  The activity indicators of M dwarfs are distinctly different for early and
late types. The coronae of early M dwarfs display high X-ray luminosities and
temperatures, a pronounced inverse FIP effect, and frequent flaring to the
extent that no quiescent level can be defined in many cases. For late M dwarfs,
fewer but more violent flares have been observed, and the quiescent X-ray
luminosity is much lower. To probe the relationship between coronal properties
with spectral type of active M dwarfs, we analyze the M3.5 and M4.5 components
of the EQ Peg binary system in comparison with other active M dwarfs of
spectral types M0.5 to M5.5. We investigate the timing behavior of both
components of the EQ Peg system, reconstruct their differential emission
measure, and investigate the coronal abundance ratios based on emission-measure
independent line ratios from their Chandra HETGS spectra. Finally we test for
density variations in different states of activity. The X-ray luminosity of EQ
Peg A (M3.5) is by a factor of 6-10 brighter than that of EQ Peg B (M4.5). Like
most other active M dwarfs, the EQ Peg system shows an inverse FIP effect. The
abundances of both components are consistent within the errors; however, there
seems to be a tendency toward the inverse FIP effect being less pronounced in
the less active EQ Peg B when comparing the quiescent state of the two stars.
This trend is supported by our comparison with other M dwarfs. As the X-ray
luminosity decreases with later spectral type, so do coronal temperatures and
flare rate. The amplitude of the observed abundance anomalies, i.e. the inverse
FIP effect, declines; however, clear deviations from solar abundances remain.
