# [SciPy-user] scipy.optimize.leastsq and covariance matrix meaning

massimo sandal massimo.sandal@unibo...
Tue Nov 11 06:15:39 CST 2008

```Robert Kern wrote:
> On Mon, Nov 10, 2008 at 05:13, massimo sandal <massimo.sandal@unibo.it> wrote:
>> massimo sandal wrote:
>>
>>> I'll try to sketch up a script reproducing the core of the problem with
>>> actual data.
>> Here it is. Can anyone give it a look to help me understand if and how to
>> make sense of the covariance matrix?
>
> The covariance matrix does need some scaling before it can be
> interpreted statistically. Basically, if you are doing nonlinear least
> squares as a statistical procedure, rather than a purely numerical
> one, the residuals need to be scaled so that they are in units of
> standard deviations of the measurement error for each individual
> measurement. If you don't know what that is, then you can estimate it
> from the fitted residuals. The parameter estimate is unchanged, but
> you will need to rescale the covariance matrix of the estimate by
> multiplying it by the residual variance.
>
> scipy.odr does most of this for you. Attached is a version of your
> code using scipy.odr. Here is the text output:
>
> Fitted parameters: [  4.90666526e+06   4.78090340e+09]
> Covariance: [[  1.72438988e+31  -1.64258997e+35]
>  [ -1.64258997e+35   1.57791262e+39]]
> Residual variance: 2.83606592894e-22
> Scaled error bars: [  6.99319913e+04   6.68959208e+08]
> Scaled covariance: [[  4.89048340e+09  -4.65849344e+13]
>  [ -4.65849344e+13   4.47506422e+17]]

Thanks a lot! What I need are the scaled error bars, isn't it?

(By the way: any good tutorial reference/book on this kind of numerical
things? I am a molecular biologist now doing biophysics, and while
enjoying it a lot, I feel behind on a lot of technical stuff)

Thanks again,

m.
--
Massimo Sandal , Ph.D.
University of Bologna
Department of Biochemistry "G.Moruzzi"

snail mail:
Via Irnerio 48, 40126 Bologna, Italy

email:
massimo.sandal@unibo.it

web:
http://www.biocfarm.unibo.it/samori/people/sandal.html

tel: +39-051-2094388
fax: +39-051-2094387
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