In this work we use a sample of 318 radio-quiet quasars (RQQs) to investigate the dependence of the ratio of optical/UV flux to X-ray flux, α_ox, and the X-ray photon index, Γ_X , on black hole mass, UV relative to Eddington luminosity, and X-ray relative to Eddington luminosity. Our sample is drawn from the literature, with X-ray data from ROSAT and Chandra, and optical data mostly from the SDSS; 153 of these sources have estimates of Γ_X from Chandra. We estimate MBH using standard estimates derived from the HβMg II, and C IV broad emission lines. Our sample spans a broad range in black hole mass (10⁶ ≲ M _BH/M_⊙ ≲ 10¹⁰), redshift (0 < z < 4.8), and luminosity (10⁴³ ≲ λL_λ (2500 Å)[ergs s^-1] ≲ 1048). We find that α_ox increases with increasing M_BH and L _UV/L_Edd and decreases with increasing L_X/L _Edd. In addition, we confirm the correlation seen in previous studies between Γ_X and M_BH and both L_UV/L _Edd and L_X/L_Edd; however, we also find evidence that the dependence of Γ_X of these quantities is not monotonic, changing sign at M_BH ∼ 3 × 10⁸ M _⊙. We argue that the α_ox correlations imply that the fraction of bolometric luminosity emitted by the accretion disk, as compared to the corona, increases with increasing accretion rate relative to the Eddington rate, ṁ. In addition, we argue that the Γ_X trends are caused by a dependence of X-ray spectral index on ṁ. We discuss our results within the context of accretion models with Comptonizing corona and discuss the implications of the α_ox correlations for quasar feedback. To date, this is the largest study of the dependence of RQQ X-ray parameters on black hole mass and related quantities, and the first to attempt to correct for the large statistical uncertainty in the broad-line mass estimates.