Management of a soft-drink bottling company has the business objectives 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 drunk at the delivery point. To begins, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample 20 deliveries within a territory was selected. The delivery times and the number cases delivered were organized in the following table and stored in Delivery.
Customer Number of Cases Delivery Time (mins)
1 52 32.1
2 64 34.8
3 73 36.2
4 85 37.8
5 95 37.8
6 103 39.7
7 116 38.5
8 121 41.9
9 143 44.2
10 157 47.1
11 161 43.0
12 184 49.4
13 202 57.2
14 218 56.8
15 243 60.6
16 254 61.2
17 267 58.2
18 275 63.1
19 287 65.5
20 298 67.3
A. Use the least- Squares method to compute the regression coefficients b(0) and b(1).
B. Interpret the meaning of b(0) and b(1) in this problem.
C. Predict the mean delivery time for 150 cases of soft drinks.
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. perform a residual analysis. Is there any evidence of a pattern in the residual analysis. Is there any evidence of a pattern in the residuals? Explain
G. At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?
H. 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.
I. What conclusions can you reach from (a)-(h) about the relationship between the number of cases and delivery time?