Question

To measure profitability, La Quinta used operating margin, which is the ratio of the sum profit,...

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

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'