We present an analysis to disentangle the connection between physical quantities that characterize the conditions of ionized H ii regions -metallicity (Z), ionization parameter (U), and electron density (n e ) -and the global stellar mass (M * ) and specific star formation rate (sSFR = SFR/M * ) of the host galaxies. We construct composite spectra of galaxies at 0.027 ≤ z ≤ 0.25 from Sloan Digital Sky Survey, separating the sample into bins of M * and sSFR, and estimate the nebular conditions from the emission line flux ratios. Specially, metallicity is estimated from the direct method based on the faint auroral lines [O iii]λ4363 and [O ii]λλ7320,7330. The metallicity estimates cover a wide range from 12 + log O/H ∼ 7.6-8.9. It is found that these three nebular parameters all are tightly correlated with the location in the M * -sSFR plane. With simple physically-motivated ansätze, we derive scaling relations between these physical quantities by performing multi regression analysis. In particular, we find that U is primarily controlled by sSFR, as U ∝ sSFR 0.43 , but also depends significantly on both Z and n e . The derived partial dependence of U ∝ Z −0.36 is weaker than the apparent correlation (U ∝ Z −1.52 ). The remaining negative dependence of U on n e is found to be U ∝ n −0.29 e . The scaling relations we derived are in agreement with predictions from theoretical models and observations of each aspect of the link between these quantities. Our results provide a useful set of equations to predict the nebular conditions and emission-line fluxes of galaxies in semi-analytic models.