Chapter 8 Regression and Correlation 347
if we used foods that cover a wider
range of fat-content values?
e. Save your changes to the workbook
and write a report summarizing your
observations.
- You’ve been given a workbook contain-
ing the ages and prices of used Mustangs
from Cars.com in 2002. Perform the fol-
lowing analysis:
a. Open the Mustang workbook from
the Chapter08 folder and save it as
Mustang Regression Analysis.
b. Compute the Pearson and Spearman
correlations (and p values) between
age and price.
c. Plot price against age. Does this scat-
ter plot cause you any concern about
the validity of the correlations?
d. How do the correlations change if you
concentrate only on cars that are less
than 20 years old?
e. Excluding the old classic cars (older
than 19 years), perform a regression of
price against age and fi nd the drop in
price per year of age.
f. Do you see any problems in the diag-
nostic plots of the residuals?
g. Save your changes to the workbook
and write a report summarizing your
observations.
- Return to the Calculus data set you ex-
amined in this chapter and perform the
following analysis:
a. Open the Calculus workbook from
the Chapter08 folder and save it as
Calculus Regression Analysis.
b. Regress Calc on Alg Place and obtain
a 95% confi dence interval for the
slope.
c. Interpret the slope in terms of the in-
crease in fi nal grade when the place-
ment score increases by 1 point.
d. Do the residuals give you any cause
for concern about the validity of the
model?
e. Save your changes to the workbook
and write a report summarizing your
observations.
- The Booth workbook gives total assets
and net income for 45 of the largest
American U.S. banks in 1973. Open
the workbook and perform the fol-
lowing analysis of this historical eco-
nomic data set:
a. Open the Booth workbook from the
Chapter08 folder and save it as Booth
Regression Analysis.
b. Plot net income against total assets
and notice that the points tend to
bunch up toward the lower left, with
just a few big banks dominating the
upper part of the graph. Add a linear
trend line to the plot.
c. Regress net income against total as-
sets and plot the standard residuals
against the predictor values. (The
standardized residuals appear with
the regression output when you select
the Standardized Residuals check box
in the Regression dialog box.)
d. Given that the residuals tend to be
bigger for the big banks, you should
be concerned about the assump-
tion of constant variance. Try taking
logs of both variables. Now repeat
the plot of one against the other, re-
peat the regression, and again look
at the plot of the residuals against
the predicted values. Does the
transformation help the relation-
ship? Is there now less reason to be
concerned about the assumptions?
Notice that some banks have strongly
positive residuals, indicating good
performance, and some banks have
strongly negative residuals, indicat-
ing below-par performance. Indeed,
bank 20, Franklin National Bank, has
the second most negative residual
and failed the following year. Booth
(1985) suggests that regression is a
