Is it defense or offense that wins football games? Consider the following portio
ID: 3317745 • Letter: I
Question
Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win), the average number of yards gained, and the average number of yards allowed during the 2009 NFL season.
Estimate two simple linear regression models, where Model 1 predicts winning percentage based on Yards Gained and Model 2 uses Yards Allowed. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
Compare the two simple linear regression models.
Estimate a multiple linear regression model, Model 3, that applies both Yards Gained and Yards Allowed to forecast winning percentage. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
Is this model an improvement over the other two models?
Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win), the average number of yards gained, and the average number of yards allowed during the 2009 NFL season.
Explanation / Answer
Here, we have to create three regression models by using excel.
First model: In this model, we have to predict the value of dependent variable percentage win based on the independent variable yards gained.
Second model: In this model, we have to predict the value of dependent variable percentage win based on the independent variable yards allowed.
Third model: In this model, we have to predict the value of dependent variable percentage win based on the independent variables yards gained and yards allowed.
Required three regression models by using excel data analysis are summarised as below:
Model 1
Regression Statistics
Multiple R
0.770117042
R Square
0.593080258
Adjusted R Square
0.579516266
Standard Error
13.04738646
Observations
32
ANOVA
df
SS
MS
F
Significance F
Regression
1
7443.428384
7443.42838
43.724612
2.5524E-07
Residual
30
5107.028804
170.234293
Total
31
12550.45719
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-79.03400602
19.70076488
-4.0117227
0.0003697
-119.2683354
-38.79967667
Yards gained
0.386031242
0.058379379
6.61245883
2.552E-07
0.266804644
0.50525784
Model 2
Regression Statistics
Multiple R
0.465956928
R Square
0.217115859
Adjusted R Square
0.191019721
Standard Error
18.09747118
Observations
32
ANOVA
df
SS
MS
F
Significance F
Regression
1
2724.903293
2724.90329
8.3198464
0.007192478
Residual
30
9825.553895
327.518463
Total
31
12550.45719
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
151.0091806
35.04718665
4.30873902
0.0001624
79.43327686
222.5850843
Yards Allowed
-0.300251074
0.104094292
-2.8844144
0.0071925
-0.51283998
-0.087662169
Model 3
Regression Statistics
Multiple R
0.78502525
R Square
0.616264643
Adjusted R Square
0.589800136
Standard Error
12.8868473
Observations
32
ANOVA
df
SS
MS
F
Significance F
Regression
2
7734.403019
3867.20151
23.286458
9.29954E-07
Residual
29
4816.054169
166.070833
Total
31
12550.45719
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-30.61914754
41.42995617
-0.7390582
0.4658119
-115.3529207
54.11462561
Yards gained
0.350073747
0.063739558
5.49225251
6.464E-06
0.219711715
0.480435778
Yards Allowed
-0.108458353
0.081937389
-1.3236735
0.1959519
-0.276039129
0.059122422
Part a-1
Required table by using above regression outputs is given as below:
Variable
Model 1
Model 2
Intercept
-79.0340
151.0092
Yards Made
0.3860
NA
Yards Allowed
NA
-0.3003
se
13.0474
18.0975
R2
0.5931
0.2171
Adjusted R2
0.5795
0.1910
Part a-2
Model 1 appears to be better model for prediction because value of R square for model 1 is greater than the value of R square for model 2.
Part b-1
Required table by using above excel outputs is given as below:
Variable
Model 3
Intercept
-30.6191
Yards Made
0.3501
Yards Allowed
-0.1085
se
12.8868
R2
0.6163
Adjusted R2
0.5898
Part b-2
This model is an improvement over the other two models.
Answer:
Yes, since Model 3 has a higher adjusted R^2 than models 1 and 2.
(We use adjusted R square instead of R square for comparison of two regression models because adjusted R square is better than R square because adjusted R square increases only if the new term improves the model.)
Regression Statistics
Multiple R
0.770117042
R Square
0.593080258
Adjusted R Square
0.579516266
Standard Error
13.04738646
Observations
32
ANOVA
df
SS
MS
F
Significance F
Regression
1
7443.428384
7443.42838
43.724612
2.5524E-07
Residual
30
5107.028804
170.234293
Total
31
12550.45719
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-79.03400602
19.70076488
-4.0117227
0.0003697
-119.2683354
-38.79967667
Yards gained
0.386031242
0.058379379
6.61245883
2.552E-07
0.266804644
0.50525784
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