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George declares:
> ... in the
> circumstances of that exercise,

Regression analysis will produce a line from ANY scatter of points.
Its wonderful, but its not necessarily useful.

The "circumstances of that exercise" are artificial, with alleged
"random scatter".  Slope analysis works so well because the data
points are not random, they follow the slope except for error.
Therefore the deviation from the slope is an indication of error.

Random data points are not relevant to slope analysis.

While we have good reason to be deeply suspicious of your contrived
examples, the main problem, again, is that you seem determined to
prove that slope analysis MUST be no more useful than averaging -
resolutely ignoring the elephants in that room (eg; the elimination of
gross error).  Wrong attitude.

I would have thought the more rational approach would be to put
prejudice to one side and try to approach something unfamiliar with as
open a mind as possible.

The mention of gross error reminds me of another advantage of slope
analysis over averaging or regression analysis.  What looks like an
outlier may not be.

This has actually happened to me, on more than one occasion.  While
concentrating on the seconds, the wrong minute of time gets recorded.
Or while focused on the minutes of arc displayed by the sextant, the
wrong degree is marked (blame the scribe).

This is also another example of why it is important to THINK about
what those data points mean, rather than just feeding them into some
blind number-crunching mathematical process.  Once plotted its obvious
that the point is an outlier, an apparent gross error.  But before
discarding the point its worthwhile checking that it is not just a
whole minute of time out, or a whole degree.

I guess its still a gross error, but once the problem is identified
that data point can usefully rejoin its brothers.  From being a piece
of data that could drag the average away from the straight and narrow
(of conformity to the slope) it can be converted into orthodoxy.  The
prodigal son, back from the wilderness.

Now THAT'S magic for you.

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