Could you please help me with this linear regression problem and give a detailed

6. (20 points) Weighted Least Squares. Consider a bivariate data set (sci, pi), i = 1, . . . , 10, in which 933. is determined by design such that 933' = z'. The response variable admits a linear model with non-constant variance 2% = 50 + 51% + 33:36:31 (2) where 61's are independent and identically distributed as N (0, 1). Let (50,51) be the least squares estimate (that is, with equal weights). Under the above model assumptions, answer the following questions with derivations. (a) (5 points) What is the expectation of (/60, [31)? (b) (5 points) What is the variance of (30,31)? A A (c) (5 points) Summarize the distribution of (g, Bl). (d) (5 points) Discuss and compare the performance of the least squares estimator with the weighted least squares estimator (with correct weight)