In Exercise 2.9 we discussed the data in Appendix D, Table D.3, that relates highway fatalities (FATAL) and number of licensed vehicles (NOV) for the years 1950-1979, fitting a linear and a quadratic model. Noting that the speed limit was reduced from 65 to 55 mph in the last five years of this study, define the indicator if speed limit 55 if speed limit 65.

a. Assuming that the relation between FATAL and NOV is linear at both speeds, fit a model that will determine the two linear relations. Test the hypothesis that the slope of the two lines is the same.

b. Assuming equal slopes, refit the model and estimate the number of lives saved by reducing the speed limit.

c. From a scatter-plot of the data for the years 1950-1974, it appears that FATAL was relatively constant for NOV <75, then increased quadratically until 1974, suggesting that the rate of increase of fatalities was declining, perhaps due to saturation of highways. To examine these observations, fit a model that is linear for NOV <75 and quadratic for NOV 75.