Stat 301
Lab 6: Due October 21
Fall 2013
1. What is the relationship between the distance walked and the time it takes to deliver soft drinks to
vending machines? An industrial engineer collected 20 observations on the delivery time (in
minutes), number of cases delivered and distance walked (in feet). Delivery time includes time to
unload the cases from the delivery truck, walk to the machine and load the machine with the soft
drinks. The data are given below.
Cases
7
3
3
4
6
7
2
7
5
10
Distance
560
220
340
80
150
330
110
210
605
215
Time
16.68
11.50
12.03
14.88
13.75
18.11
8.00
17.83
21.50
21.00
Cases
4
6
9
6
7
3
10
9
8
4
Distance
255
462
448
200
132
36
140
450
635
150
Time
13.50
19.75
24.00
15.35
19.00
9.50
17.90
18.75
19.83
10.75
a) Fit a simple linear model with Time as your response variable and Distance as your explanatory
variable. Use the JMP output to answer the following questions. Be sure to attach the JMP to
your assignment.
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What is the least squares regression equation for this model?
Predict the delivery time for 6 cases and 200 feet.
Give an interpretation of the estimated slope within the context of the problem.
Give and interpretation of the estimated intercept within the context of the problem.
How much of the variation in Time is explained by the linear relationship with Distance?
Is Distance a statistically significant variable for predicting Time? Support your answer
statistically.
b) Fit a multiple regression model with Time as your response variable and Distance and Cases as
explanatory variables. Use the JMP output to answer the following questions. Be sure to attach
the JMP to your assignment.
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What is the least squares regression equation for this model?
Predict the delivery time for 6 cases and 200 feet. How does this compare to the prediction
in a)?
Give an interpretation of the estimated slope for Distance within the context of the problem.
Give an interpretation of the estimated slope for Cases within the context of the problem.
Why is there not an interpretation of the estimated intercept within the context of the
problem for this model?
Does Cases add significantly to the model with Distance? Support your answer statistically.
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c) Fit a multiple regression model with Time as your response variable and Distance, Cases, and
Distance*Cases as explanatory variables. Be careful! Remember to turn off the Center
Polynomial option before you fit the model. Use the JMP output to answer the following
questions. Be sure to attach the JMP to your assignment.
•
•
•
•
•
What is the least squares regression equation for this model?
Predict the delivery time for 6 cases and 200 feet. How does this compare to the prediction
in b)?
Does Distance*Cases add significantly to the model with Distance and Cases? Support your
answer statistically.
What does the result above tell you about interaction between Distance and Cases?
What does the result above tell you about the relationship between Time and Distance as you
change the number of delivered?
d) Fit a multiple regression model with Time as your response variable and Distance, Cases, and
(Distance – Mean Distance)*(Cases – Mean Cases) i.e. leave the Center Polynomial option
turned on. Use the JMP output to answer the following questions. Be sure to attach the JMP to
your assignment.
•
•
•
•
What is the least squares regression equation for this model?
Predict the delivery time for 6 cases and 200 feet. How does this compare to the prediction
in c)?
Does (Distance – Mean Distance)*(Cases – Mean Cases) add significantly to the model with
Distance and Cases? Support your answer statistically.
How does this compare to your results in c) about the interaction between Distance and
Cases?
e) For the “best” model for these data, compute the residuals. Plot the residuals versus Distance.
Plot the residuals versus Cases. Analyze the distribution of the residuals. Use the JMP output to
answer the following questions. Be sure to attach the JMP to your assignment.
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What do the plots of residuals versus the explanatory variables tell you about the adequacy
of the model you have chosen as “best”? What do they tell you about the equal standard
deviation condition? Be sure to support your answers by referring to the plots.
What does the analysis of the distribution of residuals tell you about the conditions of
identically and normally distributed residuals? Be sure to support your answers by referring
to the analysis.
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