Relation between metallicity gradients and μ_1.15 = log M_⋆/M_⊙ + 1.15 × log y_eff. The coefficient of log y_eff, α = 1.15, minimizes the scatter of metallicity gradients at given μ_1.15. The best-fit slope, Spearman’s rank correlation r and p-value are given in the upper right corner of this figure. The red dashed line and shaded region represent the best-fit linear relation and its 1σ uncertainties. The combination parameter μ_1.15 exhibits a strong correlation with metallicity gradients, and represents the tightest correlation observed with metallicity gradients (see Sect. 3.5 for details).