Understanding Parameter Errors in fitnlm

Following this question , I have some noisy data that I wish to fit to a sinusoid with some phase. I use fitnlm to perform this fit, and I'm interested in knowing how to find the error of the fit. I see that the output automatically calculates the standard error, but I can't find any documentation on what exactly this means. Is this the reduced chi^2? (And if so, isn't reduced chi^2 not accurate an accurate measurement of error for nonlinear models?)

Answer 1

[Jeff Miller]

Wikipedia has a pretty good explanation of the mean squared error that fitnlm provides.

And I think Torsten's suggestion for bounding will also work for bounding frequency between 40 & 50:

boundedfreq = 40 + mod(unboundedfreq,10);

[Steven Sagona]

The frequency bound parts works fine.

You are saying that the "standard error" in Mathematica is the mean-squared error. Is there a way to obtain error-bars for this estimator?

[Jeff Miller]

Regarding standard error--no, I misunderstood your question. The standard error in the "Coefficients" table is what you would use for error bars for the estimator (i.e., if you wanted an error bar of one standard error). Note also that the NonLinearModel class has a method "coefCI" that you can use to compute confidence intervals for the coefficient estimates, if you want your error bars to reflect a confidence interval.