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Each week coaches in a certain football league 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 a particular university 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. One of the models fit to data collected on five league teams from a recent season was the simple linear regression model, E(y) = beta0 + beta1*x

The regression yielded the following results: y^ = 4.95 - 0.54x r squared equals 0.17
.
Complete parts a and b below.

Give a practical interpretation of the coefficient of determination, r squared. Choose the correct answer below.

  There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.17 is near to zero.
B. There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.17 is positive.
C. Sample variations in the numbers of yards to the opposing goal line explain 17 % of the sample variation in the numbers of points scored using the least squares line.
Your answer is correct.
D.Sample variations in the numbers of yards to the opposing goal line explain 83 % of the sample variation in the numbers of points scored using the least squares line.

 

 

a ) Sample variations in the numbers of yards to the opposing goal line explain 17​% of the sample variation in the numbers of points scored using the least squares line.

b) The coefficient of correlation, r= -0.412, is negative because the estimator pf b1 is negative

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