General Linear Model

  • Robert W. Keener
Part of the Springer Texts in Statistics book series (STS)


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
$$Y = X\beta + \epsilon,$$
where 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 ε1,…, ε n are a random sample from \(N(0, \sigma^2)\), with σ > 0 an unknown parameter, so that
$$\epsilon \sim N(0, \sigma^2 I).$$


General Linear Model Simple Linear Regression Design Matrix Full Rank Unbiased Estimator 
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Copyright information

© Springer New York 2009

Authors and Affiliations

  • Robert W. Keener
    • 1
  1. 1.Department of StatisticsUniversity of MichiganAnn ArborUSA

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