Question: In Exercise, a regression equation relating x = putting distance (feet) to y = success rate (in percent) for professional golfers was given as
Success rate = 76.5 - 3.95 (Distance)
The equation was based on observations of distances ranging from 5 feet to 15 feet.
a. Use the equation to predict success rate for a distance of 2 feet and for a distance of 20 feet.
b. The original data included values beyond those used to determine the regression equation (5 feet to 15 feet). At a distance of 2 feet, the observed success rate was 93.3%, and at a distance of 20 feet, 15.8% of observed putts were successful. Compare your results in part (a) to the observed success rates for distances of 2 feet and 20 feet. Utilize 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 used to determine the equation.
c. Draw a graph 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.
Exercise: Iman (1994) reports that for professional golfers, a regression equation relating x = putting distance (in feet) and y = success rate (in percent) based on observations of distances ranging from 5 feet to 15 feet is
Success rate = 76.5 - 3.95 (Distance)
a. What percentage of success would you expect for these professional golfers if the putting distance was 10 feet?
b. Explain what the slope of 3.95 means in terms of how success changes with distance.