Chapter 13, Problem 74PS

Management of a soft-drink botting 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.

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 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, $r^2,$ 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.

i. What conclusions can you reach from (a) through (h) about the relationship between the number of cases and delivery time?