Re: [Gnuplot-info] Correlation Value

[Nathan <gnu...@lo...>]

Hi,
Firstly thanks that you take the time answering me. It is strange, 
other people
using Origin (a program I do not know at all) tell me, that they get a
correlation value. I am told, that the definition is:

kor(X,Y) =3D cov(X,Y) / (sqrt(var(x)* var(y)))

(kor stand for correlation, var stands for variance and cov stands for
covariance).
Now gnuplot gives me "variance of residuals", but what's about "cov"?

Unfortanly, another value for the goodness does not really help because I a=

m
requested to proved the correlation.

Thanks again!
Nathan


Quoting Marek Gutowski <gu...@if...>:

> Correlation is a notion taken from statistics.  It tells us how
> two (or more) random variables are "alike", i.e. how similar is
> their behavior.  Think, for example, of the height and of the
> weight of people belonging to the certain population.  The taller
> the man then (most likely) the heavier he is.  Or think of various
> stock exchange indexes and their behavior.
> If you have only one random variable (in your case it is the fitted
> parameter 'a'), then it has to be perfectly correlated with itself.
> So gnuplot gives you correct information.  It is also correct that
> correlation matrix is just a number (a 1 x 1 matrix) in this case.
>
> I have an impression that what you really need is some measure
> of 'goodness of fit'.  There are many of them, and gnuplot provides
> you with the one called 'chi square' or 'chi square per degree of
> freedom'.  VERY roughly speaking: if CHISQ/NDF falls into the range
> [1/2, 2] then the fit seems reasonable;  more precisely - there is
> no good reason to reject the hypothesis that your formula (f(x)=3Da*x)
> is satisfactory to describe your data.  Contrary, if CHISQ/NDF > 2,
> then your data are almost surely not linear, as you might think.
> But be carefull, the case of small CHISQ/NDF, say below 1/2, is
> suspected, and calls for closer investigation (or for more data).
>
> It is still more complicated to explain how the values of CHISQ,
> obtained for the formula f(x)=3Da*x, and obtained for the other but
> similar case f(x)=3Da*x+b (using the same data) are helpful in deciding
> which formula (of the two) is more appropriate for your data.
> You need some statistical tables for this.
>
>
> Marek Gutowski
>
>
> On Thu, Feb 16, 2006 at 04:10:30PM +0100, Nathan H=FCsken wrote:
>> Hello together,
>> I am fitting Data into a linear function, like f(x)=3Da*x.
>> Now I want the correlation value for the fit. All I get is the
>> correlation matrix, which is always one :(.
>> I must admit, that I do not know exactly what the correlation value is.
>> How can I get it?
>> Thanks!
>> Nathan
>>
>>
>