GATE 2020 ST – Question 58

Multivariate Analysis · Hotelling Tests and Correlation · 2 marks · Numerical answer

A centred trivariate normal has variances1 and all pairwise correlations1/3. Find partial correlation of X₂ and X₃ with X₁ fixed (two decimals).

Show answer and explanation

Correct answer: 0.25 to 0.25

Explanation

Use ρ₂₃.₁=(ρ₂₃−ρ₂₁ρ₃₁)/√[(1−ρ₂₁²)(1−ρ₃₁²)]. Numerator=1/3−1/9=2/9 and denominator=8/9. Their ratio is1/4=0.25.

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