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 at California State University, Northridge, developed a regression 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 (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, E1y2 = b0 + b1x. The regression yielded the following results: ny = 4.42 -.048 x, r2

= .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?