Suppose you want to determine if scoring average impacts how much a golfer earns
ID: 3232837 • Letter: S
Question
Suppose you want to determine if scoring average impacts how much a golfer earns. Use the data in “Problem 2 see below” to run a regression with a 97% confidence interval and answer the following five questions.
How much of the variation in earnings is explained by scoring average?
QUESTION 7
What is the coefficient for the independent variable?
QUESTION 8
Is it statistically significant?
QUESTION 9
What is the lower bound on scoring average for a 97% confidence interval?
QUESTION 10
What does the model predict for a golfer whose scoring average is 71.59?
Rank
Player
Money ($)
Scoring Average
DrDist
DrAccu
GIR
1
Vijay Singh
6,601,094
70.27
297.8
59.45
68.45
2
Phil Mickelson
5,188,875
70.28
295.7
55.27
65.81
3
Sergio Garcia
4,858,224
70.6
294.6
59.39
67.06
4
Kenny Perry
4,663,794
70.21
296
61.97
67.47
5
Anthony Kim
4,656,265
70.22
300.9
58.34
65.78
6
Camilo Villegas
4,422,641
70.6
293.3
58.15
64.6
7
Padraig Harrington
4,313,551
70.7
296.3
59.37
60.67
8
Stewart Cink
3,979,301
70.65
296.9
55.27
66.94
9
Justin Leonard
3,943,542
70.41
281.4
67.72
66.61
10
Robert Allenby
3,606,700
70.64
291.7
65.64
70.4
11
Jim Furyk
3,455,714
70.56
280.4
69.37
66.78
12
Ryuji Imada
3,029,363
71.13
278.6
59.64
61.39
13
Mike Weir
3,020,135
70.68
284.8
62.46
64.62
14
Geoff Ogilvy
2,880,099
71.38
292.1
58.18
61.89
15
K.J. Choi
2,683,442
71.01
286.1
61.38
65.48
16
Ben Curtis
2,615,798
70.96
284.7
67.2
63.45
17
Kevin Sutherland
2,581,311
70.22
291
61.93
68.2
18
Trevor Immelman
2,566,199
71.85
291.3
62.45
63.07
19
Ernie Els
2,537,290
71.44
291.6
56.88
61.33
20
Carl Pettersson
2,512,538
70.84
286
59.87
63.54
21
Stuart Appleby
2,484,630
70.86
290.9
58.19
61.9
22
Steve Stricker
2,438,304
70.83
283.6
56.25
63.81
23
Chad Campbell
2,404,770
70.37
289.9
65.68
68.44
24
Boo Weekley
2,398,751
71.12
291.7
64.75
67.87
25
D.J. Trahan
2,304,368
70.89
291.3
65.31
66.25
26
Stephen Ames
2,285,707
70.67
283.8
62.72
65.04
27
Ken Duke
2,238,885
70.61
284.9
62.27
64.8
28
Dudley Hart
2,218,817
70.84
275.5
61.18
66.11
29
Hunter Mahan
2,208,855
70.78
289.9
66.02
69.61
30
Brian Ardo
2,205,513
70.11
270.5
71.74
63.71
31
J.B. Holmes
2,166,131
71.39
310.3
52.4
62.94
32
Woody Austin
2,146,431
71.1
285.3
66.19
68.15
33
Steve Marino
2,094,267
70.29
293.5
63.84
68.36
34
Sean O'Hair
2,089,857
71.25
291.1
60.44
64.47
35
Andres Romero
2,064,612
71.85
299.1
52.83
58.79
36
Briny Baird
2,039,808
70.44
285.2
66.03
70
37
Jeff Quinney
1,999,371
71.39
272.5
61.98
61.81
38
Adam Scott
1,979,160
71.45
302.1
54.66
63.72
39
Mathew Goggin
1,969,962
70.73
295.9
64.91
67.58
40
Nicholas Thompson
1,869,329
