Management of a soft-drink bottling company wished to develop a method for allocating delivery costs to customers. Although one aspect of cost clearly relates to travel time within a particular route, another type of cost reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 customers was selected from routes within a territory and the delivery time and the number of cases delivered were measured with the following results:
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
Assuming that we wanted to develop a model to predict delivery time based on the number of cases delivered:
(a) Set up a scatter diagram.
(b) Use the least-squares method to find the regression coefficients and .
(c) State the regression equation.
(d) Interpret the meaning of and in this problem.
(e) Predict the average delivery time for a customer who is receiving 150 cases of soft drink.
(f) Would it be appropriate to use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why?
(g) Compute the coefficient of determination and explain its meaning in this problem.
(h) Compute the coefficient of correlation.
(i) Compute the standard error of the estimate.
(j) Perform a residual analysis using either the residuals or the Studentized residuals. Is there any evidence of a pattern in the residuals? Explain.
(k) At the .05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?
(l) Set up a 95% confidence interval estimate of the average delivery time for customers that receive 150 cases of soft drink.
(m) Set up a 95% prediction interval estimate of the delivery time for an individual customer who is receiving 150 cases of soft drink.
(n) Set up a 95% confidence interval estimate of the population slope.