# Question

La Quinta Motor Inns is a moderately priced chain of motor inns located across the United States. Its market is the frequent business traveler. The chain recently launched a campaign to increase market share by building new inns. The management of the chain is aware of the difficulty in choosing locations for new motels. Moreover, making decisions without adequate information often results in poor decisions. Consequently, the chain’s management acquired data on 100 randomly selected inns belonging to La Quinta. The objective was to predict which sites are likely to be profitable. To measure profitability, La Quinta used operating margin, which is the ratio of the sum of profit, depreciation, and interest expenses divided by total revenue. (Although occupancy is often used as a measure of a motel’s success, the company statistician concluded that occupancy was too unstable, especially during economic turbulence.) The higher the operating margin the greater the success of the inn. La Quinta defines profitable inns as those with an operating margin in excess of 50%; unprofitable inns are those with margins of less than 30%. After a discussion with a number of experienced managers, La Quinta decided to select one or two independent variables from each of the following categories: competition, market awareness, demand generators, demographics, and physical location.

To measure the degree of competition, they determined the total number of motel and hotel rooms within 3 miles of each La Quinta inn. Market awareness was measured by the number of miles to the closest competing motel. Two variables that represent sources of customers were chosen. The amount of office space and college, and university enrollment in the surrounding community are demand generators. Both of these are measures of economic activity. A demographic variable that describes the community is the median household income. Finally, as a measure of the physical qualities of the location La Quinta chose the distance to the downtown core. These data are stored using the following format:

Column 1: y = operating margin, in percent

Column 2: x1 = Total number of motel and hotel rooms within 3 miles of La Quinta inn

Column 3: x2 = Number of miles to closest competition

Column 4: x3 = Office space in thousands of square feet in surrounding community

Column 5: x4 = College and university enrollment (in thousands) in nearby university or college

Column 6: x5 = Median household income (in $thousands) in surrounding community

Column 7: x6 = Distance (in miles) to the downtown core

Adapted from Sheryl E. Kimes and James A. Fitzsimmons, “Selecting Profitable Hotel Sites at La Quinta Motor Inns,” INTERFACES 20 March–April 1990, pp. 12–20.

a. Develop a regression analysis.

b. Test to determine whether there is enough evidence to infer that the model is valid.

c. Test each of the slope coefficients.

d. Interpret the coefficients.

e. Predict with 95% confidence the operating margin of a site with the following characteristics.

There are 3,815 rooms within 3 miles of the site, the closest other hotel or motel is .9 miles away, the amount of office space is 476,000 square feet, there is one college and one university with a total enrollment of 24,500 students, the median income in the area is $35,000, and the distance to the downtown core is 11.2 miles.

f. Refer to part (e). Estimate with 95% confidence the mean operating margin of all La Quinta inns with those characteristics.

To measure the degree of competition, they determined the total number of motel and hotel rooms within 3 miles of each La Quinta inn. Market awareness was measured by the number of miles to the closest competing motel. Two variables that represent sources of customers were chosen. The amount of office space and college, and university enrollment in the surrounding community are demand generators. Both of these are measures of economic activity. A demographic variable that describes the community is the median household income. Finally, as a measure of the physical qualities of the location La Quinta chose the distance to the downtown core. These data are stored using the following format:

Column 1: y = operating margin, in percent

Column 2: x1 = Total number of motel and hotel rooms within 3 miles of La Quinta inn

Column 3: x2 = Number of miles to closest competition

Column 4: x3 = Office space in thousands of square feet in surrounding community

Column 5: x4 = College and university enrollment (in thousands) in nearby university or college

Column 6: x5 = Median household income (in $thousands) in surrounding community

Column 7: x6 = Distance (in miles) to the downtown core

Adapted from Sheryl E. Kimes and James A. Fitzsimmons, “Selecting Profitable Hotel Sites at La Quinta Motor Inns,” INTERFACES 20 March–April 1990, pp. 12–20.

a. Develop a regression analysis.

b. Test to determine whether there is enough evidence to infer that the model is valid.

c. Test each of the slope coefficients.

d. Interpret the coefficients.

e. Predict with 95% confidence the operating margin of a site with the following characteristics.

There are 3,815 rooms within 3 miles of the site, the closest other hotel or motel is .9 miles away, the amount of office space is 476,000 square feet, there is one college and one university with a total enrollment of 24,500 students, the median income in the area is $35,000, and the distance to the downtown core is 11.2 miles.

f. Refer to part (e). Estimate with 95% confidence the mean operating margin of all La Quinta inns with those characteristics.

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