A national motel chain has a model for the operating margin of its franchises. The operating margin is defined to be the ratio of net profit to total revenue (as a percentage). The company plans to use this model to help it identify profitable sites to locate new hotels. The response in the model is the operating margin, and the explanatory variables are the number of available hotel rooms currently within 3 miles of the site (Rooms) and the square feet of offce space (Office, in thousands of square feet) near the site. The estimated regression based on sites of 100 motels operated by this chain is
Estimated Margin = 54 - 0.0073 Rooms + 0.0216 Office
with R2 = 45% and se = 8.4.
(a) Two possible sites are similar, except that one is near an office complex with 400,000 square feet, whereas the other is near 50,000 square feet of offices. Within a mile of the location near the office complex, a competing hotel has 2,250 rooms, whereas competitors near the other location offer 300 rooms. Which site would you expect to generate a higher operating margin? How much higher?
(b) What is the interpretation of the intercept in this equation?
(c) What does it mean that the partial slope for Rooms is negative?
(d) Interpret the partial slope for Office.