  In this paper, the dependence of the broad Fe K$\alpha$ line on the physical
parameters of AGN, such as the black hole mass $M_{BH}$, accretion rate
(equivalently represented by Eddington ratio $\lambda_{Edd}$), and optical
classification, is investigated by applying the X-ray spectra stacking method
to a large sample of AGN which have well measured optical parameters. A broad
line feature is detected ($>3\sigma$) in the stacked spectra of the high
$\lambda_{Edd}$ sub-sample ($\log\lambda_{Edd}>-0.9$). The profile of the broad
line can be well fitted with relativistic broad line model, with the line
energy consistent with highly ionized Fe K$\alpha$ line (i.e. Fe xxvi). A model
consisting of multiple narrow lines cannot be ruled out, however. We found
hints that the Fe K line becomes broader as the $\lambda_{Edd}$ increases. No
broad line feature is shown in the sub-sample of broad-line Seyfert 1 (BLS1)
galaxies and in the full sample, while a broad line might be present, though at
low significance, in the sub-sample of narrow-line Seyfert 1 (NLS1) galaxies.
We find no strong dependence of the broad line on black hole masses. Our
results indicate that the detection/properties of the broad Fe K$\alpha$ line
may strongly depend on $\lambda_{Edd}$, which can be explained if the
ionization state and/or truncation radius of the accretion disc changes with
$\lambda_{Edd}$. The non-detection of the broad line in the BLS1 sub-sample can
be explained if the the average EW of the relativistic Fe K$\alpha$ line is
weak or/and the fraction of sources with relativistic Fe K$\alpha$ line is
small in BLS1 galaxies.
