STAT5044: Regression and ANOVA
Homework #4
Problem# 1.
A large, national grocery retailer tracks productivity and costs of its facilities closely.
Data were obtained from a single distribution center for a one year period.
Each
data point for each variable represents one week of activity. The variables included
are the number of cases shipped (
X
1
), the indirect costs of the total labor hours as
a percentage (
X
2
), a qualitative predictor called holiday that is coded 1 if the week
has a holiday and o otherwise (
X
3
), and the total labor hours (
Y
)
(a) Fit multiple linear regression model to the data for three predictor variables. State
the estimated regression function. How are
b
1
,
b
2
, and
b
3
interpreted here?
(b) Obtain the residuals and prepare a box plot of the residuals. What information
does this plot provide?
(c) Plot the residuals against
Y
,
X
1
,
X
2
,
X
3
, and
X
1
X
2
on separate graphs. Also
prepare a normal probability plot. Interpret the plots and summarize your findings.
(d) Prepare a time plot of the residuals. Is there any indication that the error terms
are correlated. Discuss. (In this problem, time plot is the “plot(c(1:n), residuals)” in
R, where n is the total sample size)
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 Fall '11
 Staff
 Regression Analysis

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