Howie’s Bakery is one of the most popular bakeries in town, and the favorite at Howie’s is French bread. Each day of the week, Howie’s bakes a number of loaves of French bread, more or less according to a daily schedule. To maintain its fine reputation, Howie’s gives away to charity any loaves not sold on the day they are baked. Although this occurs frequently, it is also common for Howie’s to run out of French bread on any given day—more demand than supply. In this case, no extra loaves are baked that day; the customers have to go elsewhere for their French bread. Although French bread at Howie’s is always popular, Howie’s stimulates demand by running occasional 10% off sales.
Howie’s has collected data for 20 consecutive weeks, 140 days in all. These data are listed in the file Howies Bakery.xlsx. The variables are Day (Monday–Sunday), Supply (number of loaves baked that day), OnSale (whether French bread is on sale that day), and Demand (loaves actually sold that day). Howie’s would like you to see whether regression can be used successfully to estimate Demand from the other data in the file. Howie reasons that if these other variables can be used to predict Demand, then he might be able to determine his daily supply (number of loaves to bake) in a more cost-effective way.
How successful is regression with these data? Is Howie correct that regression can help him determine his daily supply? Is any information missing that would be useful? How would you obtain it? How would you use it? Is this extra information really necessary?