Remarks on correlation

Abstract

The fundamental problem of the mathematical theory of correlation is this: given two statistical variables x and y, we want to know if there may be said to exist some kind of dependence between them, and we want a method permitting us to give a simple and quantitative description of the formal nature of this dependence. This problem once solved in a particular case, another question immediately arises: to study the real nature of the connection between the variables — this, however, generally falls quite outside the scope of the mathematical theory of correlation. Of course our problem can be generalized to any number of variables; as far as concerns the questions dealt with in this paper, it will be sufficient to consider the case of two variables.