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    Re: Linear regression and other tools
    From: Brad Morris
    Date: 2018 Oct 11, 11:10 -0400
    Hello Lars

    Perhaps my understanding is faulty.

    My understanding is that linear regression is used to fit a line to a set of points in which noise or error is present.  Multiple sets (X,Y) of points, Y as a function of X, are used to fit that line.  I did not consider averaging of multiple different Y values at a single X value to be linear regression, as we obtain a point, not a line.   If simple averaging is linear regression, then my understanding is clearly wrong.

    Further, I understood that linear regression was computationally expensive.  I don't think of sketching or fairing a curve of altitude as linear regression when there is no mathematical rigor.  Of course, by eye it probably looks okay, but is it optimized?  Does the hand faired curve obtain precisely the same values as linear regression? I think the answer to that to be a no. Given a set of points, will three different navigators fair in, by hand, the same curve?  Again, I believe the answer to be no. 

    One can discuss the magnitude of error and the utility of the result when it contains error, but this merely muddies the water.  No mathematical rigor results in an imprecise result.  Linear regression provides rigor, repeatability and precision for a given data set.

    When the rigor is applied, for example a least squares fit, then the sheer volume of calculations required makes the task daunting for a navigator who has only non-electronic means.  Once an electronic calculator or computer becomes available to the navigator, then the drudgery is avoided.  

    Due to the computationally expensive nature of linear regression and the corresponding lack of computational tools available to pre-calculator navigators, I assumed that the navigator would not avail himself of the use.  I cannot readily find instructions or admonitions to use linear regression in my navigational library.  Practical linear regression can become a useful tool to navigators once the simple means to perform it becomes available.  The means to perform it wasn't generally available, consequently, it wasn't generally practiced.  Again, my understanding.

    I may have all of this wrong

    Brad

    I have studiously avoided commentary on non-electronic calculators such as a slide rule combined with linear regression.  













    On Thu, Oct 11, 2018, 6:47 AM Lars Bergman <NoReply_Bergman@fer3.com> wrote:

    Brad wrote "While regression can obviously be used in CN now, I do not believe it was generally used then".

    Averaging times and altitudes (or lunar distances) have been used for a long time. This is in effect equal to linear regression, see my post "Slopes and least squares" from 2010 Dec 9 in the archive.

    Lars, 59°N 18°E

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