which is deployed to measure the correlation strength between metallicity $Z$ and $M_*$ (or $\Sigma_*$) while controlling the effects of $\Sigma_*$ (or $M_*$). There are three different statistical parameters in PCOR: one parametric statistic (Pearson) and two non-parametric statistics (Spearman and Kendall). The Pearson product-moment correlation coefficient is a measure of the linear correlation between two variables [@Pearson1895], Spearman’s correlation coefficient is a nonparametric measure of statistical dependence between the ranking of two variables [@Spearman1904], and the Kendall correlation coefficient is used to measure the ordinal association between two measured quantities [@Kendall1938]. We perform the analyses with these three statistical methods on metallicity using <span style="font-variant:small-caps;">pcor</span> code [^4] in R language. The resultant significance ($p$ values) is listed in Table \[table1\]. We find that all the $p$ values for $M_*$ – $Z$ and $\Sigma_*$ – $Z$ are large, implying that metallicity have partial dependence on both $M_*$ and $\Sigma_*$. However, we also note that all $p$ values for the $\Sigma_*$ – $Z$ relation are slightly larger than those for the $M_*$ – $Z$ relation, indicating that $\Sigma_*$ is more closely related to local metallicity than $M_*$.

The Relation Between Stellar Mass, Mass Surface Density And Metallicity  {#subsec:relation-z-mass-surface}
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The global 