of ($g-r$) and $\mu_i$ in Eq.\[eq-zhnag\] using AC1 and test this calibration on the GASS data. Since both samples have consistent sources of input parameters and stellar mass measurements, any systematic trend caused by inconsistencies therein should be removed. The AC1-calibrated version of Eq.\[eq-zhnag\] is then

$$\rm{log~M_{HI}/M_{*}}=-2.332\it{(g-r)}+\rm{0.168\mu_{i}-2.528}
\label{eq-zhnag_new}$$

In Fig. \[fig-alfa-gass-two-par\] we now compare the observed and estimated  for the newly derived coefficients in Eq.\[eq-zhnag\_new\] in the AC1 and GASS samples (blue and red points respectively). The first important result demonstrated by Fig. \[fig-alfa-gass-two-par\], is that Eq.\[eq-zhnag\_new\] does not perform well at estimating the data on which it is calibrated (AC1), indicating that AC1 can not be well fit with the parametrization in Eqs. \[eq-zhnag\] and \[eq-zhnag\_new\]. Application to the GASS sample also results in a strong systematic offset. Importantly, the mean offset between the estimated (using Eq. \[eq-zhnag\_new\]) and the observed GASS data is still $\sim0.45$ dex, the same as was inferred between AC1 and GASS using the original coefficients in Eq. \[eq-zhnag\]. This difference can no longer be attributed to differences in inhomogeneous stellar mass estimates or photometry, which were derived identically for the two samples. As we will demonstrate below, the offset is due to the fundamentally 