# Question: A national motel chain has a model for the operating

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.

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.

**View Solution:**## Answer to relevant Questions

This table gives further details of the multiple regression estimated in Exercise 31. Assume that the MRM satisfies the conditions for using this model for inference. (a) Fill in the t-statistics. (b) Estimate the p-values ...These data describe the sales over time at a franchise outlet of a major US oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The ...An analyst at the United Nations is developing a model that describes GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) among developed countries. She is using national ...If the R2 of a multiple regression with two predictors is larger than 80%, then the regression explains a statistically significant fraction of the variance in y. Modern steel mills are very automated and need to monitor their substantial energy costs carefully to be competitive. In making cold-rolled steel (as used in bodies of cars), it is known that temperature during rolling and ...Post your question