BIVARIATE STRUCTURAL RELATION

Abstract

SUMMARY Given n observations (x t , y t ), each subject to an error of measurement ascertained independently , the existence of a structural relation for the true points ( X, Y ) is discussed. For a linear relation a Ø-number is defined from which either a confidence or a structural theory can be developed. The relation is treated in toto . Structural theory is described in terms of three hypotheses of regularity, which enable confidence and fiducial theories to be contrasted. It is shown that the theory provides a solution for the curvilinear relation wherein all the alternative hypotheses are incorporated, and it is suggested that the latter is a necessary requirement. The alternative hypothesis implicit in the Ø-number treatment of the linear relation is deduced from the general theory.