388 Statistical Methods
d. Create a normal plot of the residu-
als. Does your plot support a conclu-
sion that the residuals are normally
distributed?
e. Save your changes to the workbook
and write a report summarizing your
observations.- The regression performed in the previ-
ous exercise assumed that prices would
change linearly with miles and age. It
could also be the case that the prices
will change instead as a percentage so
that instead of dropping $1000 per year,
the price would drop 10% per year. You
can check this assumption by perform-
ing a logarithm of the used car sales
price.
a. Open the Toyota workbook from the
Chapter09 folder and save it as Toyota
Log Regression.
b. Create a new variable named LogPrice
equal to the log(price) value.
c. Repeat the regression from the last ex-
ercise using the log(price) rather than
price.
d. Does this improve the multiple cor-
relation? Have the p values associated
with the miles and age coeffi cients
become more signifi cant?
e. When log(price) is used as the
dependent variable, the regression
can be interpreted in terms of
percentage drop in Price per year of
age, instead of a fi xed drop per year
of Age when Price is used as the de-
pendent variable. Does it make more
sense to have the price drop by 16.5%
each year or to have the price drop by
$721 per year? In particular, would an
old car lose as much value per year as
it did when it was young?
f. Save your changes to the workbook
and write a report summarizing your
conclusions.
10. The Cars workbook contains data based
on reviews published in Consumer
Reports®, 2003–2008. See Exercise 10
of Chapter 2. The workbook includes
observations from 275 car models on the
variables Price, MPG (miles per
gallon), Cyl (number of cylinders),
Eng size (engine displacement in liters),
Eng type (normal, hybrid, turbo, turbod-
iesel), HP (horsepower), Weight (vehicle
weight in pounds), Time0–60 (time to
accelerate from 0 to 60 miles per hour in
seconds), Date (month of publication),
and Region (United States, Europe, or
Asia). There is an additional variable
Eng type01 that is 1 for hybrids and
diesels and 0 otherwise.
a. Open the Cars workbook from the
Chapter09 folder and save it as Cars
Multiple Regression.
b. Create a correlation matrix (excluding
Spearman’s rank correlation) and a
scatter plot matrix of the seven quan-
titative variables Price, MPG, Cyl, Eng
size, HP, Weight, and Eng type01.
c. Regress MPG on Cyl, Eng size, HP,
Weight, Price, and Eng type01.
d. Note that the regression coeffi cients
for Cyl and Eng size are not signifi -
cant at the .05 level. Compare this to
the p values for these variables in the
correlation matrix. What accounts for
the lack of signifi cance? (Hint: Look at
the correlations among Cyl, Eng size,
HP, Price, and Weight.)
e. Create a scatter plot of the regression
residuals versus the predicted values.
Judging by the scatter plot, do the as-
sumptions of the regression appear to
be violated? Why or why not?
f. Create a new variable, GPM100, that
displays 100 divided by the miles per
gallon. This measures the fuel neces-
sary to go 100 miles. Some statisti-
cians and car magazines use this