Analytical Use of Linear Regression. Part II: Statistical Error in Both Variables

Abstract

Abstract This paper critically evaluates the literature techniques that attempt to incorporate the existence of both x- and y- errors into linear regression statistics. This evaluation focuses on the relative theoretical and practical merits of 4 techniques: (1) the effective variance approach, (2) the constant variance ratio approach, (3) the York approach, and (4) the Williamson approach. The practical use of these different approaches is illustrated with the aid of actual results from an interlaboratory comparison study. On the basis of our comparative evaluation, the constant variance ratio approach is sound, yet simple, and is strongly recommended as long as the constant ratio criterion can be satisfied. However, the Williamson approach is applicable in more situations and is also highly recommended because of its theoretical virtues, mathematical consistencies, and practical applications. The other 2 methods are not recommended for use because of reasons that are summarized in this paper. The lack of available software remains an impediment to widespread use of many of the described statistical procedures.