Question: The original data for the putting success of professional golfers included values beyond those we used for this example (5 feet to 15 feet), in both directions. At a distance of 2 feet, 93.3% of the putts were successful. At a distance of 20 feet, 15.8% of the putts were successful.
a. Use the equation in Exercise to predict success rates for those two distances (2 feet and 20 feet). Compare the predictions to the actual success rates.
b. Use your results from part a to explain why it is not a good idea to use a regression equation to predict information beyond the range of values from which the equation was determined.
c. Based on the picture in Figure 10.4 and the additional information in this exercise, draw a picture of what you think the relationship between putting distance and success rate would look like for the entire range from 2 feet to 20 feet.
d. Explain why a regression equation should not be formulated for the entire range from 2 feet to 20 feet.
Exercise: The regression equation relating distance (in feet) and success rate (percent) for professional golfers, based on 11 distances ranging from 5 feet to 15 feet, is
Success rate = 76.5 - (3.95)(distance)
a. What percent success would you expect for these professional golfers if the putting distance is 6.5 feet?
b. Explain what the slope of -3.95 means in terms of how success changes with distance.