# Correlation Coefficient Calculator

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Instructions:
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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").

## 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.

### Can I use z-scores to compute the correlation coefficient

Certainly! You have seen z-scores everywhere in Statistics and naturally, you wonder if you can compute the correlation with z-scores . You can definitely do it, and in fact, it is the customary way of doing it in Social Sciences stats.

### Other calculators similar to this correlation calculator

Also, there is the concept of multiple correlation coefficient , when you have more than one predictor, which is obtained by computing the correlation between the observed \(Y\) values and the predicted values \(\hat Y\) by the regression.