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Thread: Curve equation to model this data

  1. #1
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    Curve equation to model this data

    I regularly encounter a type of curve which cannot be easily expressed using a simple curve equation (e.g. trendlines available in Excel). See attached the example curve data. In the spreadsheet I had begun to try fitting an exponential approach-type curve, though to little avail.

    Curves.xls

    I was wondering whether the great minds of this forum knew of a better curve type that could characterise this data? I'm trying to avoid using high-order polynomials as they seem to be unreliable and the shape of the curves are, in reality, controlled by just a handful of parameters (4 to 6 inputs at most). The example data in the spreadsheet provides a range of different shapes to try fitting an equation to; if one type of equation works for all four examples, then I imagine it will work on all my other examples.

    Thanks in advance for any help with this curve fitting!
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  2. #2
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    Re: Curve equation to model this data

    I can't edit the above post, so apologies for the double post already.

    I've found that an equation of the form:

    y = [A.x/(1 + (x/B)^C)] + D

    ... looks to be promising. I'm unsure what this type of equation is called.

    D is solved by inputting the minimum x value, and its associated y value, and then rearranging the equation. A, B and C are the curve fitting parameters.

    For example, I found that A = -103, B = 1.62 and C = 1.5 provided a reasonable match to dataset 1 in the previously attached spreadsheet. I think this could be improved with a solver solution, however.

    The above equation form looks to be a promising start. However, I'd be interested to see if anyone else has a better equation to use.
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  3. #3
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    Re: Curve equation to model this data

    Typically "splines", http://mathworld.wolfram.com/Spline.htm, i.e. piece-wise polynomials, will give a "nicer" fit to a large number of points than high degree polynomials.
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  4. #4
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    Re: Curve equation to model this data

    Using splines or other functions which are only valid for certain ranges isn't suitable for what I am aiming to do. Essentially I want a simple(ish) equation that fits the curves, and then I want to determine how the coefficients in that equation vary with different input parameters.
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