We investigate the relationship between the rest-frame equivalent width (EW) of the C IV lambda1549 broad-emission line, monochromatic luminosity at rest-frame 5100 A, and the Hbeta-based Eddington ratio in a sample of 99 ordinary quasars across the widest possible ranges of redshift (0 < z < 3.5) and bolometric luminosity (10^{44} <~ L <~ 10^{48} erg s^{-1}). We find that EW(C IV) is primarily anti-correlated with the Eddington ratio, a relation we refer to as a modified Baldwin effect (MBE), an extension of the result previously obtained for quasars at z < 0.5. Based on the MBE, weak emission line quasars (WLQs), typically showing EW(C IV) <~ 10 A, are expected to have extremely high Eddington ratios. By selecting all WLQs with archival Hbeta and C IV spectroscopic data, nine sources in total, we find that their Hbeta-based Eddington ratios are typical of ordinary quasars with similar redshifts and luminosities. Four of these WLQs can be accommodated by the MBE, but the other five deviate significantly from this relation, at the >~3 sigma level, by exhibiting C IV lines much weaker than predicted from their Hbeta-based Eddington ratios. Assuming the supermassive black-hole masses in all quasars can be determined reliably using the single-epoch Hbeta-method, our results indicate that EW(C IV) cannot depend solely on the Eddington ratio. We briefly discuss a strategy for further investigation into the roles that basic physical properties play in controlling the relative strengths of broad-emission lines in quasars.
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