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    Re: Linear Regression In Reverse
    From: George Huxtable
    Date: 2005 Jun 5, 15:50 +0100

    I'm still in a bit of difficulty over Peter Fogg's proposal for determining
    altitude of a body at the exact moment it's on the observer's prime
    vertical (his East-West line).
    >George has written, on the process of LINEAR REGRESSION IN REVERSE:
    >> I just don't understand what Peter is proposing here. My fault, rather
    >> than
    >> his, no doubt.
    >> Could he provide a bit more detail, please, perhaps with an example?
    >> Couldn't the moment, at which the Sun was theoretically on the East-West
    >> line, be precalculated ...
    >Yes, precalculation is what I am proposing, to give the moment of east or
    >west azimuth (prime vertical).
    How is that precalculation done, I ask? What's the expression that's used
    to provide the moment when the body is exactly East or West? I can see that
    it could be determined by plugging an azimuth of 90 degrees into a standard
    navigational triangle, but what's the resulting trig expression?
    Presumably the precalculation is based on an assumed position. How
    sensitive is the result to errors in that assumed position, and does that
    matter? Does the method provide for reiteration if the observation shows up
    significant errors in that assumed position?
    How important is it, anyway, to know the exact moment when the Sun is on
    the prime vertical? As I see it, it's a very undemanding requirement.
    >Then a series of observations of the body (it can be any celestial object
    >for which almanac data is available, just as observation of meridian passage
    >can, in theory, be made with any body).
    >From then on it is the application of what seems a favourite hobby-horse of
    >mine, comparing the slope with the sights.
    Is this a precalculated slope? If so, how is it calculated? What's the
    expression used to give the slope? What's the slope used for? If the
    calculated slope doesn't correspond with the observed slope of the sights,
    around the precalculated moment, what happens next? Is something then
    adjusted to fit?
    Its something I have written
    >about here time and again; once with the title 'Good Data from Bad'. Now
    >there's an approach you can appreciate.
    >The practical advantage here is that it is not necessary to manage to make a
    >timed observation at exactly the precalculated moment. So long as a series
    >of sights encompasses that moment the time can be selected later from the
    >graphed time axis and related, via the slope, to its accompanying altitude
    >on the other axis.
    To clarify matters to me, let me ask: If you DID manage to make that
    altitude observation at exactly that precalculated moment, would any of
    this "slope" business be required?
    >Rather than churn out more words I would encourage you to provide your own
    >example, just as I have with Fred. Give it a whirl. I hesitate to say much
    >more; for fear of becoming a bore just banging on about his id?e fixe, but I
    >will say that the moment I understood this slope method was an Eureka moment
    >for me and it has become part of the process of timed sights, just like
    >recording the compass bearing of the body at the time of observation. Good
    >or bad, the only reason I do these things is because they work a treat.
    Peter, please don't hesitate to say more, in response to these requests, to
    explain just what you do and how you do it. In those circumstances, nobody
    will accuse you of "just banging on about his idee fixe".
    I don't see how you can expect me to "provide my own example", when your
    methods remain unclear to me (perhaps because of my own naivety). Only you
    can do that, to illustrate those very methods.
    >How do you like the new name: LINEAR REGRESSION IN REVERSE. Nifty, huh?
    It's not what it's called, it's what it DOES, that's more important.
    In a later message, Peter added-
    >George asked, on the subject of Reverse Linear Regression (is this a better
    >version of my identifying title?):
    >> Could he provide a bit more detail, please, perhaps with an example?
    >Hidden away in a back alley of the Starpath site is an informative article
    >on this, complete with an example showing how this technique is superior for
    >its purpose; compared to its relative with whom it is often confused: linear
    >The other one-stop shop that has everything needed: example, slope
    >calculator, the form incorporating graph paper specifically designed for the
    >purpose (and much more) is George Bennett's book "The Complete On-Board
    >Celestial Navigator". It is available from Celestaire, who deserve our
    >patronage and support, being uniquely dedicated to supplying the tools
    >navigators need.
    Well, I wasn't asking about the general topic of linear regression
    (reversed or otherwise) but about the specific details of how Peter himself
    carries out his observation and analysis, questions that I have spelled out
    in detail above. Bennett's book provides no answers to those questions.
    Somehow, I doubt whether "a back alley of the Starpath site", to quote
    Peter's woolly reference, would do so either. A direct response from Peter
    is requested, please.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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