Question

If the multiple correlation coefficient of X₁ on X₂ and X₃ is zero, then:
1. r₁₂ ≠ 0, r₁₃ = 0
2. r₁₂ = 0, r₁₃ ≠ 0
3. r₁₂ ≠ 0, r₁₃ ≠ 0
4. r₁₂ = 0, r₁₃ = 0

Answer 1

Correct Answer - Option 4 : r₁₂ = 0, r₁₃ = 0

Explanation:

The general formula for multiple correlation coefficient

\(\rm R^2_1{.}{_2}{_3} = \frac{r_{12}^{2}+r_{13}^{2}-2r_{12}r_{13}r_{23}}{1-r_{23}^{2}}\)

A multiple correlation coefficient is a non-negative coefficient.

It is the value ranges between 0 and 1. It cannot assume a minus value.

If the multiple correlation coefficient of X1 on X2 and X3 is zero, then:

If R1.23 = 0 then r12 = 0 and r13 = 0

R1.23 is the same as R1.32