Programmer Guide/Command Reference/EVAL/var

Compute the variance, covariance or covariance-matrix.

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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)

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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)

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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

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