  We use six different cosmological models to study the recently-released
compilation of X-ray and UV flux measurements of 2038 quasars (QSOs) which span
the redshift range $0.009 \leq z \leq 7.5413$. We find, for the full QSO data
set, that the parameters of the X-ray and UV luminosities $L_X-L_{UV}$ relation
used to standardized these QSOs depend on the cosmological model used to
determine these parameters, i.e, it appears that the full QSO data set include
QSOs that are not standardized and so cannot be used for the purpose of
constraining cosmological parameters. Subsets of the QSO data, restricted to
redshifts $z \lesssim 1.5-1.7$ obey the $L_X-L_{UV}$ relation in a
cosmological-model-independent manner, and so can be used to constrain
cosmological parameters. The cosmological constraints from these lower-$z$,
smaller QSO data subsets are mostly consistent with, but significantly weaker
than, those that follow from baryon acoustic oscillation and Hubble parameter
measurements.
