Refer to Example 11 and Exercise 13.40, with ŷ = predicted winning the high jump and x1 = number of years since 1928. When equations are fitted separately for males and for females, we get ŷ = 1.98 + 0.0055×1 for males and ŷ = 1.60 + 0.0065x1 for females.
a. In allowing the lines to have different slopes, the overall model allows for ____________________ between gender and year in their effects on the winning high jump. (Fill in the correct word.)
b. Show that both equations yield the same predicted winning high jump when x1 = 380 (that is, 380 years after 1928, or in 2308).
c. Is it sensible to use this model to predict that in the year 2308 men and women will have about the same winning high jump? Why or why not?
b. Males: ŷ = 1.98 + 0.0055(380) = 4.07 Females: ŷ = 1.60 + 0.0065(380) = 4.07
c. It is not sensible to use this model to predict for the year 2308 because it is dangerous to extrapolate beyond our existing data. We do not know whether trends will change in the future.