STAT3503 Lab 4 Due Nov. 3
(This is Problem 6.9 and related questions from the text.)
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 (X1), the indirect costs of the
total labour hours as a percentage (X2), a qualitative predictor called holiday that is coded 1 if the week has
a holiday and 0 otherwise (X3), and the total labour hours (Y).
a) The cases are given in consecutive weeks. Do a time plot for each predictor variable. What do the plots
show?
b) Obtain the scatterplot matrix and the correlation matrix. What information do you obtain from these
diagnostic aids?
c) Fit the model involving X1, X2 and X3 (each as a linear term) to the data. Give the resulting estimated
regression model. Interpret b0, b1, b2 and b3.
d) Plot the residuals against predicted Y, X1, X2, X3, X1*X2, X1*X3, X2*X3 on separate graphs. Also do
a normal probability plot of the residual. Interpret each plot and summarize your findings.
e) Divide the 52 cases into two groups, placing the 2 cases with the smallest fitted values into group 1 and
the other 26 cases into group 2. Conduct the Brown-Forsythe test for constancy of the error variance using
99% confidence.
f) Test whether there is a regression relation, using 95% confidence.
g) Estimate jointly, using Bonferroni, with family confidence level of 95%, the regression coefficients for
X1 and X3.
h) What is the value of the coefficient of multiple determination and what does it mean?
i) Management wants simultaneous interval estimates of the total labour hours for the following five typical
weekly shipments:
Obs. #
1
2
3
4
5
X1
302,000
245,000
280,000
350,000
295,000
X2
7.2
7.4
6.9
7.0
6.7
X3
0
0
0
0
1
j) Four separate shipments with the following characteristics must be processed next month:
Obs.#
1
2
3
4
X1
230,000
250,000
280,000
340,000
X2
7.5
7.3
7.1
6.9
X3
0
0
0
0
Develop the needed results if management wants 95% family confidence in these predictions.
k) Three new shipments are to be received, each with X1=282,000, X2=7.1 and X3=0. Give the 95%
prediction interval for the average handling time for these new shipments. Then convert the interval
obtained into a 95% prediction interval for the total labour hours for he these shipments.
l) For the following situations, determine if you should use your model:
X1
400,000
400,000
X2
7.2
9.9
X3
0
0