  We use sunspot group observations from the Royal Greenwich Observatory (RGO)
to investigate the effects of intercalibrating data from observers with
different 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 would
have seen. The synthesised annual means of $R_B$ are then re-scaled to the
observed RGO group number $R_A$ using a variety of regression techniques. It is
found 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 maximum
values can be over 30% too large even for such levels of $r_{AB}$). In
generating the backbone sunspot number, Svalgaard and Schatten [2015] force
regression fits to pass through the scatter plot origin which generates
unreliable fits (the residuals do not form a normal distribution) and causes
sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is
demonstrated that the use of Quantile-Quantile (Q-Q) plots to test for a normal
distribution is a useful indicator of erroneous and misleading regression fits.
Ordinary least squares linear fits, not forced to pass through the origin, are
sometimes reliable (although the optimum method used is shown to be different
when matching peak and average sunspot group numbers). However other fits are
only reliable if non-linear regression is used. From these results it is
entirely possible that the inflation of solar cycle amplitudes in the backbone
group sunspot number as one goes back in time, relative to related
solar-terrestrial parameters, is entirely caused by the use of inappropriate
and non-robust regression techniques to calibrate the sunspot data.
