the median values of $\Sigma_*$, local SFRs and metallicities in the bin regions with $\Delta R/R_e=0.3$ for each galaxy, see detail in Section \[subsec:metallicity-correlation\].

In the $top$ panels of Figure \[fig:fmr\_fit\], we show the comparisons between the observed metallicity derived with N2O2 index and our best-fit $\Sigma_*$ – $Z$ as well as $M_*$ – $\Sigma_*$ – $Z$ relations. The contours cover the metallicities for $85\%$ of all spaxels, and the solid, unity lines are overplotted for eye guidance. These black dashed lines show the scatters for all spaxels, which are 0.096 dex for $\Sigma_*$ – $Z$ relation, while are 0.070 dex for $M_*$ – $\Sigma_*$ – $Z$ relation. The mean values $\mu_{all}$ and standard deviation (scatters) $\sigma_{all}$ for residuals ($\rm \Delta 12+log(O/H) = \rm 12+log(O/H) - 12+log(O/H)_{FIT}$) are shown in the legends. Note that the scatter $\sigma_{\rm all}$ in $M_*$ – $\Sigma_*$ – $Z$ relation is significantly smaller than the value in the $\Sigma_*$ – $Z$ relation. When the global stellar mass is taken into account, the scatter of the metallicity scaling relation is reduced by 27$\%$ for N2O2 index. This result means that above one quarter of the total scatter in $\Sigma_* \-- Z$ relation is due to the 