The message
from Terry Fields contains these words:

You might be interested in the following exercise, where I took my BP
data and treated it to a) a 10-point smoothing exercise, and b) a
linear regression, which had a lower variance than a second-order
polynomial (not shown)(all data manipulation courtesy of Excel
spreadsheet).

Snip all detail

Terry, I don't have Excel so don't have any familiarity with the
underlying mechanics of Excels smoothing filters (which in essence what
that regression is). The Met Office filter, at least when it has the
full range of numbers, has the advantage that it weights the closest
data higher than the more distant data while introducing no variation in
the overall total. Where it seems to go wrong is the fiddle used to
extend the smoothed curve up to the end of the data. I could be wrong
but it doesn't appear that Excel does anything to correct any possible
bias that is introduced by a short term effect at the end of the
sequence but almost certsainly there is some form of weighting in its
polynomial regression. It wouldn't work with a non linear data
otherwise.

You can place too much reliance on manipulated data. For instance your
straight line, the 'linear regression' is almost certainly an artifact.

I can't be sure but I suspect that your moving average is the simple one
with no weighting.

As you have Excel it would be relatively simple for you to take the Met
Office figures and see how polynomial regression differs from the MO
filter both during the period where the filter can work on all 21 years
and in the final 10 where the end bias gets stronger and stronger.

--
Roger Chapman