Chapter 11.5, Problem 11.69ACB

Going for it on fourth-down in the NFL Each week coaches in the National Football League (NFL) face a decision during the game. On fourth-down, should the team punt the ball or go for a first-down? To aid in the decision-making process, statisticians developed a regression model for predicting the number of points scored (y) by a team that has a firstdown with a given number of yards (x) from the opposing goal line (Chance, Winter 2009). One of the models fit to data collected on five NFL teams from a recent season was the simple linear regression model, E (y) = β₀ + β₁x. The regression yielded the following results: $\hat{y}=4.42-048x,r^2=\mathrm{.18.}$

a. Give a practical interpretation of the coefficient of determination, r².

b. Compute the value of the coefficient of correlation, r, from the value of r². Is the value of r positive or negative? Why?