Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a) The estimated regression equation for this data is  ŷ = 24.799 + 0.302x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

H₀: β₀ = 0
H_a: β₀ ≠ 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =  

(c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

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

Fill in the blanks in the following table. At which level of output do we obtain maximum profit? What is the relationship between marginal revenue and marginal cost at the profit-maximizing level of output?

Suppose that you need to buy a refrigerator for your office. You recognize that there are two alternative models in the market that might meet your needs. If you buy model A, you have to pay AZN 1000 but with this model you will decrease your electricity bills by AZN 50 per year for the next 5 years. If you prefer model B, you have to pay AZN 800 but you don’t see any decrease in your electricity bills. If the interest rate is 5%, which model will you buy?

Explain the effect of minimum wage policy on labor market. What are the arguments for supporters and opponents of minimum wage policy?

Suppose the price elasticity of demand for Azercell cards is -2. If Azercell managers want to increase their profits, how should they change the price of Azercell cards? Explain in detail.

Suppose the income elasticity of demand for AZAL flight tickets is 1.75. If the average income level decreases by 6%, what would be the effect of this recession on the demand for AZAL flight tickets? Explain in detail.

We have an array of numbers, and we start at index 0.

At every point, we're allowed to jump from index i to i+3, i+4, or stop where we are.

We'd like to find the maximum possible sum of the numbers we visit.

For example, for the array [14, 28, 79, -87, 29, 34, -7, 65, -11, 91, 32, 27, -5], the answer is 140.

(starting at the 14, we jump 4 spots to 29, then 3 spots to 65, another 3 to 32, then stop. 14 + 29 + 65 + 32 = 140)

What's the maximum possible sum we could visit for this array:

[95, 69, 68, 44, 0, 53, 34, -83, -8, 38, -63, -89, 34, -91, 1, 39, -7, -54, 85, -25, -47, 89, -57, -18, -22, -50, -74, -91, -38, 99, 73, 7, 44, -47, -35, -70, 26, -54, -28, 7, -26, -73, -48, -76, -18, 94, -54, 65, -71, -10, 5, 64, 55, 68, 7, 41, -52, 57, -75, 90, -21, -47, -88, -5, -9, 46, -8, 71, 34, 82, 10, -37, 37, 1, 49, 91, 80, 57, -56, 83, -58, 24, -34, 30, -65, 42, -28, -84, -58, -62, 20, 89, -43, -16, 9, 37, -21, -71, -27, 93, 93, 3, 24, 51, 19, -54, -20, 43, 96, 15, -4, -30, -12, -88, 95, -89, 63, 63, 26, 34, 9, 66, 40, 59, -69, -29, -3, -89, -58, 45, 68, 