Finding the Formula for a Curve

Question

Is there a program that will take "response curve" values from me, and provide a formula that approximates the response curve?

It would be cool if such a program would take a numeric "percent correct" (perhaps with a standard deviation) so that it returns simplified formulas when laxity is permissable, and more precise (viz. complex) formulas when the curve needs to be approximated closely.

My interest is to play with the response curve values and "laxity" factor, until such a tool spits out a curve-fit formula simple enough that I know it will be high performance during machine computations.

Answer 1

Check our Eureqa, a free (as in beer) utility from Cornell University.

What's particularly interesting about Eureqa is that it uses genetic algorithms to fit the input curve you specify, and you can say what functions to allow or not in the fit. So if you wanted to stay away from sine and cosine, for instance, it wouldn't even consider those. It will also show you the best approximation with the fewest steps, and the most accurate approximation (regardless of steps). You can also run the fitting tool across multiple networked computers to speed up getting your results.

It's a very interesting tool -- check out their how-to videos.

Answer 2

Matlab, mathematica, octave, maple, numpy, scilab are just six among thousands of programs that will do this.

Answer 3

SigmaPlot - does exactly what you're looking for. Statistics and visualization of data.

_{(source: sigmaplot.com)}