  Using a sample of dwarf galaxies observed using the VIMOS IFU on the VLT, we
investigate the mass-metallicity relation (MZR) as a function of star formation
rate (FMR$_{\text{SFR}}$) as well as HI-gas mass (FMR$_{\text{HI}}$). We
combine our IFU data with a subsample of galaxies from the ALFALFA HI survey
crossmatched to the Sloan Digital Sky Survey to study the FMR$_{\text{SFR}}$
and FMR$_{\text{HI}}$ across the stellar mass range 10$^{6.6}$ to 10$^{8.8}$
M$_\odot$, with metallicities as low as 12+log(O/H) = 7.67. We find the
1$\sigma$ mean scatter in the MZR to be 0.05 dex. The 1$\sigma$ mean scatter in
the FMR$_{\text{SFR}}$ (0.02 dex) is significantly lower than that of the MZR.
The FMR$_{\text{SFR}}$ is not consistent between the IFU observed galaxies and
the ALFALFA/SDSS galaxies for SFRs lower than 10$^{-2.4}$ M$_\odot$ yr$^{-1}$,
however this could be the result of limitations of our measurements in that
regime. The lowest mean scatter (0.01 dex) is found in the FMR$_{\text{HI}}$.
We also find that the FMR$_{\text{HI}}$ is consistent between the IFU observed
dwarf galaxies and the ALFALFA/SDSS crossmatched sample. We introduce the
fundamental metallicity luminosity counterpart to the FMR, again characterized
in terms of SFR (FML$_{\text{SFR}}$) and HI-gas mass (FML$_{\text{HI}}$). We
find that the FML$_{\text{HI}}$ relation is consistent between the IFU observed
dwarf galaxy sample and the larger ALFALFA/SDSS sample. However the 1$\sigma$
scatter for the FML$_{\text{HI}}$ relation is not improved over the
FMR$_{\text{HI}}$ scenario. This leads us to conclude that the
FMR$_{\text{HI}}$ is the best candidate for a physically motivated fundamental
metallicity relation.
