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:<math> Y_{ij} = \beta_{0j} + \beta_{1j} X_{i1} + \beta_{2j}X_{i2} + \ldots + \beta_{pj} X_{ip} + \epsilon_{ij}</math> or more compactly <math>Y_{ij} = \beta_{0j} + \sum \limits_{k=1}^{p} { \beta_{kj} X_{ik}} + \epsilon_{ij}</math>
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.
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