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Simple nonlinear least squares curve fitting in JMP

In his Walking Randomly blog, Mike Croucher shows how to fit a simple nonlinear curve using five different statistical programming libraries: R, MATLAB, Maple, Julia and Python/numpy. The idea is to provide concrete examples for a commonly asked modeling question that is simple to state but not so simple to solve.

For a the given data set of 10 x and y values, the problem is to find the best values for parameters p1 and p2 so that the following curve best fits the y values:

 p1 cos( p2 x ) + p2 sin( p1 x )

Since nonlinear fitting involves an iterative search of the solution space, we need starting parameter values, which Croucher gives as

p1=1.0, p2 = 0.2.

So how would you do the same thing in JMP?

Normally, you would start with a data table and use the Nonlinear platform under the Analyze menu to interactively launch the fit. For a model like this, which isn't built-in to JMP, you could add it in a formula column and use that in the Nonlinear dialog. But like most everything in JMP, it can be completely driven by a JSL script if you want.

Here's my JSL version:

xv= [-2, -1.64, -1.33, -0.7, 0, 0.45, 1.2, 1.64, 2.32, 2.9];

yv = [0.699369, 0.700462, 0.695354,  1.03905,  1.97389,

      2.411430, 1.910910, 0.919576, -0.730975, -1.42001];


dt New Table("Data",

    New Column("x", Set Valuesxv )),

    New Column("y", Set Valuesyv ))



dt << Nonlinear( Y( :y ), X( :x ),

      Model( Parameter( {p1 1, p2 0.2},

            p1 *Cosine( p2 *:x ) + p2 *Sine( p1 *:x ) )),

      Finish, Confidence Limits );

That script produces the following interactive output.

Some of the other languages require a bit of extra work to get the confidence intervals, so it's nice to see it's just one option away in JMP.