Correlation

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

(1)

where

• = variance of a set of data and
• = covariance of a set of data
• 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 , the latter does not imply the former.

References

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

#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;
}

The correlation of x and y is: -0.278132

Parameters

Returns