In a sense it can be thought of multivariate regression though multiple regression is actually a special case of canonical correlation. To begin with, it helps to visualize what we’re about to do. The figure below gives us an idea of what is going to happen. Just like in MR we want to create linear combinations of the set of IVs (X1-X3). However, now we have a set of DVs and will want to create a linear combination of those also (Y1-Y3). Canonical correlation analysis will create linear combinations (variates, X* and Y* above) of the two sets that will have maximum correlation with one another. The advantage that canonical correlation has over typical MR is that it can take into account the complex nature of data: we don’t have to restrict ourselves to one DV, and it also allows for the possibility that the two sets of variables have a relationship along more than one dimension. In other words we may find that there are other linear combinations of the two sets of variables such that would result in the variates having a sizable (though lesser) correlation that also would be of practical significance. In a given analysis you will be provided with X number of canonical correlations equal to the number of variables in the smaller set. The mechanics of canonical correlation are covered in many multivariate texts (see references below for some examples).
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