Is it defense or offense that wins football games? Consider the following portio
ID: 3368888 • 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
By using MINITAB,
Regression Analysis: Win versus yards gained
Model Summary
S R-sq R-sq(adj) R-sq(pred)
13.0474 59.31% 57.95% 53.72%
Coefficients
Term Coef SE Coef T-Value P-Value
Constant -79.0 19.7 -4.01 0.000
yards gained 0.3860 0.0584 6.61 0.000
Regression Analysis: Win versus yards allowed
Model Summary
S R-sq R-sq(adj) R-sq(pred)
18.0975 21.71% 19.10% 11.84%
Coefficients
Term Coef SE Coef T-Value P-Value
Constant 151.0 35.0 4.31 0.000
yards allowed -0.300 0.104 -2.88 0.007
a 1] variable Model 1 Model 2
Intercept -79.00 151.00
yards gained 0.3860
yards allowed -0.3000
SE 13.0407 18.0975
R^2 0.5931 0.2171
Adj R^2 0.5795 0.1910
a2] Model 1 appears to be the better model for prediction.
b1] Regression Analysis: Win versus yards gained, yards allowed
Model 3 Summary
S R-sq R-sq(adj) R-sq(pred)
12.8868 61.63% 58.98% 53.48%
Coefficients
Term Coef SE Coef T-Value P-Value
Constant -30.6 41.4 -0.74 0.466
yards gained 0.3501 0.0637 5.49 0.000
yards allowed -0.1085 0.0819 -1.32 0.196
b2] Yes since Model 3 has a higher adjusted R2 than Models 1 and 2.
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