The Scottish hill races considered in Exercises 14 and 29 are run by both men and women. We can combine the data to fit a single model for both. Here is one such model. The variable Climb*Sex is the product of the variable Climb and the indicator variable Sex, which is 0 for women and 1 for men.

a) What is the purpose of including the variable Climb*Sex in this model?
b) What does the coefficient of that variable mean in this model?

Data From Exercise 14

Hill running—races up and down hills— has a written history in Scotland dating back to the year 1040. Races are held throughout the year at different locations around Scotland. A recent compilation of information for 90 races (for which full information was available and omitting two unusual races) includes the Distance (km), the Climb (m), and the Record Time (minutes). A regression to predict the men’s records as of 2008 looks like this:

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Time 225 150 75 500 + 1000 1500 Climb (m) 0 Men 1 Women 2000