11.88 Refer to Exercise 11.45, where we presented data on the number of highway deaths and the number of licensed vehicles on the road for the years 1950–1979. We mentioned that the number of deaths Y may also have been affected by the existence of the national 55-mile-per-hour speed limit during the years 1974–1979 (i.e., years 25–30). Define the dummy variable a Introduce the variable x2 into the second-order model of Exercise 11.45 to account for the presence or absence of the 55-mile-per-hour speed limit in a given year. Include terms involving the interaction between x2 and x1.

b Refer to your model for part (a). Sketch on a single piece of graph paper your visualization of the two response curves, the second-order curves relating Y to x1 before and after the imposition of the 55-mile-per-hour speed limit.

c Suppose that x1 and x2 do not interact. How would that fact affect the graphs of the two response curves of part (b)?

d Suppose that x1 and x2 interact. How would this fact affect the graphs of the two response curves?

x2 = c 1 if 55-mile-per-hour speed limit was in effect 0 if not