1. The data file "LaQuinta" (posted on Canvas) contains information on a random sample of 100 hotels within the La Quinta chain. Profit is measured as a margin (%). Rooms 100 is the total number of motel rooms (in hundreds) within a 3-mile radius of the hotel. Highway is the number of miles between the hotel and its nearest highway interchange (in miles). Office1000 measures the amount of office space (in thousands of sq ft) within the surrounding area. Enroll 1000 measures the number of students (in thousands) enrolled in educational institutions within the surrounding area. Income1000 is median income within the surrounding area (thousands of dollars). Distatwn is the distance the hotel is from the city core (in miles). (a) Estimate a multiple regression model where profit is the dependent variable and all the other variables are independent variables. Write down your estimated regression equation. (b) Identify and interpret the Adjusted-R. (c) Identify and interpret the slope coefficient associated with the variable Highway. (d) Construct and conduct appropriate hypothesis tests to determine which slope coefficients are statistically significant. Use a 5% level of significance. (e) Using your results from part (d), what advice would you offer to the executives at La Quinta about how best to increase the profitability of locations generally? What factor should be given priority consideration? (f) A new location is under consideration and it has the following characteristics: 2500 competing hotel rooms 0.5 miles from highway interchange 400,000 square feet of office space 15,000 enrolled in higher education $42,500 median household income 8.4 miles from the city core Calculate a point estimate and a 95% prediction interval for the predicted profit margin. Can the executives guarantee a prospective franchisee at least a 40% profit margin at this location