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# Covariance

Calculates the covariance of a given set of data
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C++

## Covariance

 template doublecovariance( int n T* data T* data1 )
The covariance of two random variables and with mean and respectively is defined as

The covariance of a random variable with itself is simply the variance

Covariance captures a measure of the correlation of two variables.

Positive covariance indicates that as increases, so does . Negative covariance indicates decreases as increases and vice versa. Zero covariance can indicate that and are uncorrelated. Covariance is defined as:

In the example below the covariance of two random variables is calculated, yielding the result: <em> -1.64 </em>. These two variables are also displayed in the following graphs.

### Example 1

#include <codecogs/statistics/moments/covariance.h>
#include <iostream>
int main()
{
int x[5] = {2 , 4 , 8 , 9 , 3};
int y[5] = {3 , 5 , 7 , 2 , 9};
double cov = Stats::Moments::covariance<int>(5, x , y);
std::cout << "The covariance of x and y is: " << cov << std::endl;
return 0;
}
Output:
The covariance of x and y is: -1.64

### Parameters

 n the size of the first array and of the second array data the actual population data given as the first array data1 the second array

### Returns

the covariance of a given population

### 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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