Forecasting labour costs is a key aspect of hotel revenue management that enables hoteliers to appropriately allocate hotel resources and fix pricing strategies. Mary, the President of Hellenic Hoteliers Federation (HHF) is interested in investigating how labour costs (variable L_COST) relate to the number of rooms in a hotel (variable Total_Rooms). Suppose that HHF has hired you as a business analyst to develop a linear model to predict hotel labour costs based on the total number of rooms per hotel using the data provided.

3.1 Use the least squares method to estimate the regression coefficients b0 and b1

3.2 State the regression equation

3.3 Plot on the same graph, the scatter diagram and the regression line

3.4 Give the interpretation of the regression coefficients b0 and b1 as well as the result of the t-test on the individual variables (assume a significance level of 5%)

3.5 Determine the correlation coefficient of the two variables and provide an interpretation of its meaning in the context of this problem 3.6 Check statistically, at the 0.05 level of significance whether there is any evidence of a linear relationship between labour cost and total number of rooms per hotel

I need only the 3.4 and 3.5 questions.

Total_Rooms   L_COST
412   2.165.000
313   2.214.985
265   1.393.550
204   2.460.634
172   1.151.600
133   801.469
127   1.072.000
322   1.608.013
241   793.009
172   1.383.854
121   494.566
70   437.684
65   83.000
93   626.000
75   37.735
69   256.658
66   230.000
54   200.000
68   199.000
57   11.720
38   59.200
27   130.000
47   255.020
32   3.500
27   20.906
48   284.569
39   107.447
35   64.702
23   6.500
25   156.316
10   15.950
18   722.069
17   6.121
29   30.000
21   5.700
23   50.237
15   19.670
8   7.888
20  
11  
15   3.500
18   112.181
23  
10   30.000
26   3.575
306   2.074.000
240   1.312.601
330   434.237
139   495.000
353   1.511.457
324   1.800.000
276   2.050.000
221   623.117
200   796.026
117   360.000
170   538.848
122   568.536
57   300.000
62   249.205
98   150.000
75   220.000
62   50.302
50   517.729
27   51.000
44   75.704
33   271.724
25   118.049
42  
30   40.000
44  
10   10.000
18   10.000
18  
73   70.000
21   12.000
22   20.000
25   36.277
25   36.277
31   10.450
16   14.300
15   4.296
12  
11  
16   379.498
22   1.520
12   45.000
34   96.619
37   270.000
25   60.000
10   12.500
270   1.934.820
261   3.000.000
219   1.675.995
280   903.000
378   2.429.367
181   1.143.850
166   900.000
119   600.000
174   2.500.000
124   1.103.939
112   363.825
227   1.538.000
161   1.370.968
216   1.339.903
102   173.481
96   210.000
97   441.737
56   96.000
72   177.833
62   252.390
78   377.182
74   111.000
33   238.000
30   45.000
39   50.000
32   40.000
25   61.766
41   166.903
24   116.056
49   41.000
43   195.821
9  
20   96.713
32   6.500
14   5.500
14   4.000
13   15.000
13   9.500
53   48.200
11   3.000
16   27.084
21   30.000
21   20.000
46   43.549
21   10.000

Forecasting labour costs is a key aspect of hotel revenue management that enables hoteliers to appropriately allocate hotel resources and fix pricing strategies. Mary, the President of Hellenic Hoteliers Federation (HHF) is interested in investigating how labour costs (variable L_COST) relate to the number of rooms in a hotel (variable Total_Rooms). Suppose that HHF has hired you as a business analyst to develop a linear model to predict hotel labour costs based on the total number of rooms per hotel using the data provided.

3.1 Use the least squares method to estimate the regression coefficients b0 and b1

3.2 State the regression equation

3.3 Plot on the same graph, the scatter diagram and the regression line

3.4 Give the interpretation of the regression coefficients b0 and b1 as well as the result of the t-test on the individual variables (assume a significance level of 5%)

3.5 Determine the correlation coefficient of the two variables and provide an interpretation of its meaning in the context of this problem 3.6 Check statistically, at the 0.05 level of significance whether there is any evidence of a linear relationship between labour cost and total number of rooms per hotel

Total_Rooms   L_COST
412   2.165.000
313   2.214.985
265   1.393.550
204   2.460.634
172   1.151.600
133   801.469
127   1.072.000
322   1.608.013
241   793.009
172   1.383.854
121   494.566
70   437.684
65   83.000
93   626.000
75   37.735
69   256.658
66   230.000
54   200.000
68   199.000
57   11.720
38   59.200
27   130.000
47   255.020
32   3.500
27   20.906
48   284.569
39   107.447
35   64.702
23   6.500
25   156.316
10   15.950
18   722.069
17   6.121
29   30.000
21   5.700
23   50.237
15   19.670
8   7.888
20  
11  
15   3.500
18   112.181
23  
10   30.000
26   3.575
306   2.074.000
240   1.312.601
330   434.237
139   495.000
353   1.511.457
324   1.800.000
276   2.050.000
221   623.117
200   796.026
117   360.000
170   538.848
122   568.536
57   300.000
62   249.205
98   150.000
75   220.000
62   50.302
50   517.729
27   51.000
44   75.704
33   271.724
25   118.049
42  
30   40.000
44  
10   10.000
18   10.000
18  
73   70.000
21   12.000
22   20.000
25   36.277
25   36.277
31   10.450
16   14.300
15   4.296
12  
11  
16   379.498
22   1.520
12   45.000
34   96.619
37   270.000
25   60.000
10   12.500
270   1.934.820
261   3.000.000
219   1.675.995
280   903.000
378   2.429.367
181   1.143.850
166   900.000
119   600.000
174   2.500.000
124   1.103.939
112   363.825
227   1.538.000
161   1.370.968
216   1.339.903
102   173.481
96   210.000
97   441.737
56   96.000
72   177.833
62   252.390
78   377.182
74   111.000
33   238.000
30   45.000
39   50.000
32   40.000
25   61.766
41   166.903
24   116.056
49   41.000
43   195.821
9  
20   96.713
32   6.500
14   5.500
14   4.000
13   15.000
13   9.500
53   48.200
11   3.000
16   27.084
21   30.000
21   20.000
46   43.549
21   10.000