71.38
295.4
66.85
63.14
41
Dustin Johnson
1,789,895
71.5
309.7
53.05
63.71
42
Pat Perez
1,756,038
70.7
294.2
63.27
66.91
43
Billy Mayfair
1,750,683
70.76
284
72.16
68.12
44
Tim Clark
1,722,030
70.87
281.1
64.98
63.61
45
Bart Bryant
1,719,153
71.22
279.5
73.87
64.88
46
Rod Pampling
1,702,952
71.39
288
65.65
63.61
47
Davis Love III
1,695,237
71.21
301.3
58.22
64.74
48
Aaron Baddeley
1,665,587
70.86
290.3
59.45
62.02
49
Jerry Kelly
1,652,400
71.49
277
66.21
63.36
50
Paul Goydos
1,640,737
71.6
273.2
70.85
62.96
51
Daniel Chopra
1,630,690
71.51
294.2
52.76
59.77
52
Zach Johnson
1,615,123
71.06
275.1
73.73
67.59
53
Fredrik Jacobson
1,597,423
71.26
282.7
59.95
61.82
54
Mark Wilson
1,578,337
70.44
284.6
70.73
66.93
55
Rory Sabbatini
1,559,277
71.05
292
61.99
66.08
56
Bubba Watson
1,533,523
71.07
315.1
55.16
67.6
57
Brandt Snedeker
1,531,442
71.27
280.8
60.51
63.36
58
Steve Lowery
1,524,275
71.96
287
59.92
59.38
59
Charlie Wi
1,515,395
70.41
287.4
67.33
66.44
60
Tommy Armour III
1,501,256
70.99
287.7
63.35
66.51
61
Heath Slocum
1,491,916
71.17
279.9
73.95
66.77
62
Ben Crane
1,488,505
70.38
287.8
67.64
65.76
63
Ian Poulter
1,488,214
71.84
283.6
59.77
59.75
64
Peter Lonard
1,462,894
70.93
281.6
65.91
64.9
65
Ryan Palmer
1,453,183
70.48
294.2
62.94
66.75
66
Charles Howell III
1,449,232
71.15
293.6
56.78
66.78
67
Matt Kuchar
1,447,638
71.03
275
65.53
63.89
68
Chez Reavie
1,444,102
71.03
281.8
72.56
66.61
69
Retief Goosen
1,431,965
71.71
287.1
56.79
59.39
70
Johnson Wagner
1,431,001
71.65
283.2
61.02
61.6
71
Rocco Mediate
1,420,875
71.61
278.6
64.66
62.58
72
Nick O'Hern
1,370,771
70.89
274.9
72.27
64.38
73
George McNeill
1,361,532
70.94
295
59.42
68.44
74
Scott Verplank
1,359,620
70.84
278.6
73.57
65.09
75
Kevin Streelman
1,352,705
70.63
292.8
62.21
67.44
76
Dean Wilson
1,350,002
70.98
276.2
61.7
65.61
77
Tom Pernice, Jr.
1,336,277
70.54
280.6
63.99
64.1
78
Marc Turnesa
1,329,920
71.16
285.1
65.31
63.45
79
Cameron Beckman
1,312,837
71.09
281.9
67.64
65.82
80
John Merrick
1,312,005
70.97
299
65.23
67.72
81
Parker McLachlin
1,311,839
71.07
286.2
58.84
62.5
82
Steve Elkington
1,291,114
70.67
282
70.43
67
83
John Senden
1,269,083
70.9
288.8
68.2
69.08
84
Steve Flesch
1,265,059
71.17
281.9
60.98
64.62
85
Ryan Moore
1,214,900
71.5
292.7
65.74
61.73
86
Troy Matteson
1,212,018
71.4
295.2
61.36
67.38
87
Greg Kraft
1,204,559
71.56
273.6
68.71
59.49
88
John Mallinger
1,201,433
71.02
279
69.39
60.82
89
Tim Wilkinson
1,167,607
71.02
279.8
66.72
65.39
90
Michael Letzig
1,166,977
71.01
291.1
64.44
63.29
91
Tim Herron
1,164,999
70.66
293
61.1
62.25
92
Paul Casey
1,156,414
71.75
299.2
62.43
65.71
93
Brian Davis
1,151,558
70.73
277.7
72.47
65.23
94
Cliff Kresge
1,068,207
