Design of Experiments for Most Precise Slope Estimation or Linear Extrapolation

Abstract

Abstract This paper discusses the problems of slope-estimation and of linear extrapolation when the precision of the Y-measurements changes with different values of x. Tables are presented which show, for each of these problems, the optimum placement of x-values and the optimum distribution of the N observations for selected relationships between σ and x. The optimum placements are seen to be the same for the two problems, but for the latter, the optimum distributions depend on the nearness or remoteness of the extrapolation.