variables that share the same set of explanatory variables and hence are estimated simultaneously with each other: or more compactly for all observations indexed as i = 1, ... , n and for all dependent variables indexed as j = 1, ... , m. Note that, since each dependent variable has its own set of regression parameters to be fitted, from a computational point of view the general multivariate regression is simply a sequence of standard multiple linear regressions using the same explanatory variables. Comparison to generalized linear model The general linear model and the generalized linear model (GLM)Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications. are two commonly used families of statistical methods to relate some number of continuous and/or categorical predictors to a single outcome variable. The main difference between the two approaches is that the general linear model strictly assumes that the residuals will follow a conditionally normal distribution, while the GLM loosens this assumption and allows for a variety of other distributions from the exponential family for the residuals. Of note, the general linear model is a special case of the GLM in which the distribution of the residuals follow a conditionally normal distribution. The distribution of the residuals largely depends on the type and distribution of the outcome variable; different types of outcome variables lead to the variety of models within the GLM family. Commonly used models in the GLM family include binary logistic regression for binary or dichotomous outcomes, Poisson regression for count outcomes, and linear regression for continuous, normally distributed outcomes. This means that GLM may be spoken of as a general family of statistical models or as specific models for specific outcome types. Applications An application of the general linear model appears in the analysis of multiple brain scans in scientific experiments where contains data from brain scanners, contains experimental design variables and confounds. It is usually tested in a univariate way (usually referred to a mass-univariate'' in this setting) and is often referred to as statistical parametric mapping. See also Bayesian multivariate linear regression F-test t-test Notes References Regression models