Question

In: Statistics and Probability

THe Golfing Statistics provides data for a portion of the 2010 professional season for the top...

THe Golfing Statistics provides data for a portion of the 2010 professional season for the top 25 golfers.

A) Find the best multiple regression model for predicting earnings/event as a function of the remaining variables.

B) Find the best multiple regression model for predicting average score as a function of the other variables except earning sand events.

Golfing Statistics
Earnings/Event Events Avg. Score GIR (%)* Driving Distance Driving Accuracy (%) Putts/Round
$239,493.68       22           70.37       67.9                 288.4                         60.2             31.82
$177,249.18       28           69.43       69.4                 286.9                         67.9             31.30
$218,619.18       22           70.23       67.1                 276.0                         71.0             31.81
$186,380.08       24           70.46       68.0                 308.5                         56.4             31.81
$209,511.75       20           69.78       68.3                 282.9                         68.5             31.43
$181,987.29       21           70.34       65.1                 299.1                         52.7             31.72
$162,536.13       23           69.92       66.3                 287.8                         65.2             31.68
$174,534.95       21           70.25       65.3                 277.0                         62.4             31.52
$135,353.70       27           70.64       68.0                 291.8                         67.9             32.35
$212,540.82       17           69.93       68.7                 294.2                         61.3             31.55
$297,079.50       12           70.26       69.3                 298.7                         61.3             32.31
$168,904.45       20           69.96       66.0                 291.4                         64.8             31.79
$135,791.58       24           70.21       68.5                 309.8                         55.7             31.73
$133,695.52       23           70.53       68.2                 289.1                         64.8             31.86
$112,192.04       26           70.59       66.5                 279.7                         71.2             31.30
$215,121.67       12           70.22       66.5                 292.4                         60.1             32.29
$183,922.93       14           70.86       62.9                 287.2                         52.0             31.99
$150,251.76       17           70.94       66.2                 300.0                         62.6             32.31
$183,356.69       13           71.13       66.9                 291.7                         67.1             32.06
$130,274.35       17           71.53       62.5                 286.8                         62.7             32.47
$286,285.40        5           69.73       69.4                 308.4                         70.6             32.09
$72,708.05       19           70.79       61.9                 292.1                         56.7             31.50
$99,597.31       13           71.07       64.1                 295.8                         57.2             31.52
$85,557.56        9           71.10       64.1                 290.4                         69.3             31.95
$46,406.25        8           71.24       61.1                 289.9                         65.5             32.31
*GIR: Greens in Regulation

Solutions

Expert Solution

Here i copied all data intoExcel:

A) then go to data analysis-> Regression -> In place Input Y range input vector Earnings/Event -> In place of Input X range input all vector other than Earnings/Event-> In cell of labels tick mark. -> Also tick for residuals,standardies residuals -> Select output range -> Then press ok.

Then we get following output.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.907422179
R Square 0.82341501
Adjusted R Square 0.764553347
Standard Error 29533.55374
Observations 25
ANOVA
df SS MS F Significance F
Regression 6 73209748917 12201624820 13.98898648 6.49787E-06
Residual 18 15700154337 872230796.5
Total 24 88909903254
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1437821.623 1347403.762 1.067105246 0.300028237 -1392968.633 4268611.879 -1392968.633 4268611.879
Events -4747.681755 1287.532815 -3.687425828 0.001685195 -7452.687819 -2042.675692 -7452.687819 -2042.675692
Avg. Score -45049.73715 19510.79217 -2.308965047 0.033023094 -86040.39037 -4059.083927 -86040.39037 -4059.083927
GIR (%)* 22416.76093 4698.689378 4.770853981 0.000152822 12545.18087 32288.34099 12545.18087 32288.34099
Driving Distance -3429.311291 995.8982298 -3.443435472 0.002898633 -5521.615828 -1337.006753 -5521.615828 -1337.006753
Driving Accuracy (%) -5413.9034 1450.334544 -3.732865237 0.001522986 -8460.943204 -2366.863596 -8460.943204 -2366.863596
Putts/Round 57949.81073 23557.912 2.459887393 0.024242869 8456.474262 107443.1472 8456.474262 107443.1472
RESIDUAL OUTPUT
Observation Predicted Earnings/Event Residuals Standard Residuals
1 214353.3044 25140.3756 0.982936408
2 195162.1174 -17912.93735 -0.700358602
3 186200.664 32418.51596 1.267496562
4 154109.3185 32270.76149 1.26171967
5 210720.1049 -1208.354893 -0.047244164
6 155801.2113 26186.07871 1.023821225
7 160886.2832 1649.846847 0.064505581
8 176021.9942 -1487.04422 -0.058140337
9 158059.8278 -22706.12781 -0.887762382
10 234355.2581 -21814.43814 -0.85289917
11 285287.2656 11792.23444 0.461051846
12 162796.8305 6107.619451 0.23879522
13 171275.7761 -35484.1961 -1.387358281
14 184136.2119 -50440.69187 -1.972126164
15 94216.33916 17975.70084 0.702812524
16 251264.6734 -36143.00345 -1.413116278
17 176537.2319 7385.698139 0.288765439
18 149926.8976 324.8624437 0.012701446
19 165663.1729 17693.5171 0.691779726
20 94403.02563 35871.32437 1.402494191
21 248276.4951 38008.90487 1.486069144
22 62891.1652 9816.884801 0.383819782
23 113843.7961 -14246.48611 -0.557007982
24 109411.4995 -23853.93946 -0.93263943
25 83751.35566 -37345.10566 -1.460115975

