Going for it on fourth down in the NFL. Each week coaches in the National Football League...

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, E(y) = β0 + β1x. The regression yielded the following results:  r2 = .18 .

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

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