NavList:

There have recently been some discussions regarding evaluation of observational data with the help of a straight line of "best fit". I haven't followed the discussions in all details, but have some comments on one issue that possibly isn't well known.

Given a set of data pairs (times and altitudes (or distances)), it is possible to calculate a line of best fit using the method of least squares. This line gets a certain slope and intercept, that minimize the sum of the squared distances between the observed values and that line. Now, if you calculate the average value of times and the average value of altitudes, this data pair is placed exactly on this line. This is a mathematical fact (pointed out by Alex E a couple of years ago, on this list). Thus there is no reason to calculate and plot the line of best fit in order to find a "better" value for sight reduction, just use the average of times and altitudes.

Furthermore, if you want to use a pre-determined slope, that you know your observatinal series should follow, then this line with a given slope also passes exactly through the point of average time and average altitude, irrespective of slope, when adjusted to minimize the sum of squares. This line actually pivots around the "average point". As soon as you move the line off the "average point" the sum of squares will increase, minimum sum is obtained when using the "least square slope" mentioned in previous section. Thus there is no reason to calculate the expected slope either, just use the average of times and altitudes.

Detecting blunders can be done by inspection.

Lars, 59N 18E
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