Winning marathon times. Refer to the Chance (Winter 2000) study of men’s and women’s winning times in the Boston Marathon, presented in Exercise 11.146 (p. 675).

Suppose the researchers want to build a model for predicting winning time (y) of the marathon as a function of year 1x12 in which race is run and gender of winning runner 1x22.

a. Set up the appropriate dummy variables (if necessary)

for x1 and x2.

b. Write the equation of a model that proposes parallel straight-line relationships between winning time (y)

and year 1x12, one line for each gender.

c. Write the equation of a model that proposes nonparallel straight-line relationships between winning time

(y) and year 1x12, one line for each gender.

d. Which of the models do you think will provide the best predictions of winning time (y)? Base your answer on the graph displayed in Exercise 11.146.