numpy/scipy: correlation
Robert Kern
robert.kern at gmail.com
Sun Nov 12 00:03:55 CET 2006
robert wrote:
> Is there a ready made function in numpy/scipy to compute the correlation y=mx+o of an X and Y fast:
> m, m-err, o, o-err, r-coef,r-coef-err ?
And of course, those three parameters are not particularly meaningful together.
If your model is truly "y is a linear response given x with normal noise" then
"y=m*x+o" is correct, and all of the information that you can get from the data
will be found in the estimates of m and o and the covariance matrix of the
estimates.
On the other hand, if your model is that "(x, y) is distributed as a bivariate
normal distribution" then "y=m*x+o" is not a particularly good representation of
the model. You should instead estimate the mean vector and covariance matrix of
(x, y). Your correlation coefficient will be the off-diagonal term after
dividing out the marginal standard deviations.
The difference between the two models is that the first places no restrictions
on the distribution of x. The second does; both the x and y marginal
distributions need to be normal. Under the first model, the correlation
coefficient has no meaning.
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco
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