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How to extend multiple regression hypothesis tests to multivariate?

I have a basic multivariate regression model $\mathbf{Y}$ = $\mathbf{XB}$ + error $\begin{bmatrix}y_{1i} \\ y_{2i} \\ \vdots \\ y_{ki} \end{bmatrix}$ = $\begin{bmatrix} X_{11} & ... & X_{1p} ...
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Multivariate multiple regression in R

I have 2 dependent variables (DVs) each of whose score may be influenced by the set of 7 independent variables (IVs). DVs are continuous, while the set of IVs consists of a mix of continuous and ...