  We derive data of 4615 star-forming early-type galaxies (ETGs), which come
from cross-match of the $Galaxy~Zoo~1$ and the catalogue of the MPA-JHU
emission-line measurements for the Sloan Digital Sky Survey Data Release 7. Our
sample distributes mainly at $\rm -0.7<log(SFR[M_{\sun}yr^{-1}])<1.2$, and the
median value of our SFRs is slightly higher than that shown in Davis \& Young.
We display a significant trend of lower/higher stellar mass ETGs to have
lower/higher SFR, and obtain our sample best fit of log(SFR)=$
(0.74\pm0.01)$log$(M_{*}/M_{\sun})-(7.64\pm0.10)$, finding the same slope as
that found in Cano-D\'{i}az et al. In our star-forming ETG sample, we
demonstrate clearly the correlation of the stellar mass and metallicity (MZ)
relation. We find that higher metallicity measurements may be introduced by the
diffuse ionized gas, when the D16, Sanch18, and Sander18 indicators are used to
calibrate the metallicity of ETGs. We show the relations between SFR and
12+log(O/H) with different metallicity estimators, and suggest that their
correlations may be a consequence of the SFR-stellar mass and MZ relations in
ETGs.
