is a random vector in \(\mathbb{R}^n, X\) is an*n*×*p*matrix of known constants, \(\beta \in \mathbb{R}^p\) is an unknown parameter, and $$ is a random vector in ℝ^{ n }of unobserved errors. We usually assume that ε_{1},…, ε_{ n }are a random sample from \(N(0, \sigma^2)\), with σ > 0 an unknown parameter, so that$$\epsilon \sim N(0, \sigma^2 I).$$

(14.2)

## Keywords

General Linear Model Simple Linear Regression Design Matrix Full Rank Unbiased Estimator
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© Springer New York 2009