In this paper, multiwavelength chromatic luminosity at radio (
\(\log L _{\mathrm{R}}\)), optical (
\(\log L_{\mathrm{O}}\)), X-ray (
\(\log L _{\mathrm{X}}\)), and
\(\gamma \)-rays (
\(\log L_{\gamma }\)) for a sample of 442 Fermi blazars with known redshifts are collected from Fan et al. (
2016), to study the correlations between the
\(\gamma \)-rays and the low-energy bands using a multiple linear regression analysis. In this way, we can see which band is more important for the
\(\gamma \)-ray emissions. Mutual correlation analysis is also used to discuss the correlations between the
\(\gamma \)-ray and the low energy bands for the whole sample and subclasses. We come to following conclusions:
- 1.
The multiple linear correlation indicates that the \(\gamma \)-rays are correlated with the radio, optical and the X-ray emissions for the whole sample and the subclasses of flat spectrum radio quasars (FSRQs) and BL Lac objects (BL Lacs), the correlation between the \(\gamma \)-rays and the radio emissions is the strongest one.
- 2.
For BL Lacs, the optical emissions are more important than the X-rays for the \(\gamma \)-rays, while the X-ray emissions are more important than optical ones in FSRQs.
- 3.
The \(\gamma \)-ray emissions in HBL are from an synchrotron self-Compton, while those in FSRQs may be from external Compton and synchrotron self-Compton as well.
