Correlation

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Calculates the correlation of a given set of data.

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Contents

Interface
Correlation
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Interface

C++

Correlation

template<class T>doublecorrelation(	int n	`1`
	T*data	`0`
	T*	`data1`	)[inline]

The correlation coefficient provides a normalized view of correlation based on covariance:

$corr(X,Y)= \frac{cov(X,Y)}{\sqrt{var(X)var(Y)}}$

(2)

where

$\inline var(X)$ = variance of a set of data and
$\inline cov(X,Y)$ = covariance of a set of data
$\inline corr(X,Y)$ ranges from -1 (for negatively correlated variables) through zero (for uncorrelated variables) to +1

(for positively correlated variables).

While if X and Y are independent we have $\inline corr(x,y)=0$ , the latter does not imply the former.

References:

PlanetMath, http:planetmath.org/encyclopedia/Covariance.html

Example 1

#include <codecogs/statistics/moments/correlation.h>
#include <iostream>
int main()
{
  int x[4] = {3 , 7 , 5 , 6 };
  int y[4] = {4 , 3 , 7 , 1 };
  double corr = Stats::Moments::correlation<int>(4, x , y);
  std::cout << "The correlation of x and y is: " << corr << std::endl;
  return 0;
}

Output:

The correlation of x and y is: -0.278132

Parameters

data1

the actual population data given as the second array

Returns

the correlation of the given set of data

Authors

Anca Filibiu (August 2005)

Source Code

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