  We report on a detailed analysis of the correlation between the optical-UV
(Lo) and X-ray (Lx) luminosities of quasars by means of Monte Carlo
simulations, using a realistic luminosity function. We find, for a quasar
population with an intrinsically constant, mean X-ray loudness alpha_ox, that
the simulated alpha_ox - Lo relation can exhibit various `apparent' properties,
including an increasing alpha_ox with Lo, similar to what has been found from
observations. The determining factor for this behavior turns out to be the
relative strength of the dispersions of the luminosities, i.e. their deviations
from the mean spectral energy distribution at the optical and X-ray bands, such
that a dispersion larger for the optical luminosity than for the X-ray
luminosity tends to result in an apparent correlation. We suggest that the
observed alpha_ox - Lo correlation can be attributed, at least to some extent,
to such an effect, and is thus not an underlying physical property. The
consequences of taking into account the luminosity dispersions in an analysis
of the observed luminosity correlations is briefly discussed. We note that
similar considerations might also apply for the Baldwin effect.
