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We use sunspot group observations from the Royal Greenwich Observatory (RGO)to investigate the effects of intercalibrating data from observers withdifferent visual acuities. The tests are made by counting the number of groups$R_B$ above a variable cut-off threshold of observed total whole-spot area(uncorrected for foreshortening) to simulate what a lower acuity observer wouldhave seen. The synthesised annual means of $R_B$ are then re-scaled to theobserved RGO group number $R_A$ using a variety of regression techniques. It isfound that a very high correlation between $R_A$ and $R_B$ ($r_{AB}$ > 0.98)does not prevent large errors in the intercalibration (e.g. sunspot maximumvalues can be over 30% too large even for such levels of $r_{AB}$). Ingenerating the backbone sunspot number, Svalgaard and Schatten [2015] forceregression fits to pass through the scatter plot origin which generatesunreliable fits (the residuals do not form a normal distribution) and causessunspot cycle amplitudes to be exaggerated in the intercalibrated data. It isdemonstrated that the use of Quantile-Quantile (Q-Q) plots to test for a normaldistribution is a useful indicator of erroneous and misleading regression fits.Ordinary least squares linear fits, not forced to pass through the origin, aresometimes reliable (although the optimum method used is shown to be differentwhen matching peak and average sunspot group numbers). However other fits areonly reliable if non-linear regression is used. From these results it isentirely possible that the inflation of solar cycle amplitudes in the backbonegroup sunspot number as one goes back in time, relative to relatedsolar-terrestrial parameters, is entirely caused by the use of inappropriateand non-robust regression techniques to calibrate the sunspot data.

Tests of sunspot number sequences: 3. Effects of regression procedures on the calibration of historic sunspot data