Linear ‘Curves of Best Fit’ and Regression Lines

Abstract

IN a recent communication, Austen and Pelzer¹ have discussed the problem of fitting a straight line when both the variables v, w are subject to error : their solution first seems to have been derived by Kummell² without the restriction that the standard deviations be constant throughout the range; he only assumed the ratio of the standard error of one variable to that of the other was the same for all pairs of readings. Kummell's paper does not seem to be obtainable in England, but this particular result is quoted by Deming³. The same solution was given later by K. Pearson and again by Gini, and there is a bibliography of work related to the subject in a Paper by Roos⁴. Attention may also be directed to a recent paper by Wald⁵.