The hope of such multivariate analyses is, that the consideration of possible dependencies between the outcomes may lead to procedures with better power (in case of inference) or accuracy (in case of prediction) compared to separate univariate analyses. Unlike univariate multiple regression (with d = 1), which also includes multiple features X ∈ R p, multivariate regression wants to specify the relationship of several outcome variables with X , i.e. we want to perform a multivariate (also called multi-output) regression analysis. Then, we are often interested in finding a functional relationship between the output Y and some feature variables X ∈ R p Data are said to be multivariate if the response not only consists of one variable, but of d ≥ 2 output variables, say Y ∈ R d. Multivariate data occur in a variety of disciplines, for example in biomedical research, the social sciences, or econometrics.
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