Sports HW4 - Professor Lucius Riccio PDF

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Professor Lucius Riccio...

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Zachary Greenberg March 11, 2021 Sports Analytics HW 4 Earnings/Event - =K4/E4

Golf Performance Measurement Data Spreadsheet: PGA Tour 2016 Summary Data The spreadsheet contains summary data for the top players on the PGA Tour for 2016. Use the spreadsheet data to answer the following questions: 1) Regress: Predict Column L (Earnings/Event) and Column O (Storkes) - figure out the value in one less stroke in money winnings a. What is the value (in money winnings) of improving a player’s average score per round by one stroke over the course of the season? Is this a significant predictor of money winnings? i. Regress Money Winnings per Event Entered on Average Score per Round. Step 1) Create Column Earnings/Event : =K4/E4 (Earnings/Event) for each observation Step 2) Regression : Input Y Range: $L$3:$L$203 Input X Range: $P$3:$P$203 with labels and residuals SUMMARY OUTPUT

Regression Statistics Multiple R

0.740610 41

R Square

0.548503 78

Adjusted R Square

0.546223 5

46019.89 Standard Error 98

Observations 200

ANOVA df

SS

MS

F

Significanc eF

Regression

1

5.0943E+1 5.0943E+ 240.5418 4.9256E1 11 8 36

Residual

198

4.1933E+1 2117831 1 178

199

9.2876E+1 1

Total

Coefficie Standard nts Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

5736993. 365288.67 15.70536 1.2431E- 5016638.0 6457349. 5016638. 6457349. 73 7 97 36 8 39 08 39

Average Strokes

69746.76 90067.04 69746.76 79906.90 5152.1556 15.50941 4.9256E- 7 9 3 36 90067.049 7 8 6

RESIDUAL OUTPUT

Observation Predicted Earnings/Event

Residuals

1

209673.088

216017.139

2

198406.214

203849.361

3

185860.829

137793.646

4

171797.214

149901.981

5

129925.994

72915.9706

6

181865.484

81871.2065

7

118019.864

77416.3956

8

103476.807

63228.7484

9

140793.333

41552.4929

10

112106.753

53835.1068

11

97883.3236

49486.8907

12

176911.256

5935.47159

13

127289.066

19382.8528

14

147505.514

26747.2047

15

155975.646

-9064.9342

16

118179.678

42734.8652

17

112106.753

16999.4003

18

116901.168

66932.6218

19

119697.909

12659.429

20

104435.69

22392.2285

21

157893.412

84776.0742

22

92609.4677

42258.7523

23

147026.072

11183.1184

24

116421.726

8309.59297

25

143590.075

72553.6583

26

98762.2996

-7986.7319

27

101718.855

33263.3266

28

143190.54

11337.2227

29

169879.448

154357.474

30

75189.7617

45866.4591

31

126569.904

-23716.921

32

127209.159

32727.9411

33

134081.153

-16100.131

34

71673.8577

51953.2756

35

96524.9061

-3170.295

36

62404.6564

27172.9793

37

71354.2301

20459.8366

38

117380.609

25094.6144

39

124811.952

-32810.248

40

108031.501

-8439.8551

41

44026.0675

47032.444

42

90931.4226

-537.59566

43

35955.4698

49699.934

44

47142.437

24970.4699

45

131683.946

-15830.346

46

81901.942

-8831.6527

47

106513.27

-31910.199

48

110109.081

-31110.601

49

71913.5785

-28.759939

50

97963.2305

-28882.859

51

52016.7583

11399.2783

52

59607.9146

18049.7104

53

79824.3624

-15010.43

54

125211.486

-47205.377

55

75908.9239

12611.0761

56

69995.8127

-7055.2769

57

99721.1825

-12492.657

58

114424.054

-42811.449

59

89413.1913

-26349.747

60

44265.7883

39034.9317

61

72552.8337

-13805.873

62

61365.8666

6998.72924

63

70155.6265

910.243085

64

154697.135

6237.89477

65

59288.287

2295.45917

66

80783.2453

-19452.964

67

75189.7617

-11619.138

68

92369.7469

891.188367

69

99241.741

-36568.765

70

89573.0051

-18377.21

71

66400.0018

-21118.296

72

133122.27

-23250.527

73

69915.9058

-15522.421

74

114823.588

-42305.838

75

143829.796

-49253.296

76

54174.2449

-3969.877

77

53534.9896

11689.0485

78

78865.4795

