Consider the linear regression model y = β0 + β1x + ε, with E[ε] = 0, Var(ε) = σ2. and the ε independent. (a) Show that E[M SR] = σ2 + β2 1 Sxx. (b) Show that E[M SRes] = σ2.
Added by Montserrat C.
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- Data: y_i = β0 + β1 x_i + ε_i with E[ε_i]=0, Var(ε_i)=σ^2, ε_i independent. - Sxx = Σ (x_i - x̄)^2. - The OLS slope estimator: β1_hat = S_xy / Sxx, where S_xy = Σ (x_i - x̄)(y_i - ȳ). - The fitted values: ŷ_i = β0_hat + β1_hat x_i, and SSR = Σ (ŷ_i - ȳ)^2. - It Show more…
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