In the Pronto Pizza case, visited previously in Chapter 10, the company was facing stiff competition in its pizza delivery service, and the owners were particularly concerned about being able to provide call-in customers with a guarantee as to how quickly their pizza would arrive. Manager Tony Scapelli had collected a month’s worth of data that included such variables as preparation time, wait time, travel time, and delivery distance. In this chapter, we will use simple linear regression and correlation to help Tony examine the number of travel minutes required for a delivery versus the number of miles involved in making the delivery. Using the PRONTO data file and the variables TRAVEL_TIME and DISTANCE:
1. Determine the coefficient of correlation between TRAVEL_TIME and DISTANCE. Is the sign of the coefficient of correlation positive or negative? Is this the sign you would expect to be associated with this coefficient? What percentage of the variation in the driving time to deliver a pizza is explained by the number of miles for the trip?
2. Determine the best-fit linear regression equation for estimating TRAVEL_TIME on the basis of DISTANCE. Identify and interpret the slope of the equation in the context of this situation.
3. What would be the estimated time of travel for a pizza delivery that involved a 5-mile trip?
4. Determine and interpret the 95% confidence and prediction intervals associated with a pizza delivery that involved a 5-mile trip.
5. Were there any deliveries for which the time for travel was “flagged” by your computer statistical package as being unusually long or short compared to the time that would have been estimated by the equation? What managerial implications could this have, especially considering the possibility of litigation if a delivery person were to be involved in an accident while trying to meet a delivery guarantee set by the company?