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# Correlation

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Calculates the correlation of a given set of data.
Controller: CodeCogs

C++

## Correlation

 templatedoublecorrelation( int n 1 T*data 0 T* data1 )[inline]
The correlation coefficient provides a normalized view of correlation based on covariance:

$corr(X,Y)=&space;\frac{cov(X,Y)}{\sqrt{var(X)var(Y)}}$
where
• $\inline&space;var(X)$ = variance of a set of data and
• $\inline&space;cov(X,Y)$ = covariance of a set of data
• $\inline&space;corr(X,Y)$ 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 $\inline&space;corr(x,y)=0$, 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

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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