CHAPTER 13 Simple Linear Regression

534 CHAPTER THIRTEEN Simple Linear Regression
Applying the Concepts
13.25 In Problem 13.5 on page 522, you used reported
magazine newsstand sales to predict audited sales. The data
are stored in the file circulation.xls. Perform a residual analysis
for these data.
a. Determine the adequacy of the fit of the model.
b. Evaluate whether the assumptions of regression have
been seriously violated.
SELF
Test
13.26 In Problem 13.4 on page 522, the marketing
manager used shelf space for pet food to predict
weekly sales. The data are stored in the file
petfood.xls. Perform a residual analysis for these data.
a. Determine the adequacy of the fit of the model.
b. Evaluate whether the assumptions of regression have
been seriously violated.
13.27 In Problem 13.7 on page 523, you used the weight
of mail to predict the number of orders received. Perform a
residual analysis for these data. The data are stored in the
file mail.xls. Based on these results,
a. determine the adequacy of the fit of the model.
b. evaluate whether the assumptions of regression have
been seriously violated.
13.28 In Problem 13.6 on page 522, the owner of a moving
company wanted to predict labor hours based on the
cubic feet moved. Perform a residual analysis for these
data. The data are stored in the file moving.xls. Based on
these results,
a. determine the adequacy of the fit of the model.
b. evaluate whether the assumptions of regression have
been seriously violated.
13.29 In Problem 13.9 on page 523, an agent for a real
estate company wanted to predict the monthly rent for
apartments, based on the size of the apartments. Perform a
residual analysis for these data. The data are stored in the
file rent.xls. Based on these results,
a. determine the adequacy of the fit of the model.
b. evaluate whether the assumptions of regression have
been seriously violated.
13.30 In Problem 13.8 on page 523, you used annual revenues
to predict the value of a baseball franchise. The data
are stored in the file bbrevenue.xls. Perform a residual
analysis for these data. Based on these results,
a. determine the adequacy of the fit of the model.
b. evaluate whether the assumptions of regression have
been seriously violated.
13.31 In Problem 13.10 on page 523, you used hardness
to predict the tensile strength of die-cast aluminum. The
data are stored in the file hardness.xls. Perform a residual
analysis for these data. Based on these results,
a. determine the adequacy of the fit of the model.
b. evaluate whether the assumptions of regression have
been seriously violated.
13.6 MEASURING AUTOCORRELATION:
THE DURBIN-WATSON STATISTIC
One of the basic assumptions of the regression model is the independence of the errors. This
assumption is sometimes violated when data are collected over sequential time periods because
a residual at any one time period may tend to be similar to residuals at adjacent time periods.
This pattern in the residuals is called autocorrelation. When a set of data has substantial autocorrelation,
the validity of a regression model can be in serious doubt.
Residual Plots to Detect Autocorrelation
As mentioned in Section 13.5, one way to detect autocorrelation is to plot the residuals in time
order. If a positive autocorrelation effect is present, there will be clusters of residuals with the
same sign, and you will readily detect an apparent pattern. If negative autocorrelation exists,
residuals will tend to jump back and forth from positive to negative to positive, and so on. This
type of pattern is very rarely seen in regression analysis. Thus, the focus of this section is on
positive autocorrelation. To illustrate positive autocorrelation, consider the following example.
The manager of a package delivery store wants to predict weekly sales, based on the
number of customers making purchases for a period of 15 weeks. In this situation, because
data are collected over a period of 15 consecutive weeks at the same store, you need to
determine whether autocorrelation is present. Table 13.4 presents the data (stored in the file
custsale.xls). Figure 13.14 illustrates Microsoft Excel results for these data.