Modern Math Covariance

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Covariance

Returns the sample covariance of two arrays of the same length.

Syntax

Covariance( byref x as Array( of T ), byref y as Array( of T ) ) as float64

Notes

• Positive when they rise together, negative when one rises as the other falls, near zero when they are unrelated.
• Its magnitude means nothing on its own -- it is in the product of the two units, so it changes if you measure in metres rather than feet. Correlation is the normalised version.
• The sample form, dividing by n-1.
• The arrays must be the same length.

Examples

#import "std/numeric"
#import "std/containers"
using numeric
using containers

dim as Array( of float64 ) x = { 1.0, 2.0, 3.0, 4.0, 5.0 }
dim as Array( of float64 ) y = { 2.0, 4.0, 6.0, 8.0, 10.0 }

print Covariance( x, y ) > 0            '' -1 (true) -- they rise together

'' The magnitude is in the product of the units, so scaling y scales it
dim as Array( of float64 ) z = { 20.0, 40.0, 60.0, 80.0, 100.0 }
print Covariance( x, z ) > Covariance( x, y )      '' -1 (true)

'' Correlation is the version that does not move
print abs( Correlation( x, y ) - Correlation( x, z ) ) < 1e-12   '' -1 (true) -- to within rounding

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Library: Math Library
Category: Math Library
Documented under: Members