Question: For the simple regression without a constant Yi = Xi + ui, with ui IID(0, 2). (a) Derive the OLS estimator of and

For the simple regression without a constant Yi = βXi + ui, with ui ∼ IID(0, σ2).

(a) Derive the OLS estimator of β and find its variance.

(b) What numerical properties of the OLS estimators described in problem 1 still hold for this model?

(c) derive the maximum likelihood estimator of β and σ2 under the assumption ui ∼ IIN(0, σ2).

(d) Assume σ2 is known. Derive the Wald, LM and LR tests for H0; β = 1 versus H1; β = 1.

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