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![A re-calibration of Eq.\[eq-zhnag\] based on AC1 data yield the new coefficients given in Eq.\[eq-zhnag\_new\]. This new linear relationship is applied to AC1 (blue points) and GASS (red points). The gray dashed line shows the one-to-one relation of  ($_{est}) =$ ($_{obs}$). The deviations of the estimated from the observed  in AC1 indicate that a linear combination of $g-r$ and $\mu_i$ is insufficient for estimating the HI gas fraction. A systematic error of $\sim0.45$ dex is found when the AC1 linear calibration in Eq.\[eq-zhnag\_new\] is applied to the GASS sample. This offset can no longer be due to inconsistencies in the input data. []{data-label="fig-alfa-gass-two-par"}](fig-02.pdf){width="8cm" height="6.5cm"}

To compare the performance of the linear (Zhang et al. 2009) and non-linear approaches, we follow the methods outlined in Teimoorinia & Ellison (2014), in which non-linear methods were used to determine Balmer decrements and emission line fluxes. Here, we use the AC1 sample of HI detections from ALFALFA.70, combined with the same parameters used by Zhang et al. (2009) and tested in the above linear fit tests ($g-r$ and $\mu_i$). Therefore, the only change we are making is in the methodology of the fitting, not in the parameters used. We use the Levenberg-Marquardt algorithm 