Question

To measure profitability, La Quinta used operating margin, which is the ratio of the sum profit, depreciation, and interest expenses divided by total revenue. The ratio is expressed in percent form, meaning that it could theoretically take on any value between 0 and 100, with a higher value indicating greater profitability. La Quinta defines profitable inns as those with an operating margin in excess of 50 percent; unprofitable inns are those with margins of less than 30 percent. 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, demand generators, demographics, and physical location. To measure the degree of competition, they used the total number of a motel and hotel rooms within 3 miles of the La Quinta Inn (number) and the number of miles to the closest competition (nearest). Two variables that represent sources of customers were chosen. The amount of office space (office space) and college and university enrollment (enrollment) in the surrounding community are demand generators. Both of these are measures of local economic activity. A demographic variable that describes the community is the median household income (income). Finally, as a measure of the physical qualities of the location La Quinta chose the distance to the downtown core (distance).Estimate the following multiple regression equation and present the results in a table. Margin=b₀+b₁+*number+b₂*office space+b₄*enrollment+b₅*income+b₆*distance+e

Interpret the coefficients on number and nearest. Are they statistically significant? (2 points)

Interpret the coefficients on office space and enrollment. Are they statistically significant? (2 points)

Interpret the coefficients on income and distance. Are they statistically significant? (2 points)

