  We collect a sample of 78 Fermi detected blazars with broad line region (BLR)
data and the quasi-simultaneous multi-wave band data. By analyzing the sample,
we find: (1) For whole blazar sample, there exist significant correlations
between radio, $\gamma$-ray luminosity and BLR luminosity. The slope of the
best-fit linear regression equation is close to the theoretical value 1. Our
results provided another support of jet-disk symbiosis. (2) For FSRQ sample, we
find a significant correlation between radio luminosity and optical luminosity,
and weaker correlations between X-ray luminosity and radio, optical luminosity.
It indicates that the X-ray band radiation mechanism is slightly different from
radio and optical bands. The X-ray emission is diluted by inverse Compton
scattering (IC). There is a significant correlation between BLR luminosity and
$\gamma$-ray luminosity, but no correlations between X-ray luminosity and BLR,
$\gamma$-ray luminosity, which suggests that the seed soft photons are
different for IC process. From these results we suggest that the X-ray band
emission is diluted by synchrotron self-Compton (SSC) process, $\gamma$-ray
band emission is produced by external Compton (EC) process.
