Straight-line fits with uncertainties in both coordinates: from Gauss to spreadsheets

摘要

Many disciplines involve analyses where linear fits need to be performed on sets of x-y data in which each point carries uncertainties in both the x and y values. Despite the frequency with which this problem occurs in practice, standard statistics texts offer little guidance on how to set up and implement a solution despite the fact that a general exact solution to the dual-uncertainties problem was established in the 1960s. This paper summarizes the solution of the bivariate-uncertainties linear fit at a level intended to be accessible to and useful for students and researchers who need to invoke such analyses in their studies. The technique is illustrated with examples drawn from astronomy, paleontology, geology, and climate physics. A freely-available spreadsheet for implementing the solution is described.