# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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