A general linear model is a statistical model of the form
 |
where 
is a known design matrix, 
is a vector of unknown parameters, and the random error
vector has expectation value zero. The usual
normal linear model further assumes a multivariate
normal distribution for the errors, with covariance
matrix 
.
Multiple linear regression and fixed-effects analysis of variance are instances of the general linear model. It should not be confused with a generalized linear model, which permits nonnormal response distributions and relates the mean response to a linear predictor through a link function.
