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Does it make sense to use a PCA (principal component analysis) on a set of response Y variables and then conduct a multiple regression, or carry out a multivariate multiple regression all response variables as they are?

I have 4 response variables and 2 predictor variables, which are all continuous.

ttnphns
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user3237820
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  • Is there any reason not to run four separate regressions, one for each response variable? I am not sure what you are gaining by transforming them with PCA. If you are looking for relations among the predictor and response variables maybe you should look at [canonical correlation analysis](http://en.wikipedia.org/wiki/Canonical_correlation) – JeffM Jul 22 '14 at 14:52
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    You may go both ways, but these are quite different analyses. PCA implies that you produce an extract (main component) from set1 _only_, and _then_ you regress, associate it with set2 variables. Multivariate regression is virtually another name for canonical correltation analysis (it is its "superficial side"). In this analysis, the "component" extracted from set1 (and called canonical variate) is extracted _to be associated_ with set2 from the very _beginning_. I can forward you to my answers [1](http://stats.stackexchange.com/a/65817/3277), [2](http://stats.stackexchange.com/a/31468/3277). – ttnphns Jul 23 '14 at 01:56

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