A bus company charges $30 per person for a sightseeing trip if 28 people are in the group. For each additional 2 people, they drop the price $1. How many people will maximize the revenue for the bus company.

At the end of the year, a company offered to buy 4,320 units of a product from X Company for $12.00 each instead of the company's regular price of $17.00 each. The following income statement is for the 69,400 units of the product that X Company has already made and sold to its regular customers:

Sales $1,179,800

Cost of goods sold 595,452

Gross margin $584,348

Selling and administrative costs 183,216

Profit $401,132

For the year, variable cost of goods sold were $464,286, and variable selling and administrative costs were $86,056. The special order product has some unique features that will require additional material costs of $0.75 per unit and the rental of special equipment for $2,000.

1. Profit on the special order would be

2. The marketing manager thinks that if X Company accepts the special order, regular customers will be lost unless the selling price for them is reduced by $0.16. The effect of reducing the selling price will be to decrease firm profits by

At the end of the year, a company offered to buy 4,860 units of a product from X Company for $12.00 each instead of the company's regular price of $19.00 each. The following income statement is for the 60,200 units of the product that X Company has already made and sold to its regular customers:

For the year, variable cost of goods sold were $353,374, and variable selling and administrative costs were $65,016. The special order product has some unique features that will require additional material costs of $0.85 per unit and the rental of special equipment for $3,000.

4. Profit on the special order would be

5. The marketing manager thinks that if X Company accepts the special order, regular customers will be lost unless the selling price for them is reduced by $0.14. The effect of reducing the selling price will be to decrease firm profits by

At the end of the year, a company offered to buy 4,510 units of a product from X Company for $11.00 each instead of the company's regular price of $18.00 each. The following income statement is for the 61,100 units of the product that X Company has already made and sold to its regular customers:

For the year, fixed cost of goods sold were $120,367, and fixed selling and administrative costs were $76,375. The special order product has some unique features that will require additional material costs of $0.70 per unit and the rental of special equipment for $5,000.

4. Profit on the special order would be

5. The marketing manager thinks that if X Company accepts the special order, regular customers will be lost unless the selling price for them is reduced by $0.16. The effect of reducing the selling price will be to decrease firm profits by

A company with annual sales of $22,000,000 is considering changing its payment terms from net 40 to net 30 to encourage customers to pay more promptly. The company forecasts that customers would respond by paying on day 32 rather than day 44 as at present (assume a 360 day year) but would decrease their purchases by $400,000 per year. The company also forecasts that its idle cash balance would decrease by $80,000 and administrative costs would be reduced by $30,000 per year. The company's variable costs average 62% of sales, it is in the 35% marginal tax bracket, and it has an 8% cost of capital.

Part A: Calculate the incremental cash flows from accepting this proposal, and organize your cash flows from part A into a cash flow spreadsheet.

Part B: Calculate the proposal's NPV, IRR, and NAB.

Part C: Should the company shorten its payment terms?

At the end of the year, a company offered to buy 4,650 units of a product from X Company for $11.00 each instead of the company's regular price of $17.00 each. The following income statement is for the 68,900 units of the product that X Company has already made and sold to its regular customers:

For the year, variable cost of goods sold were $457,496, and variable selling and administrative costs were $93,704. The special order product has some unique features that will require additional material costs of $0.89 per unit and the rental of special equipment for $2,500.

4. Profit on the special order would be

5.  The marketing manager thinks that if X Company accepts the special order, regular customers will be lost unless the selling price for them is reduced by $0.11. The effect of reducing the selling price will be to decrease firm profits by

1. At the end of the year, a company offered to buy 4,510 units of a product from X Company for $12.00 each instead of the company's regular price of $17.00 each. The following income statement is for the 62,400 units of the product that X Company has already made and sold to its regular customers:

Sales $1,060,800

Cost of goods sold 504,192

Gross margin $556,608

Selling and administrative costs 156,000

Profit $400,608

For the year, fixed cost of goods sold were $122,304, and fixed selling and administrative costs were $78,000. The special order product has some unique features that will require additional material costs of $0.71 per unit and the rental of special equipment for $2,500. Profit on the special order would be?

2. The marketing manager thinks that if X Company accepts the special order, regular customers will be lost unless the selling price for them is reduced by $0.16. The effect of reducing the selling price will be to decrease firm profits by