You are an industrial engineer employed by a soft drink beverage bottler to analyze the product delivery and service operations for vending machines. You suspect that the time required by a route deliveryman to load and service machines is related to the number of cases of product delivered. You visit 25 randomly chosen retail outlets having vending machines and observe the in-out delivery time (in minutes) and the volume of product delivered (in cases) for each.

The data are available in a file, Delivery Time,mpj.

1. Plot the data. Briefly comment.

2. Fit a simple linear regression equation.

a. How would you explain what the intercept of the equation is telling you about delivery time and the number of cases delivered?

b. What does the slope of the equation tell you?

3. Note that there were four retail outlets to which 7 cases were delivered, yet the four deliveries did not all require the same amount of time. What feature of the linear regression model is illustrated by this?

4. Estimate the mean number of additional minutes required per one additional case delivered, using a 95% confidence interval.

5. Using a 95% confidence interval, estimate the mean time required to deliver 10 cases.

6. Suppose that your supervisor insists that the intercept of your equation should be zero, since obviously, if the number of cases to be delivered is zero, the time required should also be zero. In order to see if you could do just as well using an equation with a zero intercept, fit this model. Check the box for No Intercept in Stat>Regression>Regression>Options and check the box that constrains the intercept to zero.

Using the General Linear Models Test approach, test the null hypothesis of no significant reduction in error when using full model as compared to the model without the intercept. Show all of your steps.

7. Refer to the Delivery Time data that you analyzed for the first test.

a. Fit a simple linear regression relating delivery time to number of cases delivered. Save the residuals.

i. Is the assumption of normally distributed residuals reasonable here? Are there any outliers to be concerned with?

ii. Divide the deliveries into two groups: one for fewer than 15 cases delivered and the other for 15 or more cases delivered. Are the variances of the residuals the same (apart from sampling variability) in the two groups? Which test(s) are appropriate?

iii. What does the Lack of Fit test tell you?

b. Your team tells you that observation 22 should not be removed. . However, they do agree with you that you should remove observation 9, the delivery of 30 cases. Fit a simple linear regression relating delivery time to number of cases for the remaining deliveries.

i. Is the assumption of normally distributed residuals reasonable here?

ii. Divide the deliveries into two groups: one for fewer than 15 cases delivered and the other for 15 or more cases delivered. Are the variances of the residuals the same (apart from sampling variability) in the two groups?

iii. What does the Lack of Fit test tell you?

iv. What point has been made by this question?