GATE Multivariate Analysis: Hotelling Tests and Correlation – Previous Year Questions
8 GATE previous year questions on Hotelling Tests and Correlation (Multivariate Analysis, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q19 – Independent vectors X₁,X₂,X₃∼N₄(0,Σ₁) and Y₁,…,Y₄∼N₄(0,Σ₂) have positive definite covariance matrices. Let X=[X₁ X₂ X₃],Y=[Y₁ Y₂ Y₃ Y₄],and…
- GATE 2021 ST Q33 – (Y,X₁,X₂) has mean (5,2,0)ᵀ and covariance rows (10,.5,−.5),(.5,7,1.5),(−.5,1.5,2). Find the multiple correlation coefficient between Y and its best…
- GATE 2021 ST Q34 – Three iid observations from a bivariate normal population with unknown mean μ and positive definite covariance Σ are (1,2)ᵀ,(4,−2)ᵀ,(−5,0)ᵀ. Find the…
- GATE 2021 ST Q53 – Y∼N₈(0,I₈). The quadratic forms YᵀΣ₁Y and YᵀΣ₂Y are independent central chi-square variables with 3 and 4 degrees of freedom. P:Σ₁ and Σ₂ are…
- GATE 2022 ST Q17 – X₁,…,X₂₀ are iid N₆(μ,Σ),Σ nonsingular,μ and Σ unknown. Let X̄=ΣX i/20 and S=Σ(X i−X̄)(X i−X̄)ᵀ/19. I:19S∼Wishart₆(19,Σ). II:(X₃−μ)ᵀS⁻¹(X₃−μ)∼χ²₆.…
- GATE 2022 ST Q39 – X∼N₃(μ,Σ),μ=(2,−3,2)ᵀ,Σ has rows (4,−1,1),(−1,2,a),(1,a,2). The partial correlation of X₂ and X₃ given X₁ is 5/7. Find a.
- GATE 2023 ST Q48 – X₁,…,X₁₀ are iid N₃(μ,Σ),μ and nonsingular Σ unknown. Split into groups of five. Let X̄₁,X̄₂ be the group means and S₁,S₂ their covariance matrices…
- GATE 2025 ST Q64 – X N 3(0,pmatrix1&.4&0\\.4&1&.6\\0&.6&1pmatrix). Find the partial correlation of X₁,X₂ given X₃ to two decimals.