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.. | :<code>''v'' = sum<sub>i = 0..nrow(''x'')-1</sub> ( (''x''<sub>i</sub>-avr(''x''))^2 ) / (nrow(''x'')-1)</code> | ||
---- | ---- | ||
;Usage 2: '''<code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>''' | ;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<sub>i = 0.. | :<code>''v'' = sum<sub>i = 0..nrow(''x'')</sub> ( (''x''<sub>i</sub>-avr(''x'')) * (''y''<sub>i</sub>-avr(''y'')) ) / (nrow(''x'')-1)</code> | ||
---- | ---- | ||
;Usage 3: '''<code>var(''x''<sub>matrix</sub>)</code>''' | ;Usage 3: '''<code>var(''x''<sub>matrix</sub>)</code>''' | ||
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:'''<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<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>) ) / ( | :<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: | :The column averages a<sub>i=0..ncol(''x'')</sub> are computed as follows: | ||
::{|class="einrahmen" | ::{|class="einrahmen" | ||
Revision as of 14:33, 8 April 2011
Compute the variance, covariance or covariance-matrix.
- Usage 1
var(xvector)- Result 1
- The variance v of vector x.
v = sumi = 0..nrow(x)-1 ( (xi-avr(x))^2 ) / (nrow(x)-1)
- Usage 2
var(xvector, yvector)- Result 2
- The covariance v of the vectors x and y.
v = sumi = 0..nrow(x) ( (xi-avr(x)) * (yi-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.
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
