When a golfer hits a golf ball at the starting point, the shot is called a drive and the driving distance is the distance that the ball travels. The fairway is the closely mown area that runs from the starting point almost all the way to the hole. The fairway accuracy is the percentage of drives in which the ball comes to rest on the fairway (not on longer grass, sand traps, and ponds). Access the data about professional golfers, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.
a. Construct a scatterplot that describes the association between the driving distances and fairway accuracies for female professional golfers. Do the same for the male professional golfers. Show both scatterplots in the same co- ordinate system if you know how to use colors or shapes to identify which points are for which gender.
b. Which gender tends to have larger driving distances? Explain how you can tell this from the scatterplots.
c. Describe the four characteristics of the female association. Compute and interpret r as part of your analysis. Do the same for the male association.
d. For each of the two associations, find the coefficient of de- termination. What do your results mean in this situation?
e. Even though the female association and the male association are weak, find the linear regression equation for each association. Also find the linear regression equation for all golfers.
f. On the basis of the scatterplots, explain why it makes sense that the regression line for all golfers is less steep than the regression lines for female golfers and for male golfers.
g. From January 1 to September 14, 2014, Tim Clark had the second-best fairway accuracy in the PGA, with 775 out of 1047 drives coming to rest on fairways. Estimate his mean driving distance.