NavList:

Nope. Terrible idea. You don't want a regression here. That will place undue emphasis on bad data points. We know the rate of change of a lunar in almost every case. You use that for the slope and, if you really want a line to compare against (why?), you find the best line fit by sliding the line with the right slope up and down (only one free parameter), and you use that same process to throw out an oulier potentially (but only if you have at least five sights in practical terms, and you can achieve the same by picking the median point among the set, in terms of distance from the line with the appropriate slope).

Running a quadratic regression with three observed data points is wrong on multiple levels. Never do that. The curve you get is an illusion and completely defeats the purpose of a regression in the first place. Similarly, never run a third-power regression on four data points. And if you run a linear (frst power) regression on two data points, you surely better recognize that you have accomplished nothing. You're clearly still confused about the great difference between fitting a polynomial to exactly-calculated points and noisy observed data points. The mathematical tool to perform the task is nearly the same, but the goals and the process are very different. Over-fitting curves to data is one of the classic square-one beginners' mistakes in data analysis. 

Your description of the process of taking altitudes before and after a set of lunars is rather misguided. You need at most one before and one after on each body, and you average. The quality of these altitudes can be rather poor without affecting the clearing process so a simple average will work fine, or a time-proportioned one if the altitudes do not properly, symmetrically "wrap" the lunar distance sights in between. In addition to being entirely un-necessary, a regression would be a mistake for all the usual reasons.

As for mentioning Dunthorne's and Young's methods, this is little more than name-dropping. You might as well have said George and Ringo. 

Frank Reed