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I understand that multivariate regression models contain more than 1 dependent variable, but what is the difference between running a multivariate regression with dependent a and b to a set of independent variables, rather than running two regression models, one for a and one for b against the same set of independent variables?

Paze
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    We have few, if any, significant discussions of multivariate regressions here (so far). At https://stats.stackexchange.com/a/66268/919 I posted a detailed, illustrated example of a (particular kind of) regression with two interdependent variables, including comparing it to separate regressions of those variables: it might serve to illustrate some of the distinctions between ordinary and multivariate regression. – whuber Jan 10 '20 at 14:16

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The multivariate regression can take into account potential dependence between the two dependent (response) variables. Running two regressions separately cannot.

Christian Hennig
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  • I'm just having a problem visualizing an example of this. Can you help? – Paze Jan 10 '20 at 14:45
  • It should be 'two independent variables'. For the seperate regression models, the dependent variables remain the same. However, once more than one independent variable is used, you may control for the other variables. Given that the other variables remain constant, and the variable of interest increases with one unit, how much is the dependent variable affected. – Nadia Merquez Jan 10 '20 at 14:45
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    @Nadia Merquez: No, I meant "dependent variables" in the sense of the questioner, also called response variable. You may be thinking of *multiple* as opposed to *multivariate* regression. The latter has more than one response variable. – Christian Hennig Jan 10 '20 at 14:50
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    @Paze: whuber has linked an example in the comments. – Christian Hennig Jan 10 '20 at 14:51
  • I noticed that, adding '(response) variables' clarified the confusion. – Nadia Merquez Jan 10 '20 at 14:51
  • The example linked is probably good example for a statistician, which I, unfortunately, am not. Is there any easy way of explaining it with a clinical example like "say we have 30 patients with this disease and this other dependent variable and we want to...." ? – Paze Jan 10 '20 at 17:15
  • Googling for "multivariate regression example" throws up lots of examples. – Christian Hennig Jan 11 '20 at 01:04