When errors in both coordinates make a difference in the fitting of straight lines by least squares

摘要

The problem of assessing the incidence of the x errors on the fitting parameters and their uncertainties in straight-line fittings is addressed. The case in which the x and y errors are proportional to each other is studied in detail. Limits for the maximum expected variation of the fitting values due to the inclusion of the x errors are given in terms of the standard fitting results, namely those obtained disregarding the x errors. Closed expressions for the parameters' values and their uncertainties are also given in terms of the standard fitting results. The main inaccuracies of the standard fitting are investigated analytically. The general case of point-dependent errors is also briefly discussed.