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 11.87

(p. 652). 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, E1y2 = b0 + b1x + b2x2. The regression yielded the following results: yn = 6.13 + .141x - .0009x2, R2

= .226.

a. If possible, give a practical interpretation of each of the b-estimates in the model.

b. Give a practical interpretation of the coefficient of determination, R2.

c. In Exercise 11.87, 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.

d. What test of hypothesis would you conduct to determine if the quadratic model is a better fit than the straight-line model?