The use of relative residues in linear regression of experimental data with errors in both fit variables

A new regression model which mininizes the sum of squares of relative residues for data with errors in both fit variables is presented for linear fits. Expressions are derived for the slope, intercept and their respective errors. A detailed comparison is made between the new improved relative least squares (IRLS) model and other linear regression models, using three sets of data points. It is shown that IRLS provides the best compromise between, respectively, quality of fit, and a realistic representation of the physical situation of errors in both fit variables.