Question

If r₁₂ = +0.80, r₁₃ = -0.40 and r₂₃ = -0.56, then the square of multiple correlation coefficient (correct to four decimal places) \(R^2_1{.}{_2}{_3}\)is equal to:
1. 0.6434
2. 0.7586
3. -0.436
4. 0.8021

Answer 1

Correct Answer - Option 1 : 0.6434

Concept:

General Formula for multiple correlation coefficient

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

Given

 r12 = +0.80, r13 = -0.40 and r23 = -0.56

Calculation

 \(\rm R_{1.23}^{2} = \frac{r_{12}^{2}+r_{13}^{2}-2r_{12}r_{13}r_{23}}{1-r_{23}^{2}}\)

\(\rm R^2_1{.}{_2}{_3}= \frac{0.80^{2}+(-0.40)^{2}-2(0.80)(-0.40)(-0.56)}{1-(-0.56)^{2}}\)

\(\rm R^2_1{.}{_2}{_3}\)= 0.64  0.16 - 2 × 0.8 × (- 0.40)(-0.56)/[1 - (0.56)²]/[1 - (0.56)²

⇒ (0.80 - 0.3584)/(1 - 0.3136)

∴ \(\rm R^2_1{.}{_2}{_3}\) = 0.6434