GATE 2025 ST – Question 64

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

$X\sim N_3(0,\begin{pmatrix}1&.4&0\\.4&1&.6\\0&.6&1\end{pmatrix})$. Find the partial correlation of X₁,X₂ given X₃ to two decimals.

Show answer and explanation

Correct answer: 0.49 to 0.51

Explanation

Use ρ₁₂·₃=(ρ₁₂−ρ₁₃ρ₂₃)/√[(1−ρ₁₃²)(1−ρ₂₃²)]. Substitution gives .4/√(.64)=.4/.8=**.50**.

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