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Math Help - Curve Fitting

  1. #1
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    Curve Fitting

    If I have a set of data points, how can solve the curvelinear best fit equation for the Laffer Curve, -ax^2+bx=0?

    Thank you for your time,

    Dustin.
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  2. #2
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    I'm not sure exactly with you're asking Dustbin

    you have the data points and you want to find a model i.e. \displaystyle f(x)=-ax^2+bx for these points or you want to solve \displaystyle -ax^2+bx=0 once you have the model?
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  3. #3
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    I have a set of data points tax and rev/pop. I want to run a curvelinear regression to obtain the function and find the rev maximizing rate.
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  4. #4
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    Have you tried to fit a least squares on your line?

    If not maybe find a line of best fit on \displaystyle f(x)=-ax^2+bx using two points from your data set.
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  5. #5
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    How do I do that for a quadratic?
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  6. #6
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    Which one, the least squares or a simple line of best fit?
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  7. #7
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    Doesn't least squares generate the polynomial of best fit?
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  8. #8
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    It does, but it may give you one in the form of y=ax^2+bx+c instead of a laffer curve i.e y=ax^2+bx

    Therefore if tyou force the model to be y=ax^2+bx and solve for a and b using two reliable points you may get a better fit.

    Regression is a dark beast.
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  9. #9
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    The Laffer Curve is forced through the origin.
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  10. #10
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    I am aware of this hence why we don't want a curve that has a nonzero y-intercept.

    Maybe you can post your dataset?
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  11. #11
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    Alabama:
    Rate: 5, 5, 5, 5, 5, 5, 5, 5, 5, 6.5, 6.5, 6.5, 6.5, 6.5
    Rev/Pop: 76.44097206, 60.17941474, 50.72157557, 51.45070669, 54.28532149,50.89583831, 51.39448729, 41.88461272, 64.81533834, 47.43814622, 55.25741448, 72.27369959, 97.92370105, 85.43364431
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  12. #12
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    Sorry Dustbin, I have plotted that dataset and as you probably know yourself it is horrible. Is there any reason you want to fit a parabola to that?
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