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

From STX Wiki
Jump to navigationJump to search
No edit summary
No edit summary
 
(14 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{DISPLAYTITLE:{{SUBPAGENAME}}}}
{{DISPLAYTITLE:{{SUBPAGENAME}}}}
Compute the variance of ''x''.
Compute the variance, covariance or covariance-matrix.
----
----
;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( (''x''-avr(''x''))?^2 ) / (nrow(''x'')-1)</code>
:<code>''v'' = (''x''-avr(''x''))^2 / (nrow(''x'')-1)</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''.
:<code>''v'' = sum( (''x''-avr(''x'') ?* (''y''-avr(''y'')) ) / (nrow(''x'')-1)</code>
:<code>''v'' = ((''x''-avr(''x'') * (''y''-avr(''y''))) / (nrow(''x'')-1)</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''[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[i] are computed as follows:
::{|class="einrahmen"
|''y'' not supplied || a[i] = avr(''x''[*,i])
|-
|-
|Usage:
|''y''<sub>scalar</sub> || a[i] = ''y''
|var(xv)
|-
|Result type:
|scalar
|}
 
The covariance of the vector xv and <var>y</var>v.
 
{|
|-
|-
|Usage:
|''y''<sub>vector</sub> || a[i] = ''y''[i]
|var(xv,<var>y</var>s)
|-
|-
|Result type:
|scalar
|}
|}
;See also: [[../avr|avr]], [[../dev|dev]], [[../corr|corr]], [[../dist|dist]], [[../svd|svd]]


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] = <var>y</var>S or a[j] = <var>y</var>V[j]).
[[../#Functions|<function list>]]
 
{|
|-
|Usage:
|var(xm)
|-
|
|var(xm,<var>y</var>s)
|-
|
|var(xm,<var>y</var>v)
|-
|Result type:
|matrix <nowiki>-</nowiki> (ncol(xm) x ncol(xm))
|}

Latest revision as of 12:02, 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]
See also
avr, dev, corr, dist, svd

<function list>

Navigation menu

Personal tools