QUESTION A5: Unloading Times

One of the critical factors that determine the success of a catalogue store chain is the availability of products that consumers want to buy. If a store is sold out, future sales to that customer are less likely. Because of this, stores are regularly resupplied by delivery trucks operating from a central warehouse. In an analysis of a chain’s operations, the general manager wanted to determine the factors that affected how long it took to unload delivery trucks. A random sample of 50 deliveries to one store was observed. The times (in minutes) to unload the truck, the total number of boxes and the total weight (in hundreds of kilograms) of the boxes were recorded. The data are recorded in file, TIMES.xlsx.

a Estimate the multiple regression equation. Interpret the coefficients estimates and their signs.

Further to analyzing the factors that affect the amount of time taken to unload a truck, the manager realised that another variable may affect unloading time: the time of day. He recorded the following codes: 1 = morning; 2 = early afternoon; 3 = late afternoon.

b Run a regression using the codes for time of day. What is the problem associated with this model specification?

c Create dummy variables to represent time of day. Perform a regression analysis with these new variables.

d Compare the results of the models in parts a and c. Which model fits better? Why?

e Does time of day affect the time taken to unload?

f Produce predictions for the amount of time needed to unload a truck with 100 boxes of total weight 5000kg during the three times of day. 

TIMES