Question

The correlation matrix obtained for the variables bp (y) (blood pressure), age (x1) (age), smk (x2) (smoke) and WET(X3) (Weight), is given by:

BP AGE SMK WET
BP 1 0.64 0.72 0.48
AGE 1 0.32 0.78
SMK 1 0.40
WET 1
Based on this matrix please calculate the partial correlation.
a. 0.53
b. 0.48
c. 0.62
d. 0.32

Answer 1

c) 0.62

Explanation:

In this case, we are required to find the partial correlation,
`r_Y_X_1_|_X_2`.

To find the partial correlation, use the formula:

`r_Y_X_1_|_X_2 = (r_Y_X_1 - r_Y_X_2 * r_X_1_X_2)/(√(1 - r_X_1_X_2)^2 - √(1 - r_Y_X_2)^2)`

`r_Y_X_1_|_X_2 = (0.64 - 0.72 * 0.32)/(√(1 - 0.32)^2 - √(1 - 0.72)^2)`

`= (0.410)/(0.657)`

`r_Y_X_1_|_X_2 = 0.62`

The partial correlation is 0.62.

Option C