General linear model

Summary

The general linear model writes a matrix of responses as a known design matrix times an unknown coefficient matrix, plus random errors with mean zero. It contains multiple linear regression, analysis of variance, analysis of covariance, multivariate analysis of variance and the $t$-test and F-test as special cases. Its theory rests on ordinary least squares and on projections in $\R^n$. It should not be confused with the generalized linear model, which allows non-normal responses and a link function.