GATE 2022 ST – Question 54

Regression Analysis · Linear Models and Estimation · 2 marks · Numerical answer

Fit Y=β₀+β₁X+ε with independent N(0,σ²) errors to x=(0,1,2,3,4),y=(3,4,5,6,7). Let Ŷ₀ be the least-squares fitted mean at X=6. If Var Ŷ₀=cσ²,find c to one decimal.

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Correct answer: 1.8 to 1.8

Explanation

The fitted-mean variance factor is c=1/n+(x₀−x̄)²/Sxx. Here n=5,x̄=2,Sxx=4+1+0+1+4=10. Thus c=1/5+16/10=**1.8**. This is the variance of the fitted mean,not of a new noisy observation.

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