[SciPy-User] How to estimate error in polynomial coefficients from scipy.polyfit?
David Warde-Farley
dwf@cs.toronto....
Thu Mar 25 15:49:51 CDT 2010
On 25-Mar-10, at 4:32 PM, Jeremy Conlin wrote:
> Now I would like to know how I can get the uncertainties
> (standard deviations) of polynomial coefficients from the returned
> values from scipy.polyfit. If I understand correctly, the residuals
> are sometimes called the R^2 error, right?
No, that's not what R^2 is. See http://en.wikipedia.org/wiki/Coefficient_of_determination
The residuals plus some assumptions about the kind of noise present in
your data can tell you something about the standard deviation of a
given predicted function value, but I'm not sure how to turn that into
a measure of uncertainty on the coefficient itself. My first instinct
would be to do it with bootstrap samples, i.e. if you have N data
points, sample with replacement from that data to generate, say, 100
sets of size N, fit the coefficients on each of them, and take the
empirical standard deviation. I am not sure how polyfit responds to
duplicated points, however, though it should reweight your least
squares estimate a bit.
David
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