GATE 2021 ST – Question 33
(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 linear predictor from X₁,X₂,to two decimals.
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Correct answer: 0.14 to 0.18
Explanation
Write c=(.5,−.5)ᵀ and V=[[7,1.5],[1.5,2]]. Predictor variance is cᵀV⁻¹c=12/47. Squared multiple correlation is this divided by Var Y=10,giving R²=6/235. Thus R=√(6/235)≈**0.16**.