Ranking driving performance of professional golfers. Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise.
Ranking driving performance of professional golfers. Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise. Recall that the method computes a driving performance index based on a golfer’s average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). Data for the top 40 PGA golfers (as ranked by the new method) are saved in the PGADRIVER file. (The first five and last five observations are listed in the table.)
a. Write the equation of a straight-line model relating driving accuracy ( y ) to diving distance ( x ).
Rank
Player
Driving
Distance
(yards)
Driving
Accuracy
(%)
Driving
Performance
Index
1
Woods
316.1
54.6
3.58
2
Perry
304.7
63.4
3.48
3
Gutschewski
310.5
57.9
3.27
4
Wetterich
311.7
56.6
3.18
5
Hearn
295.2
68.5
2.82
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
36
Senden
291
66
1.31
37
Mickelson
300
58.7
1.30
38
Watney
298.9
59.4
1.26
39
Trahan
295.8
61.8
1.23
40
Pappas
309.4
50.6
1.17
Based on Frederick Wiseman, Ph.D., Mohamed Habibullah, Ph.D., and Mustafa Yilmaz, Ph.D, Sports Journal, Vol. 10, No. 1, Winter 2007.
b. Use simple linear regression to fit the model you found in part a to the data. Give the least squares prediction equation.
c. Interpret the estimated y -intercept of the line.
d. Interpret the estimated slope of the line.
e. In Exercise 2.157 (p. 91), you were informed that a professional golfer practicing a new swing to increase his average driving distance is concerned that his driving accuracy will be lower. Which of the two estimates, y -intercept or slope, will help you determine whether the golfer’s concern is a valid one? Explain.
You fit a straight-line model relating driving accuracy ( y ) to driving distance ( x ) to the data saved in the PGADRIVER file.
a. Give the null and alternative hypotheses for testing whether driving accuracy ( y ) decreases linearly as driving distance ( x ) increases.
b. Find the test statistic and p -value of the test you set up in part a.
c. Make the appropriate conclusion at α = .01.
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