  Using Chandra High Energy Grating (HEG) observations of 32 AGNs, we present a
systematic study of the X-ray Baldwin effect (XBE, i.e. the anti-correlation
between narrow Fe K{\alpha} line EW and X-ray continuum luminosity for AGN
samples) with the highest spectral resolution currently available. We have
previously reported an anti-correlation with EW\proptoL(2-10 keV)^-0.22 in a
HEG sample, and the correlation is much weaker after averaging multiple
observations of individual AGNs (EW\proptoL(2-10 keV)^-0.13). This indicates
that rapid variation in X-ray continuum plays an important role in producing
the XBE, and such an effect should also be visible in individual AGNs. In this
paper, by normalizing the line EWs and continuum luminosities to the
time-averaged values for each AGN in our sample with multiple HEG observations,
we find a strong anti-correlation between EW and Lx (EW/<EW>\propto
(L/<L>)^-0.82+/-0.10), consistent with the XBE expected in an individual AGN if
the narrow line flux remains constant while the continuum varies. This is first
observational evidence that the Fe K{\alpha} line flux in a large sample of
AGNs lacks of a corresponding response to the continuum variation, supporting
that the narrow Fe-K line emission originates from a region far from the
nucleus. We then performed Monte-Carlo simulations to address whether the
global XBE can be produced by X-ray continuum variation solely, and found that
such interpretation of XBE cannot be ruled out statistically. One thus should
be very cautious before reaching any scientific conclusion based on an observed
XBE.
