Task #1. Examine performance measures (i.e., putting, driving yard, driving accuracy, greens in regulation, sand save percentage) and identify important predictors of Earnings per Round AND Top-10s.
Multiple Regression
Multiple regression analysis was carried out for the performance measures and predictors of Earnings per Round and results shown in table 1. Analysis was also performed for the performance measures and predictor of Top-10s and results were shown in table 2.
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Table 1. Multiple Regression for putting, driving yard, driving accuracy, greens in regulation, sand save percentage vs. earnings per round.
| Model Summary - Earnings per Round | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Durbin-Watson |
|||||||||||||||
|
Model |
R |
R² |
Adjusted R² |
RMSE |
Autocorrelation |
Statistic |
p |
||||||||
| H₀ |
0.000 |
0.000 |
0.000 |
21037.799 |
0.869 |
0.118 |
< .001 |
||||||||
| H₁ |
0.659 |
0.434 |
0.417 |
16069.150 |
0.495 |
0.937 |
< .001 |
||||||||
| ANOVA | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Sum of Squares |
df |
Mean Square |
F |
p |
||||||||
| H₁ | Regression |
3.282e +10 |
5 |
6.564e +9 |
25.419 |
< .001 |
|||||||
| Residual |
4.286e +10 |
166 |
2.582e +8 |
||||||||||
| Total |
7.568e +10 |
171 |
|||||||||||
| Note. The intercept model is omitted, as no meaningful information can be shown. | |||||||||||||
| Coefficients | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Unstandardized |
Standard Error |
Standardized |
t |
p |
||||||||
| H₀ | (Intercept) |
22637.552 |
1604.117 |
14.112 |
< .001 |
||||||||
| H₁ | (Intercept) |
312336.800 |
119073.293 |
2.623 |
0.010 |
||||||||
| Putting Average |
-428752.084 |
56542.827 |
-0.474 |
-7.583 |
< .001 |
||||||||
| Yards/Drive |
920.506 |
206.201 |
0.405 |
4.464 |
< .001 |
||||||||
| Driving Accuracy |
706.181 |
362.162 |
0.171 |
1.950 |
0.053 |
||||||||
| Greens in Regulation |
2088.410 |
671.358 |
0.237 |
3.111 |
0.002 |
||||||||
| Sand Save Pct |
401.193 |
221.685 |
0.111 |
1.810 |
0.072 |
||||||||
Residuals vs. Predicted
Standardized Residuals Histogram
Q-Q Plot Standardized Residuals
Table 2. Multiple Regression for putting, driving yard, driving accuracy, greens in regulation, sand save percentage vs. Top 10s
| Model Summary - Top 10s | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Durbin-Watson |
|||||||||||||||
|
Model |
R |
R² |
Adjusted R² |
RMSE |
Autocorrelation |
Statistic |
p |
||||||||
| H₀ |
0.000 |
0.000 |
0.000 |
2.407 |
0.747 |
0.414 |
< .001 |
||||||||
| H₁ |
0.654 |
0.428 |
0.411 |
1.847 |
0.378 |
1.212 |
< .001 |
||||||||
| ANOVA | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Sum of Squares |
df |
Mean Square |
F |
p |
||||||||
| H₁ | Regression |
424.341 |
5 |
84.868 |
24.868 |
< .001 |
|||||||
| Residual |
566.520 |
166 |
3.413 |
||||||||||
| Total |
990.860 |
171 |
|||||||||||
| Note. The intercept model is omitted, as no meaningful information can be shown. | |||||||||||||
| Coefficients | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Unstandardized |
Standard Error |
Standardized |
t |
p |
||||||||
| H₀ | (Intercept) |
2.919 |
0.184 |
15.901 |
< .001 |
||||||||
| H₁ | (Intercept) |
24.435 |
13.689 |
1.785 |
0.076 |
||||||||
| Putting Average |
-44.320 |
6.500 |
-0.428 |
-6.818 |
< .001 |
||||||||
| Yards/Drive |
0.098 |
0.024 |
0.377 |
4.129 |
< .001 |
||||||||
| Driving Accuracy |
0.080 |
0.042 |
0.170 |
1.925 |
0.056 |
||||||||
| Greens in Regulation |
0.320 |
0.077 |
0.317 |
4.146 |
< .001 |
||||||||
| Sand Save Pct |
0.049 |
0.025 |
0.118 |
1.911 |
0.058 |
||||||||
Residuals vs. Predicted
Standardized Residuals Histogram
Q-Q Plot Standardized Residuals
Stepwise Regression Analyses
Stepwise regression analysis was carried out for the performance measures and predictors of Earnings per Round and results shown in table 3. The analysis was also performed for the performance measures and predictor of Top-10s and results were shown in table 4.
