Management of a soft-drink bottling company wants to develop 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. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were recorded in the following table:
Customer Number of cases Delivery Time
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
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 65.6
20 298 67.3
a. Develop a regression model to predict delivery time, based on the number of cases delivered.
b. Calculate SSE, SSR, and SST.
c. Predict the delivery time for 150 cases of soft drink.
d. Determine the coefficient of determination and explain its meaning in this problem.
e. 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? Use hypothesis testing to support your decision.