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 and stored in Delivery:
Customer | Number of Cases | Delivery Time (minutes) | Customer | Number of Cases | Delivery Time (minutes) |
1 | 52 | 32.1 | 11 | 161 | 43.0 |
2 | 64 | 34.8 | 12 | 184 | 49.4 |
3 | 73 | 36.2 | 13 | 202 | 57.2 |
4 | 85 | 37.8 | 14 | 218 | 56.8 |
5 | 95 | 37.8 | 15 | 243 | 60.6 |
6 | 103 | 39.7 | 16 | 254 | 61.2 |
7 | 116 | 38.5 | 17 | 267 | 58.2 |
8 | 121 | 41.9 | 18 | 275 | 63.1 |
9 | 143 | 44.2 | 19 | 287 | 65.6 |
10 | 157 | 47.1 | 20 | 298 | 67.3 |
a. Use the least-squares method to compute the regression coefficients b0 and b1.
b. Interpret the meaning of b0 and b1 in this problem.
c. Predict the delivery time for 150 cases of soft drink.
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, r2, and explain its meaning in this problem.
f. Perform a 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.
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