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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?

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    $\begingroup$ We have few, if any, significant discussions of multivariate regressions here (so far). At 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. $\endgroup$ – whuber Jan 10 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.

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  • $\begingroup$ I'm just having a problem visualizing an example of this. Can you help? $\endgroup$ – Paze Jan 10 at 14:45
  • $\begingroup$ 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. $\endgroup$ – Nadia Merquez Jan 10 at 14:45
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    $\begingroup$ @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. $\endgroup$ – Lewian Jan 10 at 14:50
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    $\begingroup$ @Paze: whuber has linked an example in the comments. $\endgroup$ – Lewian Jan 10 at 14:51
  • $\begingroup$ I noticed that, adding '(response) variables' clarified the confusion. $\endgroup$ – Nadia Merquez Jan 10 at 14:51

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