Management of a soft-drink bottling company has the business objective of developing a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. To begin, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were organized in the following table; Delivery Number Time Customer of Cases (minutes) Customer of Cases (minutes) 1 2 3 4 5 6 7 Delivery Number Time 8 9 10 52 64 73 85 37.8 37.8 95 103 116 32.1 34.8 36.2 121 143 157 39.7 38.5 41.9 44.2 47.1 11 12 13 14 15 16 17 18 19 20 161 184 202 218 243 254 267 275 287 298 43.0 49.4 57.2 56.8 60.6 61.2 58.2 63.1 65.6 67.3 a. Use the least-squares method to compute the regression coefficients 60 and bl. b. Interpret the meaning of bo and b₁ in this problem. c. Predict the mean delivery time for 150 cases of soft drink.
Management of a soft-drink bottling company has the business objective of developing a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. To begin, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were organized in the following table; Delivery Number Time Customer of Cases (minutes) Customer of Cases (minutes) 1 2 3 4 5 6 7 Delivery Number Time 8 9 10 52 64 73 85 37.8 37.8 95 103 116 32.1 34.8 36.2 121 143 157 39.7 38.5 41.9 44.2 47.1 11 12 13 14 15 16 17 18 19 20 161 184 202 218 243 254 267 275 287 298 43.0 49.4 57.2 56.8 60.6 61.2 58.2 63.1 65.6 67.3 a. Use the least-squares method to compute the regression coefficients 60 and bl. b. Interpret the meaning of bo and b₁ in this problem. c. Predict the mean delivery time for 150 cases of soft drink.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:d. Should you use the model to predict the delivery time for a customer who is receiving 500
cases of soft drink? Why or why not?
e. Determine the coefficient of determination, r 2, and explain its meaning in this problem.
f. At the 0.05 level of significance, is there evidence of a linear relationship between
delivery time and the number of cases delivered?
g. Construct a 95% confidence interval estimate of the mean delivery time for 150 cases of
soft drink and a 95% prediction interval of the delivery time for a single delivery of 150
cases of soft drink.
h. What conclusions can you reach from (a) through (h) about the relationship between the
number of cases and delivery time?
Transcribed Image Text:QUESTION 1
Management of a soft-drink bottling company has the business objective of developing a method
for allocating delivery costs to customers. Although one cost clearly relates to travel time within
a particular route, another variable cost reflects the time required to unload the cases of soft drink
at the delivery point. To begin, management decided to develop a regression model to predict
delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory
was selected. The delivery times and the number of cases delivered were organized in the
following table;
Delivery
Number Time
Customer of Cases (minutes) Customer of Cases (minutes)
1
2
3
4
5
6
Delivery
Number Time
7
8
9
10
52
64
73
85
95
103
116
121
143
157
32.1
34.8
36.2
37.8
37.8
39.7
38.5
41.9
44.2
47.1
11
12
13
14
15
16
17
18
19
20
161
184
202
218
243
254
267
275
287
298
43.0
49.4
57.2
56.8
60.6
61.2
58.2
63.1
65.6
67.3
a. Use the least-squares method to compute the regression coefficients b0 and bl.
b. Interpret the meaning of bo and be in this problem.
c. Predict the mean delivery time for 150 cases of soft drink.
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VIEWStep 2: Calculate the regression coefficients b0 and b1using least square method and interpret their meaning
VIEWStep 3: Determine the coefficient of determination and check the significance of the linear relationship
VIEWStep 4: Construct 95% confidence interval estimate and prediction interval of the delivery time for x=150
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