-26781.033

79

71514.0439

-19460.79

80

68637.3952

-10869.717

81

56171.9176

4212.07789

82

60007.4492

-12603.153

83

63922.8876

-21993.807

84

8787.12107

31804.8977

85

76947.7137

-30864.267

86

64482.236

26860.3783

87

98922.1134

-49788.249

88

74230.8788

-23202.562

89

73991.1581

-32214.803

90

59048.5663

-4043.8253

91

41069.5119

1992.29163

92

69436.4643

-32565.155

93

98282.8581

-56565.972

94

80863.1522

-40904.538

95

55772.383

-13422.316

96

99721.1825

62965.9604

97

48420.9475

-5523.9552

98

90691.7019

-50433.776

99

64002.7946

-26529.884

100

81102.8729

-39418.758

101

108670.756

-48495.456

102

29802.6379

10022.3917

103

86057.1012

-46508.616

104

43147.0915

-584.45155

105

73591.6235

-39347.826

106

48500.8544

-15415.959

107

75749.11

-26944.372

108

55292.9416

-19320.852

109

212070.295

-100510.86

110

45784.0195

-8622.4417

111

63603.26

-25462.483

112

86216.915

-50865.454

113

75109.8548

-41331.358

114

100839.879

-59582.162

115

9746.00397

25742.7099

116

93168.816

-16379.779

117

57690.1488

-14425.554

118

24448.8751

4694.96172

119

84299.1492

-49684.342

120

57770.0557

-27822.382

121

52496.1998

-12726.152

122

73831.3443

-33067.005

123

-6714.8191

45366.0891

124

61046.239

-32580.132

125

26286.7339

5721.61189

126

109070.291

-58374.957

127

83260.3594

-55445.498

128

97084.2545

-50475.798

129

21092.7849

7159.05893

130

33877.8902

-5162.2902

131

77826.6897

-18333.573

132

45784.0195

-19386.886

133

87255.7048

-55045.587

134

86057.1012

-15943.081

135

40669.9774

-16597.495

136

66320.0949

-40489.222

137

-50104.27

108036.64

138

25887.1994

-603.42533

139

23489.9922

38369.0988

140

59208.3801

-29780.521

141

191454.313

-56496.793

142

47382.1577

-24467.023

143

58728.9386

-35096.394

144

61046.239

-20113.176

145

34676.9593

-13245.549

146

8227.77271

13664.0204

147

41149.4188

-16966.479

148

70954.6956

-48440.192

149

29323.1964

-6201.5157

150

55532.6623

-33340.962

151

64721.9567

-43981.455

152

9186.65561

11515.7194

153

-1361.0563

27303.7699

154

65680.8396

-14609.999

155

28124.5928

-6526.1794

156

33957.7971

-7337.6095

157

53055.5481

-32425.17

158

47302.2508

-24607.335

159

86536.5426

-46532.571

160

96524.9061

33135.8039

161

30681.6139

-12190.984

162

29483.0103

-8229.7369

163

20373.6227

-1707.199

164

67598.6054

-45850.165

165

9506.28324

7216.29883

166

2953.91678

16956.2199

167

93488.4436

-53769.999

168

28843.755

-6823.4007

169

-197053.07

214702.728

170

28444.2205

-11775.475

171

26606.3616

3164.61576

172

75908.9239

-52863.909

173

30361.9863

-7865.0584

174

13501.6286

1929.99654

175

31480.683

-15479.427

176

15419.3944

-1566.6401

177

26366.6408

-9956.8072

178

36994.2596

-16822.399

179

26526.4547

-8453.9333

180

42028.3948

-6512.5767

181

-2.6388181

17276.4843

182

52176.5722

-31399.881

183

4152.5204

24328.7296

184

57770.0557

1121.27761

185

41149.4188

2393.08115

186

37553.608

-22436.809

187

7668.42436

8621.94898

188

169479.913

-85289.413

189

21732.0402

-10265.392

190

41948.4879

-1079.7754

191

61206.0528

-40308.966

192

28763.8481

-14151.17

193

11264.2352

5694.09811

194

33558.2626

-21490.391

195

-12148.489

33379.7746

196

51057.8754

-37206.033

197

25967.1063

-3780.3371

198

-17821.879

29516.6435

199

-10630.258

32216.3468

200

-30287.357

42883.617

Earnings/Event = 5736993.734 + (-79906.90808)Average Strokes We see that with every increase in units Average Strokes, the earnings per events goes down 79,906.9080. Average Strokes has a p-value of 4.92558E-36 and an R-Square of 0.548503783. So that is a great p-value and a decent R-Square so I would say it is a significant predictor of money winnings.

