Use CRIME3.RAW for this exercise.
(i) In the model of Example, test the hypothesis H0: β1 = β2. (Hint: Define θ1 = β1 – β2 and write β1 in terms of θ1 and ft. Substitute this into the equation and then rearrange. Do a t test on θ1.)
(ii) If ft = ft, show that the differenced equation can be written as
Alog(crimei) = δ0 + δ1∆avgclri + ∆ui, where δ1 = 2β1 and avgclr. = (clrprc4-1 + clrprc4-2)/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?
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