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Statistics › Moments ›

Covariance

Calculates the covariance of a given set of data

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Interface
Covariance
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Interface

C++

Covariance

template<class T> doublecovariance(	int	`n`
	T*	`data`
	T*	`data1`	)

The covariance of two random variables

and

with mean $\overline{X_1}$ and $\overline{X_2}$ respectively is defined as

$cov(X_1,X_2)=E[(X_1-\overline{X_1})(X_2-\overline{X_2})$

(1)

The covariance of a random variable

with itself is simply the variance

$E[X-\overline{X}^2]$

(2)

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:

$cov(x,y)=\frac{1}{N}\sum_{i=1}^Nx_iy_i-\overline{x_i}\overline{y_i}$

(3)

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

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