Programmer Guide/Command Reference/EVAL/corr: Difference between revisions

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Compute the correlation coefficient or the correlcation matrix.
----
;Usage 1: '''<code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>'''
;Result 1: The correlecation coefficient ''r'' (product moment correlation) of the vectors ''x'' and ''y''.
:<code>''r'' = var(''x'', ''y'') / sqrt( var(''x'')* var(''y'') )</code>
----
;Usage 3: '''<code>var(''x''<sub>matrix</sub>)</code>'''
:'''<code>var(''x''<sub>matrix</sub>, ''y''<sub>scalar</sub>)</code>'''
:'''<code>var(''x''<sub>matrix</sub>, ''y''<sub>vector</sub>)</code>'''
;Result 3: The covariance matrix ''v'' of the column vectors of ''x''.
:<code>''v<sub>i,j</sub>'' = sum<sub>k = 0..nrow(''x'')</sub> ( (x<sub>k,i</sub>-a<sub>i</sub>) * (x<sub>k,j</sub>-a<sub>j</sub>) ) / (nrow(''x'')-1) , with: i,j = 0..ncol(''x'')</code>
:The column averages a<sub>i=0..ncol(''x'')</sub> are computed as follows:
::{|class="einrahmen"
|''y'' not supplied || a<sub>i</sub> = avr(''x''<sub>*,i</sub>)
|-
|''y''<sub>scalar</sub> || a<sub>i</sub> = ''y''
|-
|''y''<sub>vector</sub> || a<sub>i</sub> = ''y''<sub>i</sub>
|-
|}
;See also: [[Programmer_Guide/Command_Reference/EVAL/avr|avr]], [[Programmer_Guide/Command_Reference/EVAL/dev|dev]], [[Programmer_Guide/Command_Reference/EVAL/corr|corr]]
[[Programmer_Guide/Command_Reference/EVAL#Functions|<function list>]]
{{DISPLAYTITLE:{{SUBPAGENAME}}}}
{{DISPLAYTITLE:{{SUBPAGENAME}}}}
=====corr=====
=====corr=====

Revision as of 13:39, 8 April 2011

Compute the correlation coefficient or the correlcation matrix.


Usage 1
var(xvector, yvector)
Result 1
The correlecation coefficient r (product moment correlation) of the vectors x and y.
r = var(x, y) / sqrt( var(x)* var(y) )

Usage 3
var(xmatrix)
var(xmatrix, yscalar)
var(xmatrix, yvector)
Result 3
The covariance matrix v of the column vectors of x.
vi,j = sumk = 0..nrow(x) ( (xk,i-ai) * (xk,j-aj) ) / (nrow(x)-1) , with: i,j = 0..ncol(x)
The column averages ai=0..ncol(x) are computed as follows:
y not supplied ai = avr(x*,i)
yscalar ai = y
yvector ai = yi
See also
avr, dev, corr

<function list>



corr

The product moment correlation of the vector xv and yv.

Usage:

corr(xv,yv)

Return Type:

scalar

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