Table 3. Stepwise Regression for putting, driving yard, driving accuracy, greens in regulation, sand save percentage vs. earnings per round.
| Model Summary - Earnings per Round | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Durbin-Watson |
|||||||||||||||
|
Model |
R |
R² |
Adjusted R² |
RMSE |
Autocorrelation |
Statistic |
p |
||||||||
| 1 |
0.000 |
0.000 |
0.000 |
21037.799 |
0.869 |
0.118 |
< .001 |
||||||||
| 2 |
0.438 |
0.192 |
0.187 |
18965.731 |
0.705 |
0.502 |
< .001 |
||||||||
| 3 |
0.590 |
0.348 |
0.340 |
17086.795 |
0.542 |
0.843 |
< .001 |
||||||||
| 4 |
0.642 |
0.412 |
0.401 |
16277.891 |
0.500 |
0.936 |
< .001 |
||||||||
| ANOVA | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Sum of Squares |
df |
Mean Square |
F |
p |
||||||||
| 2 | Regression |
1.453e +10 |
1 |
1.453e +10 |
40.406 |
< .001 |
|||||||
| Residual |
6.115e +10 |
170 |
3.597e +8 |
||||||||||
| Total |
7.568e +10 |
171 |
|||||||||||
| 3 | Regression |
2.634e +10 |
2 |
1.317e +10 |
45.112 |
< .001 |
|||||||
| Residual |
4.934e +10 |
169 |
2.920e +8 |
||||||||||
| Total |
7.568e +10 |
171 |
|||||||||||
| 4 | Regression |
3.117e +10 |
3 |
1.039e +10 |
39.209 |
< .001 |
|||||||
| Residual |
4.451e +10 |
168 |
2.650e +8 |
||||||||||
| Total |
7.568e +10 |
171 |
|||||||||||
| Note. The intercept model is omitted, as no meaningful information can be shown. | |||||||||||||
| Coefficients | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Unstandardized |
Standard Error |
Standardized |
t |
p |
||||||||
| 1 | (Intercept) |
22637.552 |
1604.117 |
14.112 |
< .001 |
||||||||
| 2 | (Intercept) |
726067.912 |
110671.743 |
6.561 |
< .001 |
||||||||
| Putting Average |
-396791.372 |
62422.446 |
-0.438 |
-6.357 |
< .001 |
||||||||
| 3 | (Intercept) |
640072.569 |
100620.260 |
6.361 |
< .001 |
||||||||
| Putting Average |
-480689.362 |
57764.898 |
-0.531 |
-8.321 |
< .001 |
||||||||
| Greens in Regulation |
3577.114 |
562.482 |
0.406 |
6.360 |
< .001 |
||||||||
| 4 | (Intercept) |
461874.016 |
104556.105 |
4.417 |
< .001 |
||||||||
| Putting Average |
-449993.656 |
55498.295 |
-0.497 |
-8.108 |
< .001 |
||||||||
| Greens in Regulation |
2724.835 |
571.857 |
0.309 |
4.765 |
< .001 |
||||||||
| Yards/Drive |
612.396 |
143.494 |
0.270 |
4.268 |
< .001 |
||||||||
| Note. The following covariates were considered but not included: Driving Accuracy, Sand Save Pct. | |||||||||||||
Residuals vs. Predicted
Standardized Residuals Histogram
Q-Q Plot Standardized Residuals
Table 4. Stepwise Regression for putting, driving yard, driving accuracy, greens in regulation, sand save percentage vs. Top 10s.
