# Correlation Coefficient Formula

Correlation Coefficient is a measure of the association between two variables. It is used to find the relationship is between data and a measure to check how strong it is. The formulas return a value between -1 and 1 wherein one shows -1 shows negative correlation and +1 shows a positive correlation.

The correlation coefficient value is positive when it shows that there is a correlation between the two values and the negative value shows the amount of diversity among the two values.

**Types of a correlation coefficient formula**

There are several types of correlation coefficient formulas.

But, one of the most commonly used formulas in statistics is Pearson’s Correlation Coefficient Formula.

**Pearson’s Correlation Coefficient Formula**

Also known as **bivariate correlation** is the most widely used correlation method among all the sciences.

The correlation coefficient is denoted by *r*.

To find r, let us suppose the two variables as x & y, then the correlation coefficinet r is calculated as:

\[\large r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\]

Here,

Σx = Total of the first variable value.

Σy = Total of the second variable value.

Σxy =Sum of the product of first & second value.

Σx

^{2 }= Sum of the squares of the first value.

Σy

^{2 }= Sum of the squares of the second value.

**Sample Correlation Coefficient Formula**

\[\large r_{xy}=\frac{S_{xy}}{S_{x}S_{y}}\]

$S_{x}$ and $S_{y}$ are the sample standard deviations, and $S_{xy}$ is the sample covariance.

**Population Correlation Coefficient Formula**

\[\large \rho_{xy}= \frac{\sigma_{xy}}{\sigma_{x} \sigma_{y}}\]

The population correlation coefficient uses $\sigma_{x}$ and $\sigma_{y}$ as the population standard deviations, and $\sigma_{xy}$ as the population covariance.

More topics in Correlation Coefficient Formula | |

Pearson Correlation Formula | Linear Correlation Coefficient Formula |