A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2022 May 11, 06:59 -0700
Jim Rives was puzzled about the bad result using a straight line regression a few days ago, then recalculated and came to the conclusion that "The regression line is far better than a simple average, which is what i would have expected and relieved to see is proved out."
I do not agree with this conclusion, because "a simple average" will fall exactly on the regression line. The arithmetic means of the times and the distances should fit perfectly into the linear least squares regression formula, if based on the same input data and calculated correctly.
A randomly choosen time and the correspondingly calculated distance could give a "better" or"worse" result than the average of times and distances if the calculated slope of the line does not correspond exactly to the actual slope of distance versus time. This is probably the explanation, and a short time span of the observations will increase the uncertainty in the slope determination.