2) Divide data into 3 categories and regress each category (3 models) ii. Group the data by range of average strokes (at least three ranges, say, 65-70,70-71.2,71.2-75) and regress money winnings against average strokes. Is this a better analysis? 65 - 70 SUMMARY OUTPUT

Regression Statistics Multiple R

0.436778 32

R Square

0.190775 3

Adjusted R Square

0.136826 99

98312.81 Standard Error 23 Observations

17

ANOVA df Regression

1

SS

MS

F

Significanc eF

3.4179E+10 3.4179E+ 3.536260 0.0796014

10

66

Residual

15

96654090 1.4498E+11 66

Total

16

1.7916E+11

Coefficie nts

Standard Error

t Stat

1

P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1172340 1.916723 0.074524 2476016 24760161. 8.8 6116378.69 83 95 -1313343.8 1.4 1313343.8 4

Average Strokes

1.880494 0.079601 22038.30 41 -352320.31 6 352320.31 22038.306 -165141 87817.8466 8

70-71.2 SUMMARY OUTPUT

Regression Statistics Multiple R

0.732910 04

R Square

0.537157 13

Adjusted R Square

0.534542 2

29213.90 Standard Error 08 Observations

179

ANOVA df

SS

MS

F

Significanc eF

Regression

1

1.7532E+ 205.4192 1.7532E+11 11 02 2.0003E-31

Residual

177

1.5106E+11 8534519

97 Total

178

3.2638E+11

Coefficie nts

Standard Error

t Stat

P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

5127922. 14.49790 6.6434E- 4429909.4 5825936. 4429909.4 5825936.4 92 353700.859 92 32 1 43 1 3

Average Strokes

61589.10 14.33245 2.0003E71423.51 81257.926 61589.102 31 -81257.926 2 4 4983.34201 3

71.2-75

SUMMARY OUTPUT

Regression Statistics Multiple R

0.072710 6

R Square

0.005286 83

Adjusted R Square

0.492069 8

27034.03 Standard Error 32 Observations

4

ANOVA df Regression Residual

SS

MS

F

Significanc eF

1

7768716. 0.010629 7768716.53 53 86 0.9272894

2

146167790 7308389 3 52

Total

3

Coefficie nts

146944662 0

Standard Error

t Stat

P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

137323.0 0.126003 0.911253 4826509. 4826509.9 62 1089836.24 39 7 -4551863.8 92 4551863.8 2

Average Strokes

0.103101 0.927289 62932.99 62932.991 1545.038 4 -66023.068 11 66023.068 1 3 14985.6457 2

All Distances: R2 = 54.85%, P-Value = 4.92558E-36 Earnings/Event = 5736993.734 + (-79906.90808)Average Strokes 65 - 70: R2 = 19.01%, P-Value = 0.079601406 Earnings/Event = 11723408.79 + (-165141.0031)Average Strokes 70 - 71.2: R2 = 53.71%, P-Value = 2.0003E-31 Earnings/Event = 5127922.919 + (-71423.51381)Average Strokes 71.2-75: R2 = 0.53%, P-Value = 0.9272894 Earnings/Event = 137323.0624 + (-1545.03832)Average Strokes

It is clear that the best R2 and P-Value are when you look at all of the average strokes at once. The broken up categories models are a lot worse to look at for predicting Earnings/Event.

b.

What factors most significantly predict scoring average? Which do not? i. Regress average strokes as a function of Average Driving Distance, Putts per Round, % Fairway, and GIRs).

Step 1) Reorganized each of the columns to be next to each other for regression Step 2) Ran regreesion SUMMARY OUTPUT

Regression Statistics Multiple R

0.67666 54

R Square

0.45787 607

0.44675 Adjusted R Square 558 Standard Error

0.47102 36

Observations

200

ANOVA df

SS

MS

F

Significanc eF

4

36.540064 9.13501 41.1740 5.4198E8 62 874 25

Residual

195

43.263330 0.22186 7 323

Total

199

79.803395 5

Regression

Coefficie Standard nts Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

72.4042 2.2696753 31.9007 2.5584E76.8805 67.92801 76.88054 79 7 203 79 67.92801...