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:
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.
Let's assume the following values:
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.