71.54
280.9
62.26
65
95
Vaughn Taylor
1,053,423
70.84
288
62.4
65.48
96
Kevin Na
1,041,059
70.81
280.9
67.8
63.57
97
Jonathan Byrd
1,039,584
71.36
285.3
67.31
63.01
98
Joe Ogilvie
1,035,831
70.92
287.7
65.2
64.12
99
John Rollins
1,016,032
71.54
288.9
67.94
63.48
100
Bill Haas
1,000,939
70.66
296.7
59.95
68.07
101
Lucas Glover
998,491
70.95
298.4
61.54
65.38
102
Michael Allen
981,263
71.07
286.8
69.45
66.67
103
Tim Petrovic
958,577
71.23
284
66.53
63.17
104
Scott McCarron
952,070
71.22
283.1
69.2
64.81
105
Fred Couples
949,281
71.22
299.6
57.49
65.46
106
Charley Hoffman
945,702
71.16
300.8
63.35
66.24
107
J.J. Henry
931,162
71.07
291.7
65.6
69.19
108
Corey Pavin
924,282
70.67
261.4
69.22
57.95
109
Nathan Green
912,867
71.33
283.7
59.5
59.82
110
Will MacKenzie
911,194
71.63
286
62.6
64.7
111
Bo Van Pelt
903,967
70.96
292
62.06
67.3
112
Eric Axley
899,215
71.31
287.7
56.39
61.16
113
Alex Cejka
893,998
71.69
282.7
65.42
63.12
114
Jeff Overton
890,489
71.29
297.6
54.31
64.14
115
Richard S. Johnson
884,367
71.13
282.2
64.18
65.12
116
Brett Quigley
878,216
71.28
287.5
61.76
64.53
117
Nick Watney
878,173
71.02
302.9
61.21
68.23
118
Angel Cabrera
868,182
71.94
300.2
51.11
62.64
119
Brad Adamonis
862,413
71.03
289.9
58.1
65.86
120
Martin Laird
852,752
70.81
296.6
62.25
67.03
121
Shane Bertsch
841,248
70.56
274.3
70.54
64.06
122
Bob Estes
829,395
70.69
282.6
66.48
68.69
123
Patrick Sheehan
805,897
70.93
284.1
66.48
64.8
124
Joe Durant
802,568
71.24
286.5
73.05
71.1
125
Charles Warren
800,694
72.08
301.1
65.43
66.88
Rank
Player
Money ($)
Scoring Average
DrDist
DrAccu
GIR
1
Vijay Singh
6,601,094
70.27
297.8
59.45
68.45
2
Phil Mickelson
5,188,875
70.28
295.7
55.27
65.81
3
Sergio Garcia
4,858,224
70.6
294.6
59.39
67.06
4
Kenny Perry
4,663,794
70.21
296
61.97
67.47
5
Anthony Kim
4,656,265
70.22
300.9
58.34
65.78
6
Camilo Villegas
4,422,641
70.6
293.3
58.15
64.6
7
Padraig Harrington
4,313,551
70.7
296.3
59.37
60.67
8
Stewart Cink
3,979,301
70.65
296.9
55.27
66.94
9
Justin Leonard
3,943,542
70.41
281.4
67.72
66.61
10
Robert Allenby
3,606,700
70.64
291.7
65.64
70.4
11
Jim Furyk
3,455,714
70.56
280.4
69.37
66.78
12
Ryuji Imada
3,029,363
71.13
278.6
59.64
61.39
13
Mike Weir
3,020,135
70.68
284.8
62.46
64.62
14
Geoff Ogilvy
2,880,099
71.38
292.1
58.18
61.89
15
K.J. Choi
2,683,442
71.01
286.1
61.38
65.48
16
Ben Curtis
2,615,798
70.96
284.7
67.2
63.45
17
Kevin Sutherland
2,581,311
70.22
291
61.93
68.2
18
Trevor Immelman
2,566,199
71.85
291.3
62.45
63.07
19
Ernie Els
2,537,290
71.44
291.6
56.88
61.33
20
Carl Pettersson
2,512,538
70.84
286
59.87
63.54
21
Stuart Appleby
2,484,630
70.86
290.9
58.19
61.9
22
Steve Stricker
2,438,304
70.83
283.6
56.25
63.81
23
Chad Campbell
