Aims. We use a sample of 83 core-dominated active galactic nuclei (AGN) selected from the MOJAVE (Monitoring of Jets in AGN with VLBA Experiments) radio-flux-limited sample and detected with the Fermi Large Area Telescope (LAT) to study the relations between non-simultaneous radio, optical, and gamma-ray measurements. Methods. We perform a multi-band statistical analysis to investigate the relations between the emissions in different bands and reproduce these relations by modeling of the spectral energy distributions of blazars. Results. There is a significant correlation between the gamma-ray luminosity and the optical nuclear and radio (15 GHz) luminosities of blazars. We report a well defined positive correlation between the gamma-ray luminosity and the radio-optical loudness for quasars and BL Lacertae type objects (BL Lacs). A strong positive correlation is found between the radio luminosity and the gamma-ray-optical loudness for quasars, while a negative correlation between the optical luminosity and the gamma-ray-radio loudness is present for BL Lacs. Modeling of these correlations with a simple leptonic jet model for blazars indicates that variations of the accretion disk luminosity (and hence the jet power) is able to reproduce the trends observed in most of the correlations. To reproduce all observed correlations, variations of several parameters, such as the accretion power, jet viewing angle, Lorentz factor, and magnetic field of the jet, are required.
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