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The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as

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• The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise).The errors are usually assumed to be uncorrelated across measurements, and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and U. The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable. If Y, B, and U were column vectors, the matrix equation above would represent multiple linear regression. Hypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests. In multivariate tests the columns of Y are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix. (en)
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• The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as (en)
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• General linear model (en)
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