A Multi-Way Correlation Coefficient

Abstract

Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more variables e.g. how `correlated' are a collection of variables in which non are specifically to be treated as an `outcome'? In this short article, we introduce such a measure, and show that it reduces to the modulus of Pearson's $r$ in the two dimensional case.