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Math Help - Curve fitting of experimental data

  1. #1
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    Curve fitting of experimental data

    Hi, everyone.

    I need to fit a set of data with an approximating function. I have tried functions such as polynomial, exponential & power law, but without success.

    Pls., could someone kindly help fit the set of data given below with a closely approximating curve, and give the approximating function.

    I need to use the approximating function for further analysis.


    Data:

    i 1 2 3 4 5 6 7 8 9 10 11 12 13
    x 0.161166 0.53935
    0.844731
    0.910587
    0.98339
    1.121214
    1.165118
    1.186792
    1.274044
    1.317948
    1.383526
    1.419927
    1.514681
    y
    0.039954
    0.049806
    0.074614
    0.09902
    0.12425
    0.149126
    0.17226
    0.19807
    0.246139
    0.295268
    0.393406
    0.493437
    0.689996


    Looking forward for the kind assistance.

    Thanks a lot.

    ---
    Sam
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  2. #2
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    Re: Curve fitting of experimental data

    Have you plottied the data to see what might be a good fit? It increases quickly so it looks like an exponential or a high order polynomial would fit well. I tried to fit these and you were right that an exponential fit does not work well but a quadratic or cubic relationship fits quite well.
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  3. #3
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    Re: Curve fitting of experimental data

    Did you try y = a + b exp(c x) ?

    Curve fitting of experimental data-graph.jpg
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  4. #4
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    Re: Curve fitting of experimental data

    The equation y = a + b exp(c x) generaly requires the use of a non-linear linear method of regression because the function is non-linear relatively to the parameter c.These methods are recursive and a guessed value of c is necessary to start the iterative process.
    A different method (straightforward, i.e. not recursive) is published on Scribd, "Régressions et équations intégrales", p.16-17 (in French, but the equations are very simples and understandable in any language). Link to Scribd :
    JJacquelin's Documents | Scribd
    The result with this method is shown below :

    Curve fitting of experimental data-regression.jpg
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  5. #5
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    Re: Curve fitting of experimental data

    There is a typing mistake on the first figure (message #3, 10:17 AM) : it is not c=0.08628, but c=4.045969
    Anyway, this preliminary result was less accurate than the result in message #4.
    Last edited by JJacquelin; May 14th 2014 at 03:45 AM.
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