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If I wish to find the relationship between a continuous independent variable (IV) and a single continuous dependent variable (DV), I can conduct a regression (or a correlation, as there is only one IV).

If I wish to find the relationship between a categorical IV and a single dependent variable, I can conduct an ANOVA, which is equivalent to conducting a regression with dummy-coded groups representing the categorical IV.

If I wish to find the relationship between a categorical IV and more than one continuous DV, I can conduct a MANOVA.

Is this equivalent to multivariate regression (i.e., as addressed in this question) with dummy-coded groups representing the categorical IV? In other words, does the relationship between regression and ANOVA parallel the relationship between multivariate regression and MANOVA?

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    $\begingroup$ does the relationship between regression and ANOVA parallel the relationship between multivariate regression and MANOVA? Yes, so. MANOVA is synonymic to MV linear regression in the same sense as ANOVA to UV linear regression. Note however that in some contexts people extend the class definition of MV regression to specialized multivariate techniques such as, for example, partial least squares (PLS) regression. Then "MV Regression" becomes a bit wider concept than just "MANOVA-like". $\endgroup$
    – ttnphns
    Commented Oct 27, 2015 at 9:21
  • $\begingroup$ Yes. See also the answer to stats.stackexchange.com/questions/11127, it might be helpful (especially if you know a bit of R). $\endgroup$
    – amoeba
    Commented Oct 29, 2015 at 1:38

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