Constrained Canonical Correlation Analysis on a Spreadsheet

While multiple regression is widely used for the construction of models relating a single response variable to multiple explanatory variables (or inputs), satisfactory methods for modelling the relationship between multiple responses or outputs as well as inputs in a single equation are not widely known. Such situations may arise when the dependent quantity is a composite index or weighted combination of component variables, or is an aggregate of outputs.One side of the equation may then contain the outputs (performance or response measures) and the other the explanatory, control or input variables. Certain intuitive estimation approaches for doing this turn out to have properties which make them unusable, specifically they are not units (or scale) invariant. Instead, a method based on the criterion of maximum correlation is found to be superior. Furthermore we can allow prior information to be built into the model by the inclusion of constraints. As with regression there is broad scope for application, in particular it extends singleequation regression to the case of multiple performance measures, criteria or responses