Chapter 12.6, Problem 12.55ACB

Going for it on fourth-down in the NFL. Refer to the Chance (Winter 2009) study of fourth-down decisions by coaches in the National Football League (NFL), Exercise 11.69 (p. 655). Recall that statisticians at California State University, Northridge, fit a straight-line model for predicting the number of points scored (y) by a team that has a first-down with a given number of yards (x) from the opposing goal line. A second model fit to data collected on five NFL teams from a recent season was the quadratic regression model, E(y) = β₀ + β₁x + β₂x². The regression yielded the following results: ŷ = 6.13 + .141x − .0009x² , R² = .226.

1. a. If possible, give a practical interpretation of each of the β estimates in the model.
2. b. Give a practical interpretation of the coefficient of determination, R².
3. c. In Exercise 11.63, the coefficient of correlation for the straight-line model was reported as R² = .18. Does this statistic alone indicate that the quadratic model is a better fit than the straight-line model? Explain.
4. d. What test of hypothesis would you conduct to determine if the quadratic model is a better fit than the straight-line model?