Question: 4. Consider the regression model through the origin yi = Bibi + Ei, i = 1, 2, ...,n where Ei ~N(0, 02) and Cov(Ei, E;)

4. Consider the regression model through the origin yi = Bibi + Ei, i = 1, 2, ...,n where Ei ~N(0, 02) and Cov(Ei, E;) = 0 for i * j. In Homework 2, we found the least squares estimates n Ciyi n B1 = i=1 and s = n - 1 E(yi - Bizi)?, I'M = i=1 n and Var(B1) = 02/ > (a) Find the distribution of the statistic T = (B1 - B1) /s.e. (B1). (b) Use part (a) to construct a 100(1 - a) confidence interval for B1

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