Normal linear regression MLE Suppose we have a set of known n values, T1, ..., In. Consider a random sample of the same size, Y1, . ... Y, ~ f(vi; Ti, Bo, B1, o) with f ( yi; Po, B1, 0) = 202 V2no (1) -00 0. We have three parameters, Bo, B1, ', whereas r; are known values. Note: Some of you may have noticed that this is a linear regression with a normal error, Vi = Bo+ 81+ci, where fi ~iid N(0, 6?) 1. From equation (1), show that the log likelihood is 7 (log 2n + log(0-)) - 1 202 2 (vi - Bo - Biri)?. 1= 1 2. Show that deriving MLEs of Bo and B, is equivalent of finding Bo and 6 that minimize [ (Ui - Bo - Bizz ) ? . i=1 Note: This is a special case of making a prediction model that gives the best mean squared error (MSE). 3. Show that the MLE of Bo and B, satisfy -2 (vi - Bo - Biri) = 0 (2) i=1 and - 2 ri(vi - Bo - BIT;) = 0 (3)