Wolfgang Kerzendorf wrote:
> I know this is not completely matplotlib related but perhaps you can
> help me none the less:
> I want to fit a curve to a set of data. It's a very easy curve: y=ax+b.
> But I want errors for a and b and not only the rms. Is that possible.
> What tasks do you recommend for doing that.
> Thanks in advance
> Wolfgang
>
from http://mathworld.wolfram.com/LeastSquaresFitting.html:
(but here: y = a*x+b, so a <-> b)!
For the standard errors on a and b:
n = float(len(x))
xm = mean(x)
ym = mean(y)
SSxx = dot(x,x) - n*xm**2.0
SSyy = dot(y,y) - n*ym**2.0
SSxy = dot(x,y) - n*xm*ym
r = sqrt(SSxy**2.0 / (SSxx*SSyy))
s = sqrt((SSyy - (SSxy**2.0 / SSxx)) / (n-2.0))
sea = s / sqrt(SSxx)
seb = s * sqrt(1.0/n + (xm**2.0 / SSxx))
The values of sea, seb agree with gnuplot's "Asymptotic Standard Error".
--
cheers,
steve
Random number generation is the art of producing pure gibberish as quickly as
possible.
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