CHAPTER 13 Simple Linear Regression

560 CHAPTER THIRTEEN Simple Linear Regression
13.81 Crazy Dave, a well-known baseball analyst, would
like to study various team statistics for the 2005 baseball
season to determine which variables might be useful in predicting
the number of wins achieved by teams during the
season. He has decided to begin by using a team’s earned
run average (ERA), a measure of pitching performance, to
predict the number of wins. The data for the 30 Major
League Baseball teams are in the file bb2005.xls.
(Hint: First, determine which are the independent and
dependent variables.)
a. Assuming a linear relationship, use the least-squares
method to compute the regression coefficients b 0
and b 1
.
b. Interpret the meaning of the Y intercept, b 0
, and the
slope, b 1
, in this problem.
c. Use the prediction line developed in (a) to predict the
number of wins for a team with an ERA of 4.50.
d. Compute the coefficient of determination, r 2 , and interpret
its meaning.
e. Perform a residual analysis on your results and determine
the adequacy of the fit of the model.
f. At the 0.05 level of significance, is there evidence of a
linear relationship between the number of wins and
the ERA?
g. Construct a 95% confidence interval estimate of the
mean number of wins expected for teams with an ERA
of 4.50.
h. Construct a 95% prediction interval of the number of
wins for an individual team that has an ERA of 4.50.
i. Construct a 95% confidence interval estimate of the
slope.
j. The 30 teams constitute a population. In order to use statistical
inference, as in (f) through (i), the data must be
assumed to represent a random sample. What “population”
would this sample be drawing conclusions about?
k. What other independent variables might you consider
for inclusion in the model?
13.82 College football players trying out for the NFL are
given the Wonderlic standardized intelligence test. The data
in the file wonderlic.xls contains the average Wonderlic
scores of football players trying out for the NFL and the
graduation rates for football players at selected schools
(extracted from S. Walker, “The NFL’s Smartest Team,” The
Wall Street Journal, September 30, 2005, pp. W1, W10).
You plan to develop a regression model to predict the
Wonderlic scores for football players trying out for the
NFL, based on the graduation rate of the school they
attended.
a. Assuming a linear relationship, use the least-squares
method to compute the regression coefficients b 0
and b 1
.
b. Interpret the meaning of the Y intercept, b 0
, and the
slope, b 1
, in this problem.
c. Use the prediction line developed in (a) to predict the
Wonderlic score for football players trying out for the
NFL from a school that has a graduation rate of 50%.
d. Compute the coefficient of determination, r 2 , and interpret
its meaning.
e. Perform a residual analysis on your results and determine
the adequacy of the fit of the model.
f. At the 0.05 level of significance, is there evidence of a
linear relationship between the Wonderlic score for a
football player trying out for the NFL from a school and
the school’s graduation rate?
g. Construct a 95% confidence interval estimate of the
mean Wonderlic score for football players trying out for
the NFL from a school that has a graduation rate of 50%.
h. Construct a 95% prediction interval of the Wonderlic
score for a football player trying out for the NFL from a
school that has a graduation rate of 50%.
i. Construct a 95% confidence interval estimate of the
slope.
13.83 College basketball is big business, with coaches’
salaries, revenues, and expenses in millions of dollars.
The data in the file colleges-basketball.xls contains the
coaches’ salaries and revenues for college basketball
at selected schools in a recent year (extracted from
R. Adams, “Pay for Playoffs,” The Wall Street Journal,
March 11–12, 2006, pp. P1, P8). You plan to develop a
regression model to predict a coach’s salary based on
revenue.
a. Assuming a linear relationship, use the least-squares
method to compute the regression coefficients b 0
and b 1
.
b. Interpret the meaning of the Y intercept, b 0
, and the
slope, b 1
, in this problem.
c. Use the prediction line developed in (a) to predict
the coach’s salary for a school that has revenue of
$7 million.
d. Compute the coefficient of determination, r 2 , and interpret
its meaning.
e. Perform a residual analysis on your results and determine
the adequacy of the fit of the model.
f. At the 0.05 level of significance, is there evidence of a
linear relationship between the coach’s salary for a
school and revenue?
g. Construct a 95% confidence interval estimate of the
mean salary of coaches at schools that have revenue of
$7 million.
h. Construct a 95% prediction interval of the coach’s salary
for a school that has revenue of $7 million.
i. Construct a 95% confidence interval estimate of the
slope.
13.84 During the fall harvest season in the United States,
pumpkins are sold in large quantities at farm stands. Often,
instead of weighing the pumpkins prior to sale, the farm
stand operator will just place the pumpkin in the appropriate
circular cutout on the counter. When asked why this
was done, one farmer replied, “I can tell the weight of the
pumpkin from its circumference.” To determine whether
this was really true, a sample of 23 pumpkins were mea-