Thus the regression equation is:

Earnings/Event= (-4747.681755)*Event-(45049.73715)*Avg.score+(22416.76093)*GIR-

(3429.3112)*Driving Distance-(5413.9034)*Driving Accuracy+

(57949.81073)*Putts/Round+1437821.623

B) then go to data analysis-> Regression -> In place Input Y range input vector Avg. Score -> In place of Input X range input all vector other than Avg. Score-> In cell of labels tick mark. -> Also tick for residuals,standardies residuals -> Select output range -> Then press ok.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.857899053
R Square 0.735990785
Adjusted R Square 0.647987713
Standard Error 0.313379912
Observations 25
ANOVA
df SS MS F Significance F
Regression 6 4.927970554 0.821328426 8.363239717 0.000199396
Residual 18 1.767725446 0.098206969
Total 24 6.695696
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 53.49098873 7.640887788 7.000624825 1.55168E-06 37.43807919 69.54389826 37.43807919 69.54389826
Earnings/Event -5.07228E-06 2.19678E-06 -2.308965047 0.033023094 -9.68753E-06 -4.57024E-07 -9.68753E-06 -4.57024E-07
Events -0.015690723 0.017719097 -0.885526109 0.387550073 -0.052917164 0.021535718 -0.052917164 0.021535718
GIR (%)* -0.01239611 0.074970262 -0.165347028 0.870513709 -0.169902786 0.145110566 -0.169902786 0.145110566
Driving Distance -0.012270372 0.013299185 -0.92264086 0.368397139 -0.040210923 0.015670179 -0.040210923 0.015670179
Driving Accuracy (%) -0.02112577 0.019884223 -1.0624388 0.302083597 -0.062900973 0.020649432 -0.062900973 0.020649432
Putts/Round 0.748378832 0.228860567 3.270020874 0.004253522 0.267560623 1.229197041 0.267560623 1.229197041
RESIDUAL OUTPUT
Observation Predicted Avg. Score Residuals Standard Residuals
1 70.09218605 0.277813953 1.023651831
2 69.76174916 -0.331749164 -1.222385111
3 70.12449473 0.105505271 0.388751761
4 70.15513167 0.30486833 1.123338194
5 69.87096118 -0.090961176 -0.335161622
6 70.38658676 -0.046586763 -0.171656695
7 70.28363962 -0.363639618 -1.339890807
8 70.33848736 -0.088487365 -0.32604645
9 70.73297297 -0.092972967 -0.342574399
10 70.00096642 -0.070966418 -0.261487601
11 70.15672982 0.103270184 0.380516212
12 70.34872736 -0.388727365 -1.432330791
13 70.34449886 -0.134498863 -0.495583485
14 70.53358165 -0.003581651 -0.013197191
15 70.17769894 0.412301057 1.519191993
16 70.69483861 -0.474838611 -1.749622037
17 70.8767429 -0.016742903 -0.061692019
18 70.81804045 0.121959546 0.449380281
19 70.52389203 0.60610797 2.233305876
20 71.244834 0.285165996 1.05074166
21 69.83994034 -0.109940344 -0.40509353
22 70.84867676 -0.058676757 -0.216204294
23 70.73816413 0.331835867 1.22270458
24 71.00458164 0.095418358 0.351584849
25 71.61187656 -0.371876563 -1.370241204

The regression equation :

Avg.score=(-0.015690723)*Event-(5.072*10^(-6))*Earnings/Event-(0.01239611)*GIR-

(0.012270372)*Driving Distance-(0.02112577)*Driving Accuracy+

(0.74837883)*Putts/Round+53.49098873

orchestra answered 2 years ago
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