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Dear Herbert,
I am really surprised that after such long discussion
on the "Averaging", you still say:

On Wed, 3 Nov 2004, Herbert Prinz wrote:

> Simple averaging of the altitudes is always wrong.

My impression was that in this long discussion
I managed to convince
everybody
that just the opposite is true:

Simple averaging of altitudes is almost always RIGHT.
(almost=except few situations which were explicitly described
before).

Your "math argument" is correct, of course, but if you complete
it to the end you will see that it gives EXACTLY the same answer
that I propose:-)

Just do it. You want to find the line y=ax+b of the best fit
say from 3 observations
(x_1,y_1), (x_2,y_2), (x_3,y_3).
Just do the "least square procedure" as you described, and find a and b.
Then compute the averages x=(x_1+x_2+x_2)/3
and y=(y_1+y_2+y_3)/3.
And then plug the averages to the equation y=ax+b.
If you do all your computations correctly, you will see that they fit:-)
So the "method" you propose, in the case of a linear function,
gives EXACTLY the same answer as simple averaging.

Alex.

   

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