The mechanics of canonical correlation are covered in many multivariate texts (see references below for some examples). In a given analysis you will be provided with X number of canonical correlations equal to the number of variables in the smaller set. 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. 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. Canonical correlation analysis will create linear combinations (variates, X* and Y* above) of the two sets that will have maximum correlation with one another. However, now we have a set of DVs and will want to create a linear combination of those also (Y1-Y3). Just like in MR we want to create linear combinations of the set of IVs (X1-X3). The figure below gives us an idea of what is going to happen. To begin with, it helps to visualize what we’re about to do. In a sense it can be thought of multivariate regression though multiple regression is actually a special case of canonical correlation. Canonical correlation analyzes the relationship between sets of variables, with one set of variables typically seen as the independent set and another as the dependent set, though the causal arrow is not necessarily specified. The square of that correlation between the linear combination and the dependent variable (DV) is the amount of variance in the dependent variable accounted for by the predictors.Īlthough it is easy to think of the independent variables as a set that one believes has some relation to the dependent variable, many do not as often think of a set of dependent variables that one wishes to predict. A linear combination of the independent variables (IVs) is created that will have the minimum squared errors in prediction. Many in the social sciences often employ multiple regression (MR) to solve the problem of how several variables predict another variable.