1. Let y = Px + u, i = 1, ..., n, where Assumptions 1-5 of the simple linear regression model are satisfied. Define B = +yn x1+xn Explain whether is consistent or not in this setup. (2 marks) 2. For the same model as above, show that the variance of B is larger than the variance of , where B denotes the OLS estimator. Please refrain from referring to the Gauss-Markov theorem as part of your answer. (4 marks) 3. Consider the following estimated regression model: outphr, 431.259.264wkhoursi, where outphr; denotes output per hour for worker i, i = 1, ..., n, and wkhours; denotes weekly working hours. = = Let (outphr) = 82.92, var(outphr;) = 307.45, (wkhours;) = 37.6 and var(wkhours;) : 3.217, where (.) denotes the sample average and var (.) denotes the sample variance. Find the expected weekly output of a typical worker, i.e. estimate E (outphr; wkhours;). (4 marks)