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The general linear model is a statistical linear model. It may be written as : where Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors or 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 model 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. == Multiple linear regression == Multiple linear regression is a generalization of linear regression by considering more than one independent variable, and a specific case of general linear models formed by restricting the number of dependent variables to one. The basic model for linear regression is : In the formula above we consider ''n'' observations of one dependent variable and ''p'' independent variables. Thus, ''Y''''i'' is the ''i''th observation of the dependent variable, ''X''''ij'' is ''i''th observation of the ''j''th independent variable, ''j'' = 1, 2, ..., ''p''. The values ''β''''j'' represent parameters to be estimated, and ''ε''''i'' is the ''i''th independent identically distributed normal error. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「General linear model」の詳細全文を読む スポンサード リンク
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