[Fe/H] dependency on FR and T _eff. The left panel illustrates the distribution of points of the tightest relation in FR-T _eff-[Fe/H] space and the surface they span therein. To guide the eye, the best-fit surface according to Eq. (10) is overlaid as a light-colored, distorted grid, where the grid lines indicate the isothermal and iso-FR lines. The same distribution of points is shown in the top right panel but in a coordinate frame that is rotated such that it is aligned with the FR and [Fe/H] axes. Dashed lines indicate the track of the isothermal lines on the surface. In analogy to Fig. 4, the inlay shows the most extreme spectra in terms of metallicity, as well as the two wavelength regions the FR was computed from (blue). The fit residuals with respect to FR are presented in the lower right frame. All three scatter-plots follow the same T _eff color coding as indicated by the bar on the right.