In simple linear regression with intercept,n≥3,uncorrelated mean-zero errors of variance σ², let ŷ_i be least-squares fitted values,T₁=Σ(y_i−ŷ_i)²/(n−2),T₂=Σ(ŷ_i−ȳ)². Which holds?
Correct answer: (B) T₁ unbiased, T₂ not unbiased for σ²
Explanation
Residual sum of squares has expectation (n−2)σ², so T₁ is unbiased. The regression sum T₂ has expectation σ²+β₁²S_xx, generally not σ². Thus **B**; equality at the special null slope does not make it an unbiased estimator across the full parameter space.
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