A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line

Abstract

The well-known problem of fitting a straight line to data with uncertainties in both coordinates is revisited. An algorithm which treats x- and y-data in a symmetrical way and which had been published previously is generalized to the case when there are correlations. Taking known correlations into account helps to reduce the uncertainties of the parameters of the fit which is of major importance in metrology. Although the algorithm is implemented in MATLAB, implementation in a different programming language is straightforward using the formulae presented. The effectiveness of the algorithm is demonstrated with simulated data as well as with experimental data. As application examples, measurements of the temperature coefficient for alanine dosimetry are used.