# Correlation Coefficient Calculator

Instructions: You can use this step-by-step Correlation Coefficient Calculator for two variables X and Y. All you have to do is type your X and Y data, either in comma or space separated format (For example: "2, 3, 4, 5", or "3 4 5 6 7").

X data (comma separated)
Y data (comma separated)

## Correlation Coefficient Calculator

The correlation coefficient calculated above corresponds to Pearson's correlation coefficient. The requirements for computing it is that the two variables X and Y are measured at least at the interval level (which means that it does not work with nominal or ordinal variables).

The formula for Pearson's correlation coefficient is:

$r =\frac{n \sum_{i=1}^n x_i y_i - \left(\sum_{i=1}^n x_i \right) \left(\sum_{i=1}^n y_i \right) }{\sqrt{n \sum_{i=1}^n x_i^2 - \left( \sum_{i=1}^n x_i \right)^2} \sqrt{n \sum_{i=1}^n y_i^2 - \left( \sum_{i=1}^n y_i \right)^2} }$

or equivalently

$r = \frac{\sum_{i=1}^n x_i y_i - \frac{1}{n}\left(\sum_{i=1}^n x_i \right) \left(\sum_{i=1}^n y_i \right) }{\sqrt{\sum_{i=1}^n x_i^2 - \frac{1}{n}\left( \sum_{i=1}^n x_i \right)^2} \sqrt{\sum_{i=1}^n y_i^2 - \frac{1}{n}\left( \sum_{i=1}^n y_i \right)^2}} = \frac{SS_{XY}}{\sqrt{SS_{XX}\cdot SS_{YY} }}$

If you have two or more variables, you could use our correlation matrix calculator. Also, if the data for the variables $$X$$ and $$Y$$ does not meet the parametric assumptions for Pearson's correlation, then you should use this Spearman's correlation calculator instead.

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