Baymont Inn & Suites is a moderately priced chain of hotels 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 hotels. The management of the chain is aware of the difficulty in choosing locations for new hotels. Moreover, making decisions without adequate information often results in poor decisions. Consequently, the chain's management acquired data on 100 randomly selected hotels belonging to Baymont. The objective was to predict which sites are likely to be profitable.

To measure profitability, Baymont 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 hotel'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 hotel. Baymont defines profitable hotels as those with an operating margin in excess of 50%; unprofitable hotels are those with margins of less than 30%.

After a discussion with a number of experienced managers, Baymont 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 hotel and motel rooms within 3 miles of each Baymont hotel. Market awareness was measured by the number of miles to the closest competing hotel. 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 Baymont 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 hotel and motel rooms within 3 miles of Baymont hotel
• 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

Question to be answered:

1. Which of the independent variables are related to operating margin?
2. Develop a regression analysis.
3. Assess the model fit.
4. Test to determine whether there is enough evidence to infer that the model is valid.
5. Test each of the slope coefficients.
6. Interpret the coefficients.
7. 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.
8. Refer to part 7. Estimate with 95% confidence the mean operating margin of all Baymont hotels with those characteristics
9. Assess whether the model assumptions are valid

Y=Margin	Number	Nearest	Office Space	Enrollment	Income	Distance
55.5	3203	4.2	549	8	37	2.7
33.8	2810	2.8	496	17.5	35	14.4
49	2890	2.4	254	20	35	2.6
31.9	3422	3.3	434	15.5	38	12.1
57.4	2687	0.9	678	15.5	42	6.9
49	3759	2.9	635	19	33	10.8
46	2341	2.3	580	23	29	7.4
50.2	3021	1.7	572	8.5	41	5.5
46	2655	1.1	666	22	34	8.1
45.5	2691	3.2	519	13.5	46	5.7
44.2	3471	2.2	523	12	39	5.4
29.8	3567	2.5	140	13.5	32	9.1
38.4	3264	2.7	404	22.5	29	10.4
54.4	3234	3.2	649	19.5	39	8.3
34.5	2730	0.3	171	17	33	4.3
44.9	3003	0.9	402	15.5	37	10.2
56.5	2045	1.5	562	15	38	4.3
39.3	3591	2	510	18.5	29	7.6
62.8	1613	1.7	686	21.5	29	4.1
40.3	2848	2.5	744	19	30	8.4
41.1	3098	2.3	449	11.5	34	7.7
35.7	3591	1.4	270	9.5	43	5
58.5	2210	2.7	611	17.5	35	2.7
53.5	3285	2	548	23.5	42	2.9
54.2	3018	3.1	529	20	39	8.2
43.3	3383	2.2	790	11.5	33	9.5
58	2382	3.2	484	12	39	1.3
38.1	3568	2.3	365	16.5	37	3.7
45.1	2172	1.4	198	7	35	9.2
42.8	3003	2.2	457	19.5	39	12
51.4	2640	3.8	431	19.5	37	7.6
45.4	2443	0.1	515	10.5	36	7.5
48.2	2429	2.3	498	20	33	7.6
40.2	3670	2.8	240	17.5	37	9.9
36.8	3006	2.5	456	15.5	37	4.2
54.2	2484	2.8	443	16	33	0.6
36.9	2923	1.2	449	14	40	7.6
53	2844	3.5	406	13.5	30	10.8
39.3	3159	2.7	392	11	34	0.2
54.4	3241	2.2	578	21.5	44	5.1
43.7	2915	1.6	620	13.5	36	5.3
51.5	3069	3.3	512	20.5	37	7.7
43.5	2910	1.4	418	12.5	35	1.8
48.8	2935	3.9	551	20	35	6.1
36.1	2962	0.9	164	12.5	41	8.6
33.2	2629	1.4	359	20	35	7.2
41.9	3517	2.9	516	6	38	9.1
49.8	2859	1.7	544	14.5	39	3
45	3697	2.1	236	20.5	40	9
43.2	2724	1.2	597	14.5	42	0.3
38.8	3330	2.7	410	13.5	41	4
37.8	2980	3.2	427	12	32	6.6
41	2846	3.1	231	20.5	31	8.8
48.8	2825	1.1	774	13	40	9
34.3	3548	2.5	449	13.5	31	8.3
49.6	2922	1.9	459	19.5	32	4.4
49.9	3255	2.2	551	22.5	36	8.7
39.2	2996	1.3	359	15.5	38	8.5
42.5	2403	1	345	19	32	8.2
52.6	3013	3.7	830	20	41	14.1
47.3	2642	1.8	450	9	30	4.8
41	3480	1.9	265	18	31	11
51.1	3227	1.9	711	11	37	6
52.1	3140	2.2	433	23.5	34	3.7
47.6	2751	3	426	10.5	36	9.1
40.8	2676	3.3	300	25	41	5.1
52.2	2879	2.1	747	19.5	36	2.9
60.1	2619	2.9	683	12	31	6.8
52	3354	2	614	26.5	37	7.2
51.2	3082	1.5	637	22	40	11.2
51.2	2775	2.5	497	15	39	5.6
44	2813	3.8	233	15	33	11.8
49.6	3359	1.6	473	10.5	44	2.6
47.5	3080	1.9	488	13.5	43	8.1
54.4	2756	3.2	832	14.5	39	7.9
46.2	2244	3.6	496	15.5	36	5.9
54.1	2862	2.9	809	16.5	41	11.8
43.5	3198	1.8	548	17	36	4.6
52.7	3378	3.3	815	10	34	7.6
49.5	2726	1.2	464	19	36	9.3
43.4	3597	3.9	616	15.5	35	13.2
33.5	3657	1.5	372	18	28	3.5
46.3	2554	2.1	585	10	32	9.9
42.9	3838	2.4	875	10	40	2.9
27.3	4214	2.4	358	16	34	5.6
41.6	2776	2.1	360	16	31	7.3
49	1998	3.6	461	19	41	4.9
55.4	2790	1.6	645	12	37	9.1
54.1	2432	2.9	370	17.5	35	10.3
32.4	3124	1.6	349	17	29	7.3
47.3	2761	3.4	485	16	39	6.6
30.8	3622	2.3	347	15	34	7.6
49	2826	4.2	390	17	34	1.2
57.3	2601	3.1	520	18.5	39	11
60.5	2932	1.8	469	19.5	39	6.1
53.4	2772	0.8	622	14.5	45	11.3
35.9	2786	1.9	511	15.5	37	8.5
40	3397	1.6	855	19.5	32	3.1
39.8	3823	3.6	202	17	38	4.8
35.2	3251	1.7	275	13	35	4.3