(Data file: Transact) The data in this example consists of a sample of branches of a large Australian bank (Cunningham and Heathcote, 1989). Each branch makes transactions of two types, and for each of the branches we have recorded the number t1 of type 1 transactions and the number t2 of type 2 transactions. The response is time, the total minutes of labor used by the branch. Define a = (t1 + t2)/2 to be the average transaction time, and d=t1- t2, and fit the following four mean functions M1: E(timelt 1, t2)= Bot+But1+Bt2 M2: E(timelt 1, t2)=B02 + B32a + Bad M3: E(timelt 1, t2)=B3+Bast2+ B3d M4: E(timelt 1, t2)= Bos + Bat1+ Bat2+Ba+Bud 4.2.1 In the fit of M4, some of the coefficients estimates are labeled as "aliased" or else they are simply omitted. Explain what this means and why this happens. 4.2.2 What aspects of the fitted regressions are the same? What aspects are different? 4.2.3 Why is the estimate for t2 different in M1 and M3?