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(i) Consider the simple linear regression model y = β0 + β1x + u under the first four Gauss-Markov assumptions

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(i) Consider the simple linear regression model y = β0 + β1x + u under the first four Gauss-Markov assumptions.

Define a slope estimator as β1^ = (yn − y1)/(xn − x1) . Show that β1^ is linear and unbiased.

(ii) Assuming in addition that the model is homoskedastic, derive Var(β1^|X).

(iii) Do you expect β1^ to be as efficient as OLS? Explain why