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 be either 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
