Is radio jet power linearly proportional to the product of central black
  hole mass and Eddington ratio in AGN?
  A model for the relation between radio jet power and the product of central
black hole (BH) mass and Eddington ratio of AGN is proposed, and the model is
examined with data from the literature. We find that radio jet power positively
correlates but not linearly with the product of BH mass ($m$ in solar mass) and
Eddington ratio ($\lambda$), and the power law indices ($\mu$) are
significantly less than unity for relatively low accretion ($\lambda<0.1$) AGN,
$P_{j}\propto (\lambda m)^{\mu}$, in the radio galaxies and the Seyfert
galaxies. This leads to a negative correlation between radio loudness and
$\lambda m$ for the low luminosity AGN, i.e. $R\propto (\lambda m)^{\rho}$ with
$\rho=(7/6)\mu-1<0$, which may be attributed to a contribution of BH spin to
total jet power assuming that the spin induced jet is gradually suppressed as
the accretion rate increases. Whereas, for the high-z quasars which often show
the slope $\mu\geq1$, a positive correlation between the radio loudness and
disc luminosity is predicted. We discuss that the jet powers of the high-z FRII
quasars are likely dominated by the accretion disc rather than by the BH spin.
