Least Squares Methods for Treating Problems with Uncertainty in x and y

Abstract

Methods for straight-line fitting of data having uncertainty in x and y are compared through Monte Carlo simulations and application to specific data sets. Under special circumstances, the "ignorance" methods, methods which are typically used without information about the data errors σx and σy, are equivalent to the recommended best approach. The latter is numerical rather than formulaic but is easy to implement in programs that permit user-defined fit functions. It can handle any response function, linear or nonlinear, for any σxi and σyi. Estimates for the latter must be supplied and rightfully belong in any data analysis.