  In using multiple regression methods for prediction, one often considers the
linear combination of explanatory variables as an index. Seeking a single such
index when here are multiple responses is rather more complicated. One
classical approach is to use the coefficients from the leading canonical
correlation. However, methods based on variances are unable to disaggregate
responses by quantile effects, lack robustness, and rely on normal assumptions
for inference. We develop here an alternative regression quantile approach and
apply it to an empirical study of the performance of large publicly held
companies and CEO compensation. The initial results are very promising.
