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

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;Usage 1: <code>var(''x''<sub>vector</sub>)</code>
;Usage 1: <code>var(''x''<sub>vector</sub>)</code>
;Result 1: The variance ''v'' of vector ''x''.  
;Result 1: The variance ''v'' of vector ''x''.  
:<code>''v'' = sum<sub>i = 0..ncol(''x'')</sub> ( (x<sub>i</sub> - avr(''x''))^2 )</code>
:<code>''v'' = sum<sub>i = 0..ncol(''x'')-1</sub> ( (x<sub>i</sub> - avr(''x''))^2 ) / (ncol(''x'') - 1)</code>
----
----
<math>\sigma^2</math>
;Usage 1: <code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>
;Result 1: The covariance ''v'' of the vectors ''x'' and ''y''.
:<code>''v'' = sum<sub>i = 0..ncol(''x'')</sub> ( (x<sub>i</sub> - avr(''x'')) * (y<sub>i</sub> - avr(''y'')) )</code>
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Revision as of 13:15, 8 April 2011

Compute the variance of x.


Usage 1
var(xvector)
Result 1
The variance v of vector x.
v = sumi = 0..ncol(x)-1 ( (xi - avr(x))^2 ) / (ncol(x) - 1)

Usage 1
var(xvector, yvector)
Result 1
The covariance v of the vectors x and y.
v = sumi = 0..ncol(x) ( (xi - avr(x)) * (yi - avr(y)) )
Usage: var(xv)
Result type: scalar

The covariance of the vector xv and yv.

Usage: var(xv,ys)
Result type: scalar

The covariance matrix for the column vector of the matrix xM. The column average a[j] is either calculated with avr(xM[*,j]) or through the argument y (a[j] = yS or a[j] = yV[j]).

Usage: var(xm)
var(xm,ys)
var(xm,yv)
Result type: matrix - (ncol(xm) x ncol(xm))

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