Question

O.6

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)=β0+β1x. The regression yielded the following results: y=4.76−0.42x, r squared = 0.18

**Complete parts a and b below.**

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

Choose the correct answer below.

A. There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.18 is positive.

B. Sample variations in the numbers of yards to the opposing goal line explain 82% of the sample variation in the numbers of points scored using the least squares line.

C. Sample variations in the numbers of yards to the opposing goal line explain 18% of the sample variation in the numbers of points scored using the least squares line.

D. There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.18 is near to zero.

**b.** Compute the value of the coefficient of
correlation, r, from the value of r squared. Is the value of r
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 negative because the estimator of 1β1 is positive.

B. The coefficient of correlation, r = -------, is positive because the estimator of 1β1 is positive.

C. The coefficient of correlation, r = -----, is positive because the estimator of 1β1 is negative.

D. The coefficient of correlation, r = --------, is negative because the estimator of 1β1 is negative.

Answer #1

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

r sq=0.18

18% variation in number of points scored (y) is explained by number of yards (x) from the opposing goal line.

**C. Sample variations in the numbers of yards to the
opposing goal line explain 18% 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 r squared. Is the value of r
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.)

r sq=0.18

r=sqrt(0.18)=0.424

slope is negative

so r is negative

option d

**D. The coefficient of correlation, r = 0.424, is
negative because the estimator of 1β1 is negative.**

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...

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...

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1 points
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