  We explore the general question of correlations among different waveband
luminosities in a flux-limited multiband observational data set. Such
correlations, often observed for astronomical sources, may either be intrinsic
or induced by the redshift evolution of the luminosities and the data
truncation due to the flux limits. We first address this question analytically.
We then use simulated flux-limited data with three different known intrinsic
luminosity correlations, and prescribed luminosity functions and evolution
similar to the ones expected for quasars. We explore how the intrinsic nature
of luminosity correlations can be deduced, including exploring the efficacy of
partial correlation analysis with redshift binning in determining whether
luminosity correlations are intrinsic and finding the form of the intrinsic
correlation. By applying methods that we have developed in recent works, we
show that we can recover the true cosmological evolution of the luminosity
functions and the intrinsic correlations between the luminosities. Finally, we
demonstrate the methods for determining intrinsic luminosity correlations on
actual observed samples of quasars with mid-infrared, radio, and optical fluxes
and redshifts, finding that the luminosity-luminosity correlation is
significantly stronger between mid-infrared and optical than that between radio
and optical luminosities, supporting the canonical jet-launching and heating
model of active galaxies.
