Least-squares fitting when both variables contain errors: Pitfalls and possibilities

Abstract

Least‐squares fitting is reviewed, in tutorial form, when both variables contain significant errors. Various error models are described; corresponding appropriate weighting is discussed; and the interpretation of weighting is clarified by a physically intuitive description and by graphical results. Resources in the literature on least‐squares fitting that are suitable for physics and astronomy students are reviewed. Algorithms for straight‐line fitting, indicate practical solution methods, are summarized and numerical comparisons are given. Also described are several readily available computer programs that allow fitting for both straight‐line and nonlinear situations and that are appropriate for both research and teaching applications.