Question: Problem 1 [35 points]: Suppose the following regression model is fitted to a data set with observations {(xi, yi), i = 1, 2, ..., n}:

Problem 1 [35 points]: Suppose the following regression model is fitted to a data set with observations {(xi, yi), i = 1, 2, ..., n}: iid y: = Bx; te,, e;~N(0,0?) (a) [11 points] Based on the least squares method and the fact that RSS/ o ~ x2- (df = n-1 since df = n from the data and df = 1 from estimating B), compute the least squares estimates for B and o. (b) [5 points] Is B an unbiased estimator for B? Verify. (c) [4 points] Show that the regression line passes through the point y: , but does NOT pass through the point (x, J) . (d) [7 points] Derive the maximum likelihood estimates (MLE) B and 82. (e) [8 points] Suppose (x1, X2, X3, X4, X5) = (1, 2, 3, 4, 5) and (y1, yz, y3, y4, y5) = (1, 3, 11, 26, 50). What the values of the least squares estimates / and o ? Does the sum of residuals equal to zero

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