Regression and correlation analyses of a linear relation between random intervals

In this paper we develop regression and corrclation analyses of a certain general linear relation between two random elements whose values are non-empty compact intervals. To this purpose, we firstly extend the least-squares method to deal with the involved random elements on the basis of a generalized metric defined on the space of the considered intervals. As a complementary study, a coefficient quantifying the strength of the linear relation between the two random elements is also presented, and a discussion of the extreme values for this measure is presented. A real-life example illustrates these studies.