[SciPy-User] How to estimate error in polynomial coefficients from scipy.polyfit?
Thu Mar 25 15:58:32 CDT 2010
On Thu, Mar 25, 2010 at 4:52 PM, Charles R Harris
> On Thu, Mar 25, 2010 at 2:32 PM, Jeremy Conlin <email@example.com> wrote:
>> I am using scipy.polyfit to fit a curve to my data. Members of this
>> list have been integral in my understanding of how to use this
>> function. 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? That gives an estimate of
>> how well we have fit the data. I don't know how to use rank or any of
>> the other returned values to get the uncertainties.
>> Can someone please help?
> You want the covariance of the coefficients, (A.T * A)^-1/var, where A is
> the design matrix. I'd have to see what the scipy fit returns to tell you
> more. In anycase, from that you can plot curves at +/- sigma to show the
> error bounds on the result. I can be more explicit if you want.
the easiest way to get the full statistical results for the fit is to
import scikits.statsmodels as sm
results = sm.OLS(y, np.vandermonde(x, order)).fit()
with standard deviations on parameter estimates, ...
results.params should be the same as np.polyfit
and there are somewhere the prediction errors
without statsmodels it is a few lines of code, but requires "thinking"
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