  Many studies of the solar corona have shown that the observed X-ray
luminosity is well correlated with the total unsigned magnetic flux.
  In this paper we present results from the extensive numerical modeling of
active regions observed with the \textit{Solar and
  Heliospheric Observatory} (\textit{SOHO}) Extreme Ultraviolet
  Telescope (EIT), the \textit{Yohkoh} Soft X-ray Telescope (SXT), and the
\textit{SOHO} Michelson Doppler Imager (MDI). We use potential field
extrapolations to compute magnetic field lines and populate these field lines
with solutions to the hydrostatic loop equations assuming steady, uniform
heating. Our volumetric heating rates are of the form $\epsilon_H\sim
\bar{B}^\alpha/L^\beta$, where $\bar{B}$ is the magnetic field strength
averaged along a field line and $L$ is the loop length. Comparisons between the
observed and simulated emission for 26 active regions suggest that coronal
heating models that scale as $\epsilon_H\sim \bar{B}/L$ are in the closest
argreement the observed emission at high temperatures. The field-braiding
reconnection model of Parker, for example, is consistent with our results. We
find, however, that the integrated intensities alone are insufficent to
uniquely determine the parameterization of the volumetric heating rate.
Visualizations of the emission are also needed. We also find that there are
significant discrepancies between our simulation results and the lower
temperature emission observed in the EIT channels.
