  Precise atmospheric observations have been made for a growing sample of warm
Neptunes. Here we investigate the correlations between these observations and a
large number of system parameters to show that, at 95% confidence, the
amplitude of a warm Neptune's spectral features in transmission correlates with
either its equilibrium temperature (T_eq) or its bulk H/He mass fraction
(f_HHe) --- in addition to the standard kT/mg scaling. These correlations could
indicate either more optically-thick, photochemically-produced hazes at lower
T_eq and/or higher-metallicity atmospheres for planets with smaller radii and
lower f_HHe. %Since hazes must exist in some of these planets, we favor the
former explanation. We derive an analytic relation to estimate the observing
time needed with JWST/NIRISS to confidently distinguish a nominal gas giant's
transmission spectrum from a flat line. Using this tool, we show that these
possible atmospheric trends could reduce the number of expected TESS planets
accessible to JWST spectroscopy by up to a factor of eight. Additional
observations of a larger sample of planets are required to confirm these trends
in atmospheric properties as a function of planet or system quantities. If
these trends can be confidently identified, the community will be
well-positioned to prioritize new targets for atmospheric study and eventually
break the complex degeneracies between atmospheric chemistry, composition, and
cloud properties.