2,404,770
70.37
289.9
65.68
68.44
24
Boo Weekley
2,398,751
71.12
291.7
64.75
67.87
25
D.J. Trahan
2,304,368
70.89
291.3
65.31
66.25
26
Stephen Ames
2,285,707
70.67
283.8
62.72
65.04
27
Ken Duke
2,238,885
70.61
284.9
62.27
64.8
28
Dudley Hart
2,218,817
70.84
275.5
61.18
66.11
29
Hunter Mahan
2,208,855
70.78
289.9
66.02
69.61
30
Brian Ardo
2,205,513
70.11
270.5
71.74
63.71
31
J.B. Holmes
2,166,131
71.39
310.3
52.4
62.94
32
Woody Austin
2,146,431
71.1
285.3
66.19
68.15
33
Steve Marino
2,094,267
70.29
293.5
63.84
68.36
34
Sean O'Hair
2,089,857
71.25
291.1
60.44
64.47
35
Andres Romero
2,064,612
71.85
299.1
52.83
58.79
36
Briny Baird
2,039,808
70.44
285.2
66.03
70
37
Jeff Quinney
1,999,371
71.39
272.5
61.98
61.81
38
Adam Scott
1,979,160
71.45
302.1
54.66
63.72
39
Mathew Goggin
1,969,962
70.73
295.9
64.91
67.58
40
Nicholas Thompson
1,869,329
71.38
295.4
66.85
63.14
41
Dustin Johnson
1,789,895
71.5
309.7
53.05
63.71
42
Pat Perez
1,756,038
70.7
294.2
63.27
66.91
43
Billy Mayfair
1,750,683
70.76
284
72.16
68.12
44
Tim Clark
1,722,030
70.87
281.1
64.98
63.61
45
Bart Bryant
1,719,153
71.22
279.5
73.87
64.88
46
Rod Pampling
1,702,952
71.39
288
65.65
63.61
47
Davis Love III
1,695,237
71.21
301.3
58.22
64.74
48
Aaron Baddeley
1,665,587
70.86
290.3
59.45
62.02
49
Jerry Kelly
1,652,400
71.49
277
66.21
63.36
50
Paul Goydos
1,640,737
71.6
273.2
70.85
62.96
51
Daniel Chopra
1,630,690
71.51
294.2
52.76
59.77
52
Zach Johnson
1,615,123
71.06
275.1
73.73
67.59
53
Fredrik Jacobson
1,597,423
71.26
282.7
59.95
61.82
54
Mark Wilson
1,578,337
70.44
284.6
70.73
66.93
55
Rory Sabbatini
1,559,277
71.05
292
61.99
66.08
56
Bubba Watson
1,533,523
71.07
315.1
55.16
67.6
57
Brandt Snedeker
1,531,442
71.27
280.8
60.51
63.36
58
Steve Lowery
1,524,275
71.96
287
59.92
59.38
59
Charlie Wi
1,515,395
70.41
287.4
67.33
66.44
60
Tommy Armour III
1,501,256
70.99
287.7
63.35
66.51
61
Heath Slocum
1,491,916
71.17
279.9
73.95
66.77
62
Ben Crane
1,488,505
70.38
287.8
67.64
65.76
63
Ian Poulter
1,488,214
71.84
283.6
59.77
59.75
64
Peter Lonard
1,462,894
70.93
281.6
65.91
64.9
65
Ryan Palmer
1,453,183
70.48
294.2
62.94
66.75
66
Charles Howell III
1,449,232
71.15
293.6
56.78
66.78
67
Matt Kuchar
1,447,638
71.03
275
65.53
63.89
68
Chez Reavie
1,444,102
71.03
281.8
72.56
66.61
69
Retief Goosen
1,431,965
71.71
287.1
56.79
59.39
70
Johnson Wagner
1,431,001
71.65
283.2
61.02
61.6
71
Rocco Mediate
1,420,875
71.61
278.6
64.66
62.58
72
Nick O'Hern
1,370,771
70.89
274.9
72.27
64.38
73
George McNeill
1,361,532
70.94
295
59.42
68.44
74
Scott Verplank
1,359,620
70.84
278.6
73.57
65.09
75
Kevin Streelman
1,352,705
70.63
292.8
62.21
67.44
76
Dean Wilson
1,350,002
70.98
276.2
61.7
65.61
77
Tom Pernice, Jr.
