Relations between stellar mass and metallicity. Left panel: MZRs with the stacks A, B, D by stellar mass with star, triangle and circle symbols, respectively, and color-coded by EW(CIII]). The black symbols are stacks from Cullen et al. (2019, 2021), Calabrò et al. (2021). The orange circles is the local MZRs from Zahid et al. (2017). The blue dashed line is the best fit with the shaded region at 3-σ in Eq. (10), and the black dashed line is the MZRs from Cullen et al. (2019). Right panel: MZRg with the same stacks as left panel but re-scaled with the α-enhancement. Green dashed line from Steidel et al. (2014). Red dashed line from Troncoso et al. (2014). Black symbols are values from literature (Sanders et al. 2021; Cullen et al. 2021). The orange points are the local MZRg from Andrews & Martini (2013). The Z_g scale in the y-axes corresponds to the gas-phase metallicity obtained from Eq. (11) (see text for more details).