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    Re: Averaging
    From: Herbert Prinz
    Date: 2004 Nov 5, 05:07 -0500

    Alexandre Eremenko wrote:
    > 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).
    I want nothing of the sort. As I said, my equation M * x = a refers to any
    system of linear equations.  In the problem in hand, these represent LOPs
    and the solution of the system is the FIX. I said it is wrong to go the
    roundabout way via an intermediate set of best fitted lines (be they
    straight or otherwise). But I said that several times already.
    > 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.
    Have you actually looked at the algorithm in the N.A.? Have you looked at
    the articles in the Navigation Journal? That's what I am proposing. How can
    you believe that I want to solve a linear regression, when I said in several
    messages to its proponents that this is the wrong way to go about it?
    Herbert Prinz

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