Programmer Guide/Command Reference/EVAL/var: Difference between revisions
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Compute the variance, covariance or covariance-matrix. | Compute the variance, covariance or covariance-matrix. | ||
---- | ---- | ||
;Usage 1: | ;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( (''x''-avr(''x''))?^2 ) / (nrow(''x'')-1)</code> | :<code>''v'' = sum( (''x''-avr(''x''))?^2 ) / (nrow(''x'')-1)</code> | ||
:<code>''v'' = (''x''-avr(''x''))^2 / (nrow(''x'')-1)</code> | :<code>''v'' = (''x''-avr(''x''))^2 / (nrow(''x'')-1)</code> | ||
---- | ---- | ||
;Usage 2: | ;Usage 2: <code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code> | ||
;Result 2: The covariance ''v'' of the vectors ''x'' and ''y''. | ;Result 2: The covariance ''v'' of the vectors ''x'' and ''y''. | ||
:<code>''v'' = sum( (''x''- | :<code>''v'' = sum( (''x''-avr(''x'') ?* (''y''-avr(''y'')) ) / (nrow(''x'')-1)</code> | ||
:<code>''v'' = ((''x''- | :<code>''v'' = ((''x''-avr(''x'') * (''y''-avr(''y''))) / (nrow(''x'')-1)</code> | ||
---- | ---- | ||
;Usage 3: | ;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>scalar</sub>)</code>''' | ||
:'''<code>var(''x''<sub>matrix</sub>, ''y''<sub>vector</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''. | ;Result 3: The covariance matrix ''v'' of the column vectors of ''x''. | ||
:<code>''v | :<code>''v''[i,j] = sum( (''x''[*,i]-a[i]) ?* (''x''[*,j]-a[j]) ) / (nrow(''x'')-1) , with: i,j = 0..ncol(''x'')-1</code> | ||
:The column averages a | :The column averages a[i] are computed as follows: | ||
::{|class="einrahmen" | ::{|class="einrahmen" | ||
|''y'' not supplied || a | |''y'' not supplied || a[i] = avr(''x''[*,i]) | ||
|- | |- | ||
|''y''<sub>scalar</sub> || a | |''y''<sub>scalar</sub> || a[i] = ''y'' | ||
|- | |- | ||
|''y''<sub>vector</sub> || a | |''y''<sub>vector</sub> || a[i] = ''y''[i] | ||
|- | |- | ||
|} | |} | ||
;See also: [[../avr|avr]], [[../dev|dev]], [[../corr|corr]], [[../dist|dist]], [[../svd|svd]] | |||
[[../#Functions|<function list>]] | |||
Latest revision as of 13:02, 21 April 2011
Compute the variance, covariance or covariance-matrix.
- Usage 1
var(xvector)- Result 1
- The variance v of vector x.
v = sum( (x-avr(x))?^2 ) / (nrow(x)-1)v = (x-avr(x))^2 / (nrow(x)-1)
- Usage 2
var(xvector, yvector)- Result 2
- The covariance v of the vectors x and y.
v = sum( (x-avr(x) ?* (y-avr(y)) ) / (nrow(x)-1)v = ((x-avr(x) * (y-avr(y))) / (nrow(x)-1)
- Usage 3
var(xmatrix)var(xmatrix, yscalar)var(xmatrix, yvector)- Result 3
- The covariance matrix v of the column vectors of x.
v[i,j] = sum( (x[*,i]-a[i]) ?* (x[*,j]-a[j]) ) / (nrow(x)-1) , with: i,j = 0..ncol(x)-1- The column averages a[i] are computed as follows:
y not supplied a[i] = avr(x[*,i]) yscalar a[i] = y yvector a[i] = y[i]
