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)=β0+β1x. The regression yielded the following results: y=4.83−0.41x, r2=0.19.Complete parts a and b below.

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

A.Sample variations in the numbers of yards to the opposing goal line explain 19% of the sample variation in the numbers of points scored using the least squares line.

B.There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.19 is near to zero.

C.There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.19 is positive.

D.Sample variations in the numbers of yards to the opposing goal line explain 81%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 r2. Is the value of r positive ornegative? 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 β1 is positive.

B.The coefficient of correlation, r=_______, is negative because the estimator of β1 is negative.

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

D.The coefficient of correlation,r=________,is negative because the estimator of β1 is positive.

Answer #1

Given regression equation is y=4.83−0.41x and
r^{2} = 0.19.

a) given coefficient of determination r2 = 0.19 which represents the model only explains the 19% variability of the data. In the above problem the answer is option A.

b) coefficient of correlation is the square root of coefficient of determination.

r = = = +-0.436

We have to consider negative sign because the slope is negative which says increase in x represents the reduction in y. Option B.

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...

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...

It is thought that basketball teams that make too many fouls in
a game tend to lose the game even if they otherwise play well. Let
x be the number of fouls more than (i.e., over and above)
the opposing team. Let y be the percentage of times the
team with the larger number of fouls wins the game.
x
0
4
5
6
y
51
42
33
26
Complete parts (a) through (e), given Σx = 15,
Σy =...

It is thought that basketball teams that make too many fouls in
a game tend to lose the game even if they otherwise play well. Let
x be the number of fouls more than (i.e., over and above) the
opposing team. Let y be the percentage of times the team with the
larger number of fouls wins the game. x 0 2 5 6 y 48 43 33 26
Complete parts (a) through (e), given Σx = 13, Σy =...

It is thought that basketball teams that make too many fouls in
a game tend to lose the game even if they otherwise play well. Let
x be the number of fouls more than (i.e., over and above) the
opposing team. Let y be the percentage of times the team with the
larger number of fouls wins the game. x 1 2 5 6 y 51 45 33 26
Complete parts (a) through (e), given Σx = 14, Σy =...

It is thought that basketball teams that make too many fouls in
a game tend to lose the game even if they otherwise play well. Let
x be the number of fouls more than (i.e., over and above) the
opposing team. Let y be the percentage of times the team with the
larger number of fouls wins the game. x 1 4 5 6 y 51 45 33 26
Complete parts (a) through (e), given Σx = 16, Σy =...

1. For a pair of sample x- and y-values, what is the difference
between the observed value of y and the predicted value of y? a) An
outlier b) The explanatory variable c) A residual d) The response
variable
2. Which of the following statements is false:
a) The correlation coefficient is unitless. b) A correlation
coefficient of 0.62 suggests a stronger correlation than a
correlation coefficient of -0.82. c) The correlation coefficient,
r, is always between -1 and 1....

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