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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- Nov 23rd 2010, 02:24 PMdwsmithCurve 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. - Nov 23rd 2010, 02:43 PMpickslides
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 \displaystyle f(x)=-ax^2+bx $ for these points or you want to solve $\displaystyle \displaystyle -ax^2+bx=0$ once you have the model? - Nov 23rd 2010, 02:45 PMdwsmith
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.

- Nov 23rd 2010, 02:58 PMpickslides
Have you tried to fit a least squares on your line?

If not maybe find a line of best fit on $\displaystyle \displaystyle f(x)=-ax^2+bx$ using two points from your data set. - Nov 23rd 2010, 03:01 PMdwsmith
How do I do that for a quadratic?

- Nov 23rd 2010, 03:10 PMpickslides
Which one, the least squares or a simple line of best fit?

- Nov 23rd 2010, 03:12 PMdwsmith
Doesn't least squares generate the polynomial of best fit?

- Nov 23rd 2010, 03:22 PMpickslides
It does, but it may give you one in the form of $\displaystyle y=ax^2+bx+c$ instead of a laffer curve i.e $\displaystyle y=ax^2+bx$

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

Regression is a dark beast. - Nov 23rd 2010, 03:27 PMdwsmith
The Laffer Curve is forced through the origin.

- Nov 23rd 2010, 03:31 PMpickslides
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? - Nov 23rd 2010, 03:39 PMdwsmith
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 - Nov 23rd 2010, 03:55 PMpickslides
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?