| Model Summary - Top 10s | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Durbin-Watson |
|||||||||||||||
|
Model |
R |
R² |
Adjusted R² |
RMSE |
Autocorrelation |
Statistic |
p |
||||||||
| 1 |
0.000 |
0.000 |
0.000 |
2.407 |
0.747 |
0.414 |
< .001 |
||||||||
| 2 |
0.389 |
0.152 |
0.147 |
2.224 |
0.592 |
0.747 |
< .001 |
||||||||
| 3 |
0.529 |
0.280 |
0.271 |
2.055 |
0.483 |
1.000 |
< .001 |
||||||||
| 4 |
0.637 |
0.405 |
0.395 |
1.873 |
0.427 |
1.121 |
< .001 |
||||||||
| ANOVA | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Sum of Squares |
df |
Mean Square |
F |
p |
||||||||
| 2 | Regression |
150.259 |
1 |
150.259 |
30.388 |
< .001 |
|||||||
| Residual |
840.602 |
170 |
4.945 |
||||||||||
| Total |
990.860 |
171 |
|||||||||||
| 3 | Regression |
277.401 |
2 |
138.700 |
32.855 |
< .001 |
|||||||
| Residual |
713.460 |
169 |
4.222 |
||||||||||
| Total |
990.860 |
171 |
|||||||||||
| 4 | Regression |
401.665 |
3 |
133.888 |
38.176 |
< .001 |
|||||||
| Residual |
589.195 |
168 |
3.507 |
||||||||||
| Total |
990.860 |
171 |
|||||||||||
| Note. The intercept model is omitted, as no meaningful information can be shown. | |||||||||||||
| Coefficients | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Model |
Unstandardized |
Standard Error |
Standardized |
t |
p |
||||||||
| 1 | (Intercept) |
2.919 |
0.184 |
15.901 |
< .001 |
||||||||
| 2 | (Intercept) |
-26.766 |
5.388 |
-4.968 |
< .001 |
||||||||
| Yards/Drive |
0.101 |
0.018 |
0.389 |
5.513 |
< .001 |
||||||||
| 3 | (Intercept) |
40.288 |
13.194 |
3.054 |
0.003 |
||||||||
| Yards/Drive |
0.097 |
0.017 |
0.374 |
5.720 |
< .001 |
||||||||
| Putting Average |
-37.148 |
6.769 |
-0.359 |
-5.488 |
< .001 |
||||||||
| 4 | (Intercept) |
42.007 |
12.029 |
3.492 |
< .001 |
||||||||
| Yards/Drive |
0.063 |
0.017 |
0.242 |
3.802 |
< .001 |
||||||||
| Putting Average |
-46.933 |
6.385 |
-0.453 |
-7.351 |
< .001 |
||||||||
| Greens in Regulation |
0.392 |
0.066 |
0.388 |
5.952 |
< .001 |
||||||||
| Note. The following covariates were considered but not included: Driving Accuracy, Sand Save Pct. | |||||||||||||
Residuals vs. Predicted
Standardized Residuals Histogram
Q-Q Plot Standardized Residuals
Summary and Analyses of Results
For the multiple regression using the forced entry method, the value of R-squared increased when the given performance measures were added one a time. The signs in the coefficient had the expected positive and negative values. The value of R-squared for earnings per round were 0.434 and for Top 10s was 0.428. The values showed that the given performance measures were good predictors of Earnings per Round and Top-10s. Violations of the assumptions were checked using Durbin-Watson value and the plot functions showed that there were no violations.
The equation for performance measures and earnings per round was given as:
Earnings per round = 312,336.800 + (-428,752.084*Putting average) + (920.506*Driving yard) + (706.181*driving accuracy) + (2088.410*Greens in regulation) + (401.193*Sand save percentage).
The equation for performance measures and Top-10s was given as:
Top-10s = 24.435 + (-44.320*Putting average) + (0.098*Driving yard) + (0.080*driving accuracy) + (0.320*Greens in regulation) + (0.049*Sand save percentage).
The step-wise regression provided a model for the values that were significant i.e. values that had p<0.01. The values of R-squared were similar but slightly lower than the forced entry method. Also, the Durbin-Watson score for the step-wise regression was higher than the forced entry method. For earnings per round, the values that were significant were putting average, greens in regulation, and yard drive. Therefore, when focusing on improving the earnings per round, young PGA players should prioritize these performance measures to improve their earnings per round. For Top-10s, the values that were significant were similar to that of the earnings per round. Therefore, young PGA players should focus on improving the performance measures of drive yards, putting average, and greens in regulation to improve their earnings per round and top-10s.
The equation for performance measures and earnings per round using the stepwise method was given as:
Earnings per round = 312,336.800 + (-449,993.656 *Putting average) + (612.396 *Driving yard) + (2724.835 *Greens in regulation).
The equation for performance measures and Top-10s using the stepwise method was given as:
Top-10s = 42.007 + (-46.933 *Putting average) + (0.063 *Driving yard) + (0.392*Greens in regulation).
