accurately determine the strength of these correlations. From Table \[table1\], we note that the significance $p$ values for $M_*$ – $Z$ and $\Sigma_*$ – $Z$ are both prominent, indicating the importance of the roles that local $\Sigma_*$ and global stellar mass play in determining the local metallicity. However, all of the $p$ values for $\Sigma_*$ – $Z$ are slightly larger than those for $M_*$ – $Z$, suggesting that the local stellar mass surface density is more closely related to the local metallicity than to the galaxy stellar mass.

In the previous studies, some global galaxy properties, such as SFR, specific SFR, $D\rm_{n}(4000)$ and gas fraction are introduced in order to explain the large scatter in global MZR. [@Mannucci2010a] determined the metallicity with N2 and R23 [@Nagao2006] indices, and defined a new quantity $\mu_{\alpha} = {\rm log}(M_*) - \alpha {\rm log(SFR)}$ to reduce the scatter in MZR for local galaxies, resulting in a scatter of 0.05 dex in FMR. [@Andrews2013] found the scatter in FMR to be about 0.13 dex, where the metallicity is calculated from the electron temperature $T_e$. Similarly, for the local $\Sigma_*$ – $Z$ relation, although [@Barrera-Ballesteros2016a] suggested that the $\Sigma_*$ – $Z$ relation is largely independent of 