Partial Correlation Coefficient Calculator

Formula

The formula to calculate the partial correlation coefficient is:

\[ r_{xy.z} = \frac{r_{xy} - r_{xz} \cdot r_{yz}}{\sqrt{(1 - r_{xz}^2) \cdot (1 - r_{yz}^2)}} \]

Where:

\( r_{xy.z} \) is the partial correlation coefficient
\( r_{xy} \) is the correlation between X and Y
\( r_{xz} \) is the correlation between X and Z
\( r_{yz} \) is the correlation between Y and Z

What is a Partial Correlation Coefficient?

A partial correlation coefficient measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. It provides insight into the direct relationship between two variables while controlling for the influence of other variables. This is particularly useful in multiple regression analysis and other statistical methods where the goal is to understand the relationship between variables while accounting for the influence of other factors.

Example Calculation

Let's assume the following values:

Correlation between X and Y (r_xy) = 0.8
Correlation between X and Z (r_xz) = 0.5
Correlation between Y and Z (r_yz) = 0.6

Using the formula to calculate the partial correlation coefficient:

\[ r_{xy.z} = \frac{0.8 - (0.5 \cdot 0.6)}{\sqrt{(1 - 0.5^2) \cdot (1 - 0.6^2)}} = \frac{0.8 - 0.3}{\sqrt{(1 - 0.25) \cdot (1 - 0.36)}} = \frac{0.5}{\sqrt{0.75 \cdot 0.64}} = \frac{0.5}{0.69} \approx 0.72 \]

The partial correlation coefficient is approximately 0.72.