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Math Help - Find a formula for serial data

  1. #16
    A Plied Mathematician
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    Hmm. Well, I got the Excel Solver routine to fit this curve to your data using a "manual" least-squares fit, and it's terrible. Moreover, the "hyperbola" doesn't even approach the alleged asymptote, nor does it approach the x-axis! The idea is sound, I think, but I have an error in its execution. I've spent too much time on it today already, so I'm afraid it'll have to wait.

    Very fun problem, though! Thanks for posting it.
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  2. #17
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    i dindn t know about this software before.............


    have some rest :-) but i know that your brain will continue to think about this problem. I m a biologist it happen to me the same :-)
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  3. #18
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    Quote Originally Posted by Ackbeet View Post
    Hmm. Well, I got the Excel Solver routine to fit this curve to your data using a "manual" least-squares fit, and it's terrible. Moreover, the "hyperbola" doesn't even approach the alleged asymptote, nor does it approach the x-axis! The idea is sound, I think, but I have an error in its execution. I've spent too much time on it today already, so I'm afraid it'll have to wait.

    Very fun problem, though! Thanks for posting it.
    yeah i know , i think they made this strange data with the purpose to don t be able to handle it in a n easy way in effect
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  4. #19
    A Plied Mathematician
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    I haven't forgotten you. Alas, I have no real news. I haven't gotten my hyperbolas to fit correctly, despite having verified the formulas in Excel. For some reason, my ansatz appears to break down at the scale you have for your data. That is, the parameters Excel comes up with and plots is matched by what Mathematica plots when I put those parameters in there. Something is rotten in the state of Denmark!

    I really want to get this, but I think I'm missing something basic. These hyperbolas are extraordinarily difficult to work with.

    Hopefully, I can find something simple and fix it.
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  5. #20
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    Quote Originally Posted by Ackbeet View Post
    I haven't forgotten you. Alas, I have no real news. I haven't gotten my hyperbolas to fit correctly, despite having verified the formulas in Excel. For some reason, my ansatz appears to break down at the scale you have for your data. That is, the parameters Excel comes up with and plots is matched by what Mathematica plots when I put those parameters in there. Something is rotten in the state of Denmark!

    I really want to get this, but I think I'm missing something basic. These hyperbolas are extraordinarily difficult to work with.

    Hopefully, I can find something simple and fix it.
    take your time, also because if can t, nobody can :-)
    DC
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  6. #21
    Member HappyJoe's Avatar
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    Let us know, if you do a least squares fit and if the fit is good.

    As has been pointed out already, a high-degree polynomial fit won't work well for the purpose of extrapolation. The polynomial only fits the points you tell it to, but further out (in the domain of extrapolation), the graph of the polynomial will likely begin to fluctuate.

    If Ackbeet's model doesn't fit your data well, have you considered using an appropriate polynomial in the interpolation phase, and then appending a straight line to the right end-point of the graph of the polynomial in the extrapolation phase? I don't know if this extrapolates your data well enough, but if you end up trying this after Ackbeet's model, let me know.
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  7. #22
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    Quote Originally Posted by HappyJoe View Post
    Let us know, if you do a least squares fit and if the fit is good.

    As has been pointed out already, a high-degree polynomial fit won't work well for the purpose of extrapolation. The polynomial only fits the points you tell it to, but further out (in the domain of extrapolation), the graph of the polynomial will likely begin to fluctuate.

    If Ackbeet's model doesn't fit your data well, have you considered using an appropriate polynomial in the interpolation phase, and then appending a straight line to the right end-point of the graph of the polynomial in the extrapolation phase? I don't know if this extrapolates your data well enough, but if you end up trying this after Ackbeet's model, let me know.

    do you means some like a linear or better log extrapolation between 2 point????
    i guess if Ackbeet don t figure out some (and i have the feeling he will)i will not have other way to follow.
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  8. #23
    Member HappyJoe's Avatar
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    I mean that you can use any nice function to interpolate, such as your polynomial from before. However, use only this function in the interpolation area. For extrapolation, I was thinking of joining the graph of the chosen function with that of a straight line. The interpolating function is shown in blue, while the straight line is shown in red: ImageShack® - Online Photo and Video Hosting
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  9. #24
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    in effect is not a bad idea too
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