# 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 - 1052)*(5*3964 - 1402))
= 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
```
`// <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`

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source and credits.
source and credits: http://www.geeksforgeeks.org
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