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This page contains answers to common questions.
 

   

Why don't all my data points lie exactly on the fitted curve?

Normally there is some experimental or measurement error in the data. It is rather rare to have all points lie exactly on the fitted curve, unless whatever problem you are working on has given you perfect data. When the number of coefficients equals the number of data points, it usually gives a perfect fit. There are an infinite number of equations that will fit your data perfectly, so always try to find an equation that makes sense and actually models the problem you are working on. Because the relationships in the problem being worked on are often unknown, people use the function finders to try and find the simplest and most reasonable equation that fits their data.

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Where can I find Tanh() formulas?

The "polyfunctionals", which gave you a random equation that could fit your data well, are linear combinations of functions like x squared, square root of x, sine of x, etc. - and in the case of tanh(x) the hyperbolic tangent of x. In the function finder's "Equation Family Inclusion," uncheck the polyfunctionals and possibly the polynomials - that will give you named equations only.

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How do you determine mathematically that the model fits the data points or that the result is optimal?

Some equations are solved by standard linear regression and that is not iterative. Some equations require iterative methods.

For the nonlinear iterative equations, James uses a genetic algorithm named Differential Evolution (http://www.icsi.berkeley.edu/~storn/code.html) to make an initial guess at the coefficients. He then uses iterative methods to refine that guess, until continued iteration make no practical improvement to the results. He does not use brute force as it would take too much CPU time.

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What are the formatting options for graphs?

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Last modified: 01/28/09.