Looking at sampling error correction factor for regression
for ensemble filters. Basic idea here is that there is 
some noise so that the sample statistics provide a 
sample regression factor with some mean and some standard
deviation. When I run the multi-group ensemble, I end up
getting an estimate of this mean and the standard 
deviation. Right now, I'm ignoring the fact that there
are errors in this mean and sample standard deviation
but this should be accounted for in the future. Anyway,
one can then look for a factor that is a function of
only the ratio of the standard deviation of the sample
regression coefficient to the sample mean. This factor
is adjusted so that the expected value of the squared
error of the sample regression coefficient from the actual
value is a minimum. sys_sim101.f90 simulates this. If one
selects a single group the appropriate coefficient is
returned. Fitting to this gives the following analytic
relation:

reduction factor = 1 / (ratio**2 + 1) 

where ratio is the ratio of the standard deviation to the
sample mean for the regression (or distance moved if one
prefers).
