Each week coaches in a certain football league face a decision during the game.

Question

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) = 0 + 1x. The regression yielded the following results. Y = 3.48-0.42x r2 = 0.17

Give a practical interpretation of the coefficient of determination, r². Choose the correct answer below.

A. There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.16 is near to zero.

B. Sample variations in the numbers of yards to the opposing goal line explain 16% of the sample variation in the numbers of points scored using the least squares line.

C. There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.16 is positive.

D. Sample variations in the numbers of yards to the opposing goal line explain 84% of the sample variation in the numbers of points scored using the least squares line.

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

Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.)

A. The coefficient of correlation,

r=__________ , is positive because the estimator of 1 is positive.

B. The coefficient of correlation,

r=___________ , is negative because the estimator of 1 is positive.

C. The coefficient of correlation,

r=____________ , is negative because the estimator of 1 is negative.

D. The coefficient of correlation,

r=___________ , is positive because the estimator of 1 is negative.

Explanation / Answer

Y = 3.48-0.42x

r2 = 0.17 , r2 basically tells that how much variation in dependent variable is explained by the independent variable

Hence the correct answer is B. Sample variations in the numbers of yards to the opposing goal line explain 16% of the sample variation in the numbers of points scored using the least squares line.

r can be calculated as

sqrt(r2)

sqrt(0.17)
0.412

however we notice that the slope is negative hence the correlation has to be negative , so the value is
-0.412

r = -0.412 is negative because the estimator of 1 is negative.

Hence C

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.