[SciPy-User] Least Square fit and goodness of fit

[Benedikt Riedel]

On Fri, May 14, 2010 at 14:51, <josef.pktd at gmail.com> wrote:

> On Fri, May 14, 2010 at 3:01 PM, Benedikt Riedel <briedel at wisc.edu> wrote:
> > Hey,
> >
> > I am fairly new Scipy and am trying to do a least square fit to a set of
> > data. Currently, I am using following code:
> >
> > fitfunc = lambda p,x: p[0]+ p[1]*exp(-x)
> > errfunc = lambda p, x, y: (y-fitfunc(p,x))
> > pinit = [20,20.]
> > out = leastsq(errfunc, pinit, args=(tau,R4ctsdataselect), full_output=1)
> >
> > I am now trying to get the goodness of fit out of this data. I am sort of
> > running into a brick wall because I found a lot of conflicting ways of
> how
> > to calculate it.
>
> For regression the usual is
> http://en.wikipedia.org/wiki/Coefficient_of_determination
> coefficient of determination is
>
>    R^2 = 1 - {SS_{err} / SS_{tot}}
>
> Note your fitfunc is linear in parameters and can be better estimated
> by linear least squares, OLS.
> linear regression is handled in statsmodels and you can get lot's of
> statistics without worrying about the formulas.
> If you only have one slope parameter, then scipy.stats.linregress also
> works
>
>
Thanks for the information. I am still note quite sure if this is what my
boss wants because there should not be an average y value.


> scipy.optimize.curve_fit (scipy 0.8) can also give you the covariance
> of the parameter estimates.
> http://docs.scipy.org/scipy/docs/scipy.optimize.minpack.curve_fit
>

I have been trying this out, but the fit just looks horrid compared to using
leastsq method even though they call the same function according to the
documentation.


> > I am aware of the chisquare function in stats function, but the
> > documentation seems a little confusing to me. Any help would be greatly
> > appreciates.
>
> chisquare and others like kolmogorov-smirnov are more for testing the
> goodness-of-fit of entire distributions, not for how well a curve or
> line fits the data.
>
>
That is what I thought, which brought up my confusion when I asked other
people and they told me to use that


> Josef
>
> >
> > Thanks very much in advance.
> >
> > Cheers,
> >
> > Ben
> >
> >
> >
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User at scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
> >
> _______________________________________________
> SciPy-User mailing list
> SciPy-User at scipy.org
> http://mail.scipy.org/mailman/listinfo/scipy-user
>



-- 
Benedikt Riedel
Graduate Student University of Wisconsin-Madison
Department of Physics
Office: 2304 Chamberlin Hall
Lab: 6247 Chamberlin Hall
Tel:  (608) 301-5736
Cell: (213) 519-1771
Lab: (608) 262-5916
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.scipy.org/pipermail/scipy-user/attachments/20100515/e9cd6844/attachment.html>