margin	number	nearest	officespace	enrollment	income	distance
55.5	3203	4.2	549000	8000.0	37000	2.7
33.8	2810	2.8	496000	17500.0	35000	14.4
49.0	2890	2.4	254000	20000.0	35000	2.6
31.9	3422	3.3	434000	15500.0	38000	12.1
57.4	2687	0.9	678000	15500.0	42000	6.9
49.0	3759	2.9	635000	19000.0	33000	10.8
46.0	2341	2.3	580000	23000.0	29000	7.4
50.2	3021	1.7	572000	8500.0	41000	5.5
46.0	2655	1.1	666000	22000.0	34000	8.1
45.5	2691	3.2	519000	13500.0	46000	5.7
44.2	3471	2.2	523000	12000.0	39000	5.4
29.8	3567	2.5	140000	13500.0	32000	9.1
38.4	3264	2.7	404000	22500.0	29000	10.4
54.4	3234	3.2	649000	19500.0	39000	8.3
34.5	2730	0.3	171000	17000.0	33000	4.3
44.9	3003	0.9	402000	15500.0	37000	10.2
56.5	2045	1.5	562000	15000.0	38000	4.3
39.3	3591	2.0	510000	18500.0	29000	7.6
62.8	1613	1.7	686000	21500.0	29000	4.1
40.3	2848	2.5	744000	19000.0	30000	8.4
41.1	3098	2.3	449000	11500.0	34000	7.7
35.7	3591	1.4	270000	9500.0	43000	5.0
58.5	2210	2.7	611000	17500.0	35000	2.7
53.5	3285	2.0	548000	23500.0	42000	2.9
54.2	3018	3.1	529000	20000.0	39000	8.2
43.3	3383	2.2	790000	11500.0	33000	9.5
58.0	2382	3.2	484000	12000.0	39000	1.3
38.1	3568	2.3	365000	16500.0	37000	3.7
45.1	2172	1.4	198000	7000.0	35000	9.2
42.8	3003	2.2	457000	19500.0	39000	12.0
51.4	2640	3.8	431000	19500.0	37000	7.6
45.4	2443	0.1	515000	10500.0	36000	7.5
48.2	2429	2.3	498000	20000.0	33000	7.6
40.2	3670	2.8	240000	17500.0	37000	9.9
36.8	3006	2.5	456000	15500.0	37000	4.2
54.2	2484	2.8	443000	16000.0	33000	0.6
36.9	2923	1.2	449000	14000.0	40000	7.6
53.0	2844	3.5	406000	13500.0	30000	10.8
39.3	3159	2.7	392000	11000.0	34000	0.2
54.4	3241	2.2	578000	21500.0	44000	5.1
43.7	2915	1.6	620000	13500.0	36000	5.3
51.5	3069	3.3	512000	20500.0	37000	7.7
43.5	2910	1.4	418000	12500.0	35000	1.8
48.8	2935	3.9	551000	20000.0	35000	6.1
36.1	2962	0.9	164000	12500.0	41000	8.6
33.2	2629	1.4	359000	20000.0	35000	7.2
41.9	3517	2.9	516000	6000.0	38000	9.1
49.8	2859	1.7	544000	14500.0	39000	3.0
45.0	3697	2.1	236000	20500.0	40000	9.0
43.2	2724	1.2	597000	14500.0	42000	0.3
38.8	3330	2.7	410000	13500.0	41000	4.0
37.8	2980	3.2	427000	12000.0	32000	6.6
41.0	2846	3.1	231000	20500.0	31000	8.8
48.8	2825	1.1	774000	13000.0	40000	9.0
34.3	3548	2.5	449000	13500.0	31000	8.3
49.6	2922	1.9	459000	19500.0	32000	4.4
49.9	3255	2.2	551000	22500.0	36000	8.7
39.2	2996	1.3	359000	15500.0	38000	8.5
42.5	2403	1.0	345000	19000.0	32000	8.2
52.6	3013	3.7	830000	20000.0	41000	14.1
47.3	2642	1.8	450000	9000.0	30000	4.8
41.0	3480	1.9	265000	18000.0	31000	11.0
51.1	3227	1.9	711000	11000.0	37000	6.0
52.1	3140	2.2	433000	23500.0	34000	3.7
47.6	2751	3.0	426000	10500.0	36000	9.1
40.8	2676	3.3	300000	25000.0	41000	5.1
52.2	2879	2.1	747000	19500.0	36000	2.9
60.1	2619	2.9	683000	12000.0	31000	6.8
52.0	3354	2.0	614000	26500.0	37000	7.2
51.2	3082	1.5	637000	22000.0	40000	11.2
51.2	2775	2.5	497000	15000.0	39000	5.6
44.0	2813	3.8	233000	15000.0	33000	11.8
49.6	3359	1.6	473000	10500.0	44000	2.6
47.5	3080	1.9	488000	13500.0	43000	8.1
54.4	2756	3.2	832000	14500.0	39000	7.9
46.2	2244	3.6	496000	15500.0	36000	5.9
54.1	2862	2.9	809000	16500.0	41000	11.8
43.5	3198	1.8	548000	17000.0	36000	4.6
52.7	3378	3.3	815000	10000.0	34000	7.6
49.5	2726	1.2	464000	19000.0	36000	9.3
43.4	3597	3.9	616000	15500.0	35000	13.2
33.5	3657	1.5	372000	18000.0	28000	3.5
46.3	2554	2.1	585000	10000.0	32000	9.9
42.9	3838	2.4	875000	10000.0	40000	2.9
27.3	4214	2.4	358000	16000.0	34000	5.6
41.6	2776	2.1	360000	16000.0	31000	7.3
49.0	1998	3.6	461000	19000.0	41000	4.9
55.4	2790	1.6	645000	12000.0	37000	9.1
54.1	2432	2.9	370000	17500.0	35000	10.3
32.4	3124	1.6	349000	17000.0	29000	7.3
47.3	2761	3.4	485000	16000.0	39000	6.6
30.8	3622	2.3	347000	15000.0	34000	7.6
49.0	2826	4.2	390000	17000.0	34000	1.2
57.3	2601	3.1	520000	18500.0	39000	11.0
60.5	2932	1.8	469000	19500.0	39000	6.1
53.4	2772	0.8	622000	14500.0	45000	11.3
35.9	2786	1.9	511000	15500.0	37000	8.5
40.0	3397	1.6	855000	19500.0	32000	3.1
39.8	3823	3.6	202000	17000.0	38000	4.8
35.2	3251	1.7	275000	13000.0	35000	4.3

Answer 1

Margin=b0+b1+*number+b2*office space+b4*enrollment+b5*income+b6*distance+e

Here you have given very large data so by hand it is not possible hence it is computed in R

Following are the results along with R script

Regression Out put -

From the out put we can comment about significance of the coefficient based on p-value,

coefficients on number and nearest -

coefficent of number is not significant but coefficient of nearest is significant

coefficients on office space and enrollment -

coefficent of office space is not significant but coefficient of enrollment is significant'

coefficients on income and distance -

coefficent of income is not significant but coefficient of distance is significant'