The long-solved problem of the best-fit straight line:application to isotopic mixing lines

by  Richard Wehr and Scott R. Saleska

Scientists in a wide variety of disciplines are commonly confronted with the problem of how to fit a straight line to data points that were measured with uncertainty in both X and Y. Much of the scientific literature gives the impression that this is an unsolved problem, but it was actually solved in 1969 by a geophysicist named Derek York — a fact widely known among geoscientists but almost unknown in other fields. Our paper spreads the news about York’s solution and demonstrates its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles.