Problem 4 (25 points). Suppose n data points {(18%y3'), 3' = 1, . . . ,n} are obtained from the linear model: Y=0+51$+52x+51 where IE[] = 0 and Var(5) : 0'2. However, we do not know the above true model and t the data points on the simple linear model: MY) = 50 + 13155: and obtain the least-squares estimator for 60 and 61: 31 = 231% 5X!\" g) 2221082- (3)2 &=y&i 1. (15 points) Are these estimators unbiased? If yes, prove it. If no, nd the bias. 2. (10 points) Derive the variance of 30 and the covariance between 31 and 80