B 3 marks show that the least square estimator is

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(b) [3 marks] Show that the least square estimator is unbiased, i.e. E ( ˆ β 1 ) = β 1 2
(c) [3 marks] Show that V ar ( ˆ β 1 ) = σ 2 n X i =1 x 2 i . 3
(d) [3 marks] Assume that s 2 and ˆ β 1 are independent. Construct a (1 - α )100% confidence interval for the true but unknown slope. 4
The (1 - α )100% confidence interval of β 1 is then given by ˆ β 1 ± t α/ 2 ,n - 1 s v u u t n X i =1 x 2 i .

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