these emission lines are estimated following @Ly2014.

Comparing the Balmer decrement (e.g. ${\hbox{H$\alpha$}}/{\hbox{H$\beta$}}$ ratio) to their intrinsic values that can be theoretically calculated under the “Case B” assumption, one could derive the dust attenuation (the dust geometry is postulated to be a non-scattering screen at a distance from the emitter, see @Liu13 for discussion on the complication of the dust geometry in galaxies). The Balmer decrement is insensitive to the temperature and electron density, and here we adopt a intrinsic flux ratio of $({\hbox{H$\alpha$}}/{\hbox{H$\beta$}})_0=2.86$ [@Hummer1987]. We use the [@Calzetti2000] reddening formalism to derive the color excesses $\rm E(B-V)$, and correct for the dust extinction for the emission line fluxes. When the observed flux ratio is unphysically ${\hbox{H$\alpha$}}/{\hbox{H$\beta$}}< 2.86$ (due to error scatter), we set $\rm E(B-V)$ to zero in an ad hoc manner.

![image](plot_ms_bpt.pdf){width="90.00000%"}

Sample Selection {#subsec:sample}
----------------

We retrieve the photometry of these 2812 galaxies from the NSA catalog. Since the metallicity under consideration is gas-phase metallicity, we focus on the star-forming galaxies with ${\rm NUV} - r < 4$ [@Li2015], whose metallicities can be reliably measured. Due to the same reason, we only consider the ${\hbox{H\,{\sc ii}}}$ regions of the selected galaxies, confining the spatial pixels (a.k.a. “spaxels”) 