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The multivariate linear model is Y (n×m) = X (n×p) B (p×m) + E (n×m) The multivariate linear model can be fit with the lm function in R, where the left-hand side of the model comprises a matrix of response variables, and the right-hand side is specified exactly as for a univariate linear model (i.e., with a single response variable). This paper explains how to use the Anova and linearHypothesis functions in the car package to perform convenient hypothesis tests for parameters in multivariate linear models, including models for repeated-measures data.
Fox et al. (Tue,) studied this question.