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

The problem of assessing the incidence of the x errors on the fitting param eters and their uncertainties in straight-line fittings is addressed. The c ase in which the x and y errors are proportional to each other is studied i n detail. Limits for the maximum expected variation of the fitting values d ue to the inclusion of the x errors are given in terms of the standard fitt ing results, namely those obtained disregarding the x errors. Closed expres sions for the parameters' values and their uncertainties are also given in terms of the standard fitting results. The main inaccuracies of the standar d fitting are investigated analytically. The general case of point-dependen t errors is also briefly discussed.