Detailed steps/answers would be greatly appreciated so I understand how you arri

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Detailed steps/answers would be greatly appreciated so I understand how you arrived at the answers. Thank you!

We consider a simple regression model given by y_i = Betax_i + u_i for i = 1,2, ... , n, where we assume x_i is non-random. Note that we do not have the constant term a. Though the error term u_i is independent over t, we assume that E(u_i) = 0 and E(u^2_i) = of for each i. We first assume of = a^2 for all i. Obtain the OLS estimator of 0, which we denote and find E and var Using your answer in part (a), obtain an unbiased estimator of var(beta). Now we assume heteroskedasticity, i.e., of can vary over i. In this case, is the OLS estimator beta in part (a) unbiased? How about your estimator of var(beta) in part (b)? Under the heteroskedasticity in part (c), what is var now? In order to handle heteroskedasticity, we estimate beta using the WLS (weighted least squares). Assuming that we observe of for all i, obtain the WLS estimator of beta, which wc denote Find E and var We now assume that of = cx^2_i for some constant c > 0. In this case, compare var(beta) in part (d) with var(beta) in part (e). Which one is larger? Does your answer justify the use of WLS in this case?

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Detailed steps/answers would be greatly appreciated so I understand how you arri

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