Mathematics · Linear Regression
Consider the simple linear regression model Yi = βxi + εi, i = 1, 2, ..., n, where β > 0, ∑i=1n xi2 > 0, and the uncorrelated errors εi have zero mean and finite variance σ2 (> 0). Let β̂1 = ∑i=1n ai* Yi, where ai's minimize E(∑i=1n ai Yi - β)2 with respect to scalars a1, ..., an. Let β̂2 be the ordinary least squares estimator of β. Which of the following relations is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Var(β̂1) E(β̂2)
- 2Var(β̂1) > Var(β̂2), E(β̂1) < E(β̂2)
- 3Var(β̂1) < Var(β̂2), E(β̂1 - β)2 < E(β̂2 - β)2✓
- 4Var(β̂1) > Var(β̂2), E(β̂1 - β)2 > E(β̂2 - β)2
Correct answer
Var(β̂1) < Var(β̂2), E(β̂1 - β)2 < E(β̂2 - β)2
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