Profit is measured as a margin (%).

Rooms100 is the total number of motel rooms (inhundreds) within a 3-mile radius of the hotel.

Highway is the number of miles between the hoteland its nearest highway interchange (in miles).

Office1000 measures the amount of office space (inthousands of sq ft) within the surrounding area.

Enroll1000 measures the number of students (inthousands) enrolled in educational institutions within thesurrounding area.

Income1000 is median income within the surroundingarea (thousands of dollars).

Distatwn is the distance the hotel is from thecity core (in miles).

(a) Estimate a multiple regression model where profit is thedependent variable and all the other variables are independentvariables. Write down your estimated regression equation.

(b) Identify and interpret the Adjusted-R².

(c) Identify and interpret the slope coefficient associated withthe variable Highway.

(d) Construct and conduct appropriate hypothesis tests todetermine which slope coefficients are statistically significant.Use a 5% level of significance.

(e) Using your results from part (d), what advice would youoffer to the executives at La Quinta about how best to increase theprofitability of locations generally? What factor should be givenpriority consideration?

(f) A new location is under consideration and it has thefollowing 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 thepredicted profit margin. Can the executives guarantee a prospectivefranchisee at least a 40% profit margin at this location?

profit	rooms100	highway	office1000	enroll1000	hhinc1000	disttwn
55.5	32.03	0.1	549	8	37	12.1
33.8	28.1	1.5	496	17.5	39	0.4
49	28.9	1.9	254	20	39	12.2
31.9	34.22	1	434	15.5	36	2.7
57.4	26.87	3.4	678	15.5	32	7.9
49	37.59	1.4	635	19	41	4
46	23.41	2	580	23	45	7.4
50.2	30.21	2.6	572	8.5	33	9.3
46	26.55	3.2	666	22	40	6.7
45.5	26.91	1.1	519	13.5	28	9.1
44.2	34.71	2.1	523	12	35	9.4
29.8	35.67	1.8	140	13.5	42	5.7
38.4	32.64	1.6	404	22.5	45	4.4
54.4	32.34	1.1	649	19.5	35	6.5
34.5	27.3	4	171	17	41	10.5
44.9	30.03	3.4	402	15.5	37	4.6
56.5	20.45	2.8	562	15	36	10.5
39.3	35.91	2.3	510	18.5	45	7.2
62.8	16.13	2.6	686	21.5	45	10.7
40.3	28.48	1.8	744	19	44	6.4
41.1	30.98	2	449	11.5	40	7.1
35.7	35.91	2.9	270	9.5	31	9.8
58.5	22.1	1.6	611	17.5	39	12.1
53.5	32.85	2.3	548	23.5	32	11.9
54.2	30.18	1.2	529	20	35	6.6
43.3	33.83	2.1	790	11.5	41	5.3
58	23.82	1.1	484	12	35	13.5
38.1	35.68	2	365	16.5	37	11.1
45.1	21.72	2.9	198	7	39	5.6
42.8	30.03	2.1	457	19.5	35	2.8
51.4	26.4	0.5	431	19.5	37	7.2
45.4	24.43	4.2	515	10.5	38	7.3
48.2	24.29	2	498	20	41	7.2
40.2	36.7	1.5	240	17.5	37	4.9
36.8	30.06	1.8	456	15.5	37	10.6
54.2	24.84	1.5	443	16	41	14.2
36.9	29.23	3.1	449	14	34	7.2
53	28.44	0.8	406	13.5	44	4
39.3	31.59	1.6	392	11	40	14.6
54.4	32.41	2.1	578	21.5	30	9.7
43.7	29.15	2.7	620	13.5	38	9.5
51.5	30.69	1	512	20.5	37	7.1
43.5	29.1	2.9	418	12.5	39	13
48.8	29.35	0.4	551	20	39	8.7
36.1	29.62	3.4	164	12.5	33	6.2
33.2	26.29	2.9	359	20	39	7.6
41.9	35.17	1.4	516	6	36	5.7
49.8	28.59	2.6	544	14.5	35	11.8
45	36.97	2.2	236	20.5	34	5.8
43.2	27.24	3.1	597	14.5	32	14.5
38.8	33.3	1.6	410	13.5	33	10.8
37.8	29.8	1.1	427	12	42	8.2
41	28.46	1.2	231	20.5	43	6
48.8	28.25	3.2	774	13	34	5.8
34.3	35.48	1.8	449	13.5	43	6.5
49.6	29.22	2.4	459	19.5	42	10.4
49.9	32.55	2.1	551	22.5	38	6.1
39.2	29.96	3	359	15.5	36	6.3
42.5	24.03	3.3	345	19	42	6.6
52.6	30.13	0.6	830	20	33	0.7
47.3	26.42	2.5	450	9	44	10
41	34.8	2.4	265	18	43	3.8
51.1	32.27	2.4	711	11	37	8.8
52.1	31.4	2.1	433	23.5	40	11.1
47.6	27.51	1.3	426	10.5	38	5.7
40.8	26.76	1	300	25	33	9.7
52.2	28.79	2.2	747	19.5	38	11.9
60.1	26.19	1.4	683	12	43	8
52	33.54	2.3	614	26.5	37	7.6
51.2	30.82	2.8	637	22	34	3.6
51.2	27.75	1.8	497	15	35	9.2
44	28.13	0.5	233	15	41	3
49.6	33.59	2.7	473	10.5	30	12.2
47.5	30.8	2.4	488	13.5	31	6.7
54.4	27.56	1.1	832	14.5	35	6.9
46.2	22.44	0.7	496	15.5	38	8.9
54.1	28.62	1.4	809	16.5	33	3
43.5	31.98	2.5	548	17	38	10.2
52.7	33.78	1	815	10	40	7.2
49.5	27.26	3.1	464	19	38	5.5
43.4	35.97	0.4	616	15.5	39	1.6
33.5	36.57	2.8	372	18	46	11.3
46.3	25.54	2.2	585	10	42	4.9
42.9	38.38	1.9	875	10	34	11.9
27.3	42.14	1.9	358	16	40	9.2
41.6	27.76	2.2	360	16	43	7.5
49	19.98	0.7	461	19	33	9.9
55.4	27.9	2.7	645	12	37	5.7
54.1	24.32	1.4	370	17.5	39	4.5
32.4	31.24	2.7	349	17	45	7.5
47.3	27.61	0.9	485	16	35	8.2
30.8	36.22	2	347	15	40	7.2
49	28.26	0.1	390	17	40	13.6
57.3	26.01	1.2	520	18.5	35	3.8
60.5	29.32	2.5	469	19.5	35	8.7
53.4	27.72	3.5	622	14.5	29	3.5
35.9	27.86	2.4	511	15.5	37	6.3
40	33.97	2.7	855	19.5	42	11.7
39.8	38.23	0.7	202	17	36	10
35.2	32.51	2.6	275	13	39	10.5