Use CRIME3.RAW for this exercise.
(i) In the model of Example 13.6, test the hypothesis H0 : (1 = (2 (Define (1 = (1 - (2 and write, (1 in terms of (1 and (2. Substitute this into the equation and then rearrange. Do a t test on (1.)
(ii) If (1 = (2, show that the differenced equation can be written as
(log(crimei) = (0 + (1 (avgclri + (ui,
Where (1 = 2(1 and avgclri = (clrprci-1 + clrprci-2)/2 is the average clear-up percentage over the previous two years.
(iii) Estimate the equation from part (ii). Compare the adjusted R-squared with that in (13.22). Which model would you finally use?