Correlation — Moments

Calculates the correlation of a given set of data.

You're viewing an older version of this page (#5408). View the current version.

View versions (2)

Interface

#include <codecogs/statistics/moments/correlation.h>

using namespace Statistics::Moments;

template <class T>inline double correlation(int n ,T *data ,T *data1)

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

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

(1)

where

$var(X)$ = variance of a set of data and
$cov(X,Y)$ = covariance of a set of data
$corr(X,Y)$ 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 $corr(x,y)=0$, 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 = Statistics::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: -0.370842

Parameters

the size of the first array and of the second array

data

the actual population data given as the first array

data1

the actual population data given as the second array

Returns

the correlation of the given set of data