  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.
