  Weak emission-line quasars (WLQs) are a subset of Type 1 quasars that exhibit
extremely weak Ly$\alpha +$N V $\lambda$1240 and/or C IV $\lambda$1549 emission
lines. We investigate the relationship between emission-line properties and
accretion rate for a sample of 230 `ordinary' Type 1 quasars and 18 WLQs at $z
< 0.5$ and $1.5 < z < 3.5$ that have rest-frame ultraviolet and optical
spectral measurements. We apply a correction to the H$\beta$-based black-hole
mass ($M_{\rm BH}$) estimates of these quasars using the strength of the
optical Fe II emission. We confirm previous findings that WLQs' $M_{\rm BH}$
values are overestimated by up to an order of magnitude using the traditional
broad emission-line region size-luminosity relation. With this $M_{\rm BH}$
correction, we find a significant correlation between H$\beta$-based Eddington
luminosity ratios and a combination of the rest-frame C IV equivalent width and
C IV blueshift with respect to the systemic redshift. This correlation holds
for both ordinary quasars and WLQs, which suggests that the two-dimensional C
IV parameter space can serve as an indicator of accretion rate in all Type 1
quasars across a wide range of spectral properties.
