  The relation between the $\alpha_{OX}$ index and the optical/UV luminosity
($L_{UV}$), a by product of the X-ray - optical/UV luminosity relation, is
affected by a relatively large dispersion, due to variability in the
$\alpha_{OX}$ within single sources (intra-source dispersion) and variations of
fundamental physical parameters from source to source (inter-source
dispersion). We use archival data from the XMMSSC and from the XMMOM-SUSS3. We
select a sub-sample in order to decrease the dispersion of the relation due to
the presence of Radio-Loud and Broad Absorption Line objects, and to
absorptions in both X-ray and optical/UV bands. We analyse the dependence of
the residuals of the relation on various physical parameters in order to
characterise the inter-source dispersion. We find a total dispersion of ~0.12
and, using the Structure Function, we find that intrinsic variability
contributes for 56% of the variance of the relation. We find weak but
significant dependences of the residuals of the relation on black-hole (BH)
mass and on Eddington ratio, confirmed by a multivariate regression analysis of
$\alpha_{OX}$ as a function of optical/UV luminosity and the above quantities.
We find a weak positive correlation of both the $\alpha_{OX}$ and the residuals
of the relation with inclination indicators (FWHM(H$\beta$) and EW[O$_{III}$])
suggesting a weak increase of X-ray/UV ratio with the viewing angle. Our
results suggest the possibility of selecting a sample of objects, based on
their viewing angle and/or BH mass and Eddington ratio, for which the
$\alpha_{OX}-L_{UV}$ relation is as tight as possible, in light of the use of
the X-ray - optical/UV luminosity relation to build a distance modulus (DM) -
$z$ plane and estimate cosmological parameters.