1,336,277
70.54
280.6
63.99
64.1
78
Marc Turnesa
1,329,920
71.16
285.1
65.31
63.45
79
Cameron Beckman
1,312,837
71.09
281.9
67.64
65.82
80
John Merrick
1,312,005
70.97
299
65.23
67.72
81
Parker McLachlin
1,311,839
71.07
286.2
58.84
62.5
82
Steve Elkington
1,291,114
70.67
282
70.43
67
83
John Senden
1,269,083
70.9
288.8
68.2
69.08
84
Steve Flesch
1,265,059
71.17
281.9
60.98
64.62
85
Ryan Moore
1,214,900
71.5
292.7
65.74
61.73
86
Troy Matteson
1,212,018
71.4
295.2
61.36
67.38
87
Greg Kraft
1,204,559
71.56
273.6
68.71
59.49
88
John Mallinger
1,201,433
71.02
279
69.39
60.82
89
Tim Wilkinson
1,167,607
71.02
279.8
66.72
65.39
90
Michael Letzig
1,166,977
71.01
291.1
64.44
63.29
91
Tim Herron
1,164,999
70.66
293
61.1
62.25
92
Paul Casey
1,156,414
71.75
299.2
62.43
65.71
93
Brian Davis
1,151,558
70.73
277.7
72.47
65.23
94
Cliff Kresge
1,068,207
71.54
280.9
62.26
65
95
Vaughn Taylor
1,053,423
70.84
288
62.4
65.48
96
Kevin Na
1,041,059
70.81
280.9
67.8
63.57
97
Jonathan Byrd
1,039,584
71.36
285.3
67.31
63.01
98
Joe Ogilvie
1,035,831
70.92
287.7
65.2
64.12
99
John Rollins
1,016,032
71.54
288.9
67.94
63.48
100
Bill Haas
1,000,939
70.66
296.7
59.95
68.07
101
Lucas Glover
998,491
70.95
298.4
61.54
65.38
102
Michael Allen
981,263
71.07
286.8
69.45
66.67
103
Tim Petrovic
958,577
71.23
284
66.53
63.17
104
Scott McCarron
952,070
71.22
283.1
69.2
64.81
105
Fred Couples
949,281
71.22
299.6
57.49
65.46
106
Charley Hoffman
945,702
71.16
300.8
63.35
66.24
107
J.J. Henry
931,162
71.07
291.7
65.6
69.19
108
Corey Pavin
924,282
70.67
261.4
69.22
57.95
109
Nathan Green
912,867
71.33
283.7
59.5
59.82
110
Will MacKenzie
911,194
71.63
286
62.6
64.7
111
Bo Van Pelt
903,967
70.96
292
62.06
67.3
112
Eric Axley
899,215
71.31
287.7
56.39
61.16
113
Alex Cejka
893,998
71.69
282.7
65.42
63.12
114
Jeff Overton
890,489
71.29
297.6
54.31
64.14
115
Richard S. Johnson
884,367
71.13
282.2
64.18
65.12
116
Brett Quigley
878,216
71.28
287.5
61.76
64.53
117
Nick Watney
878,173
71.02
302.9
61.21
68.23
118
Angel Cabrera
868,182
71.94
300.2
51.11
62.64
119
Brad Adamonis
862,413
71.03
289.9
58.1
65.86
120
Martin Laird
852,752
70.81
296.6
62.25
67.03
121
Shane Bertsch
841,248
70.56
274.3
70.54
64.06
122
Bob Estes
829,395
70.69
282.6
66.48
68.69
123
Patrick Sheehan
805,897
70.93
284.1
66.48
64.8
124
Joe Durant
802,568
71.24
286.5
73.05
71.1
125
Charles Warren
800,694
72.08
301.1
65.43
66.88
Explanation / Answer
Following is the output of regression:
How much of the variation in earnings is explained by scoring average?
R-square: 0.1926
That is 19.26% variation in earnings is explained by scoring average.
QUESTION 7
What is the coefficient for the independent variable?
The coeffcient of independent variable: -1077566.817
Is it statistically significant?QUESTION 8
P-value is 0.0000
Yes it is statistically signficant.
QUESTION 9
What is the lower bound on scoring average for a 97% confidence interval?
The lower bound is: -1514326.3728
QUESTION 10
What does the model predict for a golfer whose scoring average is 71.59?
The requried predcited earning is
Earning = 78326632.5254-1077566.8166*Scoring-average" = 78326632.5254 - 1077566.8166 * 71.59 = $1183624.125006
SUMMARY OUTPUT Regression Statistics Multiple R 0.438870604 R Square 0.192607407 Adjusted R Square 0.18604324 Standard Error 934929.8145 Observations 125 ANOVA df SS MS F Significance F Regression 1 2.56479E+13 2.56479E+13 29.3422448 3.0617E-07 Residual 123 1.07514E+14 8.74094E+11 Total 124 1.33161E+14 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 97.0% Upper 97.0% Intercept 78326632.53 14129408.18 5.543518279 1.72247E-07 50358335.7 106294929.3 47304700.16 109348564.9 Scoring Average, X -1077566.817 198928.7441 -5.41684823 3.06166E-07 -1471334.06 -683799.5699 -1514326.373 -640807.2604Related Questions
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