Question

The National Football League (NFL) records a variety of performance data for individuals and teams. Some of the year-end performance data for the 2005 season are contained in the table below. Each row of the data set corresponds to an NFL team and the teams are ranked by winning percentage. (32 teams in total) Partial dataset (first 5 teams): NetDiff NFC Team Indianapolis Denver Seattle jacksonville Carolina Division AFC SOUTH AFC WEST NFC WEST AFC SOUTH NFC SOUTH WinPet 0.875 0.813 0.813 0.750 0.688 Defyds/G 307.1 312.9 316.8 290.9 282.6 Offyds/G 362.4 360.4 369.7 321.8 309.3 FGPct 88.5 75.0 72.0 76.7 76.5 0 20 101 110 Descriptions of the variables Variables Description WinPct Percentage of games won Defyds/G Average number of yards per game given up on defense Offyds/G Average number of yards per game gained on offense FGPct Percentage of field goals made NetDiff Difference in Takeaways made by the team's defense and Giveaways made by the team's offense NFC A dummy variable; 1 if the team is in the NFC, if the team is in the AFC We want to build a model to predict WinPet. Model 1: WinPet (y) vs Defyds/G (X1), of Yds/G(X2), and FGPct (x3) Analysis of Variance DE 3 Source Regression Error Total P-value 0.020 Adj SS 0.405 0.986 1.392 Adj MS F-Value 0.1353 .84 0.035 28 31 Model Summary S R -sg 0.187691 29.13% R-sq(adj) 21.53% R-sq (pred) 4.54% T-Value P-value 1.90 0.068 Coefficients Term Coef Constant 1.183 De fyds/G -0.00325 Offyds/G 0.001591 FGPct -0.00195 SE Coef 0.622 0.00140 0.000866 0.00508 1.84 -0.38 0.077 0.704 Regression Equation WinPct = 1.183 -0.00325 Defyds/G + 0.001591 Offyds/G - 0.00195 FGPct

Answer 1

14)

When we fit a multiple regression model, we use the p-value in the ANOVA table to determine whether the model, as a whole, is significant. A natural next question to ask is which predictors, among a larger set of all potential predictors, are important. We could use the individual p-values and refit the model with only significant terms. But, remember that the p-values are adjusted for the other terms in the model. So, picking out the subset of significant predictors can be somewhat challenging. This task of identifying the best subset of predictors to include in the model, among all possible subsets of predictors, is referred to as variable selection.

we might choose the model that has the highest RSquare Adjusted or the lowest Root Mean Square Error. If both Square, Adjusted and Root Mean Square Error are improved over the model then it is the best to model.

Therefore, the p-value is reduced, R-square and Adj. R-square is improved in the second model so we conclude that there is a significant contribution form the Netdiff but not NFC because the p-value is not significant.

Critical Value:

The critical value for t-distribution to check the significance of predictors we have

t(0.05) at 26 df = 1.706

If the t-statistic of the respective variable is greater than the predictor is significant.

Conclusion:

The variables which have t-statistic less than 1.706 are OffYds/G, FGPct and NFC are not significantly contributing the second model.