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    Re: Linear regression and other tools
    From: Antoine Couëtte
    Date: 2018 Oct 14, 01:23 -0700

    RE : Dear Tony,

    I have checked you published values, and compared to mine to conclude that your values show absolutely no random noise whatsoever.

    Here are our results for comparison (own results in bold):

    ·         12:00UT, 60°00'N;30°00'E: HCDeneb = 43°19'12"; HCCapella = 18°22'10"

                                                           43°19’08’’ / 071.2°  18°22’07’’ / 340.2°

    ·         12:10UT, 60°02'N;30°02'E : HCDeneb = 44°32'18"; HCCapella = 17°59'26"

                                                            44°32’14’’ / 073.0°   17°59’23’’ / 342.0°

    ·         12:20UT, 60°04'N;30°04'E : HCDeneb = 45°45'59"; HCCapella = 17°39'02"

                                                            45°45’55’’ / 074.9°   17°38’59’’ / 343.8°

    ·         12:40UT, 60°08'N;30°08'E : HCDeneb = 48°14'50"; HCCapella = 17°05'17"

                                                            48°14’46’’ / 078.8°   17°05’14’’ / 347.5°

    ·         12:50UT, 60°10'N;30°10'E : HCDeneb = 49°29'51"; HCCapella = 16°51'59"

                                                            49°29’46’’ / 080.8°   16°51’56’’ / 349.3°

    ·         13:00UT, 60°12'N;30°12'E : HCDeneb = 50°45'07"; HCCapella = 16°41'05"

                                                            50°45’03’’ / 082.8°   16°41’01’’ / 351.1°

    Therefore you are observing in ideal conditions:

    - No random noise whatsoever, and perfect observations. Since real world observations are never perfect as we all know it, which implies that our Celnav fixes are necessarily in error, we can get bogged down into endless discussions about acceptable ways to deal with such observation errors (e.g. g43064). And:

    - The heights of the bodies are not close from culmination ( 45° for Deneb and 18° for Capella).

    Under such conditions, and since you need a minimum of 3 observations to compute 2nd order regression - you have more than enough of them for each body ! - we can expect all your second order coefficients to be quite excellent.

    In other words, since you are remaining within a valid time-span for the use of a second order regression, and since your are dealing with perfect measures, no surprise that in this specific case your 2nd order regression example works beautifully !

    Your example unfortunately does not constitute a general proof that 2nd regression will perform equally well under all circumstances and environments because in the real world things are not that crystal clear !  :-(

    Best Friendly Regards,

    Antoine

       
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