On the 3D structure of the mass, metallicity, and SFR space for SF
  galaxies
  We demonstrate that the space formed by the star-formation rate (SFR),
gas-phase metallicity (Z), and stellar mass (M), can be reduced to a plane, as
first proposed by Lara-Lopez et al. We study three different approaches to find
the best representation of this 3D space, using a principal component analysis,
a regression fit, and binning of the data. The PCA shows that this 3D space can
be adequately represented in only 2 dimensions, i.e., a plane. We find that the
plane that minimises the chi^2 for all variables, and hence provides the best
representation of the data, corresponds to a regression fit to the stellar mass
as a function of SFR and $Z$, M=f(Z,SFR). We find that the distribution
resulting from the median values in bins for our data gives the highest chi^2.
We also show that the empirical calibrations to the oxygen abundance used to
derive the Fundamental Metallicity Relation (Nagao et al.) have important
limitations, which contribute to the apparent inconsistencies. The main problem
is that these empirical calibrations do not consider the ionization degree of
the gas. Furthermore, the use of the N2 index to estimate oxygen abundances
cannot be applied for ~8.8 because of the saturation of the [NII]6584 line in
the high-metallicity regime. Finally we provide an update of the Fundamental
Plane derived by Lara-Lopez et al.
