@hlsmith, I want to know the practical approach of multivariate regression. my question is that, if we run a multivariate regression with 5 predictors and 2 response variables. how many regression coefficients will be there?
1 - will there be one slope from a predictor to predict two response variables?
2 - or there will be two slopes from one predictor, each for each of the response variables?
I am not very experienced with Multivariate Modeling. It is my belief that everything is pretty much the same, but there are a bunch of secondary statistics which evaluate how same terms were used on both models, etc. Sorry I am not much more help. @lindsey chan are you sure they used multivariate, some times people accidently use that term erroneously. I am not proud to say a decade ago I publish a paper where I erroneously used the term multivariate in lieu of multiple, though given the methods section, it should have been apparent it was multiple regression.
Not to complicate it further, but essentially multiple regression can be thought of as the same as multivariable but these are different from multivariate as @hlsmith pointed out.
The latter is multiple outcomes simultaneously where the former is multiple independent variables. (But you could have a univariate multivariable regression [typical cases you see with one Y as a function of >1 X] or you could have multivariate multivariable regression [multiple Y variables simulataneously as a function of >1 X variable].
I didn't know PCA was a form of multivariate regression. I haven't used PCA yet on a actual project. I used factor analysis a long time ago and regularized regression to lessen terms. I am need to incorporate it into my repertoire.