Program to find correlation coefficient
Given two array elements and we have to find the correlation coefficient between two array. Correlation coefficient is an equation that is used to determine the strength of relation between two variables. Correlation coefficient sometimes called as cross correlation coefficient. Correlation coefficient always lies between 1 to +1 where 1 represents X and Y are negatively correlated and +1 represents X and Y are positively correlated.
Where r is correlation coefficient.
Correlation coefficient = (5 * 3000  105 * 140) / sqrt((5 * 2295  105^{2})*(5*3964  140^{2})) = 300 / sqrt(450 * 220) = 0.953463
Examples –
Input : X[] = {43, 21, 25, 42, 57, 59} Y[] = {99, 65, 79, 75, 87, 81} Output : 0.529809 Input : X[] = {15, 18, 21, 24, 27}; Y[] = {25, 25, 27, 31, 32} Output : 0.953463
 C++

// <a href="#">Program to find correlation coefficient</a>
#include<bits/stdc++.h>
using
namespace
std;
// function that returns correlation coefficient.
float
correlationCoefficient(
int
X[],
int
Y[],
int
n)
{
int
sum_X = 0, sum_Y = 0, sum_XY = 0;
int
squareSum_X = 0, squareSum_Y = 0;
for
(
int
i = 0; i < n; i++)
{
// sum of elements of array X.
sum_X = sum_X + X[i];
// sum of elements of array Y.
sum_Y = sum_Y + Y[i];
// sum of X[i] * Y[i].
sum_XY = sum_XY + X[i] * Y[i];
// sum of square of array elements.
squareSum_X = squareSum_X + X[i] * X[i];
squareSum_Y = squareSum_Y + Y[i] * Y[i];
}
// use formula for calculating correlation coefficient.
float
corr = (
float
)(n * sum_XY  sum_X * sum_Y)
/
sqrt
((n * squareSum_X  sum_X * sum_X)
* (n * squareSum_Y  sum_Y * sum_Y));
return
corr;
}
// Driver function
int
main()
{
int
X[] = {15, 18, 21, 24, 27};
int
Y[] = {25, 25, 27, 31, 32};
//Find the size of array.
int
n =
sizeof
(X)/
sizeof
(X[0]);
//Function call to correlationCoefficient.
cout<<correlationCoefficient(X, Y, n);
return
0;
}
Output –
0.953463
Disclaimer: This does not belong to TechCodeBit, its an article taken from the below
source and credits.
source and credits: http://www.geeksforgeeks.org
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