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:  = 6.13 + .141x - .0009x2, R2 = .226.
a. If possible, give a practical interpretation of each of the β estimates in the model.
b. Give a practical interpretation of the coefficient of determination, R2.
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.
d. What test of hypothesis would you conduct to determine if the quadratic model is a better fit than the straight-line model?
For Information: Refer to the Chance (Winter 2009) study of fourth-down decisions by coaches in the National Football League (NFL), Exercise 11.63.