Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to 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 delivery file:
Develop a regression model to predict delivery time, based on the number of cases delivered.
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 describe its meaning in this problem.
f. Perform a residual analysis. Is there any evidence of a pattern in the residuals? describe.
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.
i. Construct a 95% prediction interval of the delivery time for a single delivery of 150 cases of soft drink.
j. Construct a 95% confidence interval estimate of the population slope.
k. describe how the results in (a) though (j) can help allocate delivery costs to customers.