More about this Partial Correlation Calculator

The partial correlation coefficient assesses the degree of association between two variables $X_1$ and $X_2$, when controlling (keeping constant) a third variable $X_3$. Mathematically, the partial correlation coefficient r between $X_1$ and $X_2$, when controlling for $X_3$ is written as $r_{12.3}$, and it is computed using the following formula:

$$r_{12.3} =\frac{r_{12} - r_{13}r_{23} }{\sqrt{1 - r_{13}^2 }\sqrt{1 - r_{23}^2 }}$$

How To Calculate Coefficient Of Partial Determination

Very simple: Once you know $r$ (the partial correlation), all you need to do is to square it, to the the coefficient of partial determination $r^2$. This $r^2$ represents the variation explained by the one of the variables, when controlling for the variables of the third variable.

If you want to compute the correlation between $X_1$ and $X_2$ without controlling for any other variable, you can use this Pearson's correlation coefficient calculator instead.

Tightly related with the concept of partial correlation is the concept of semi-partial correlation, for which you can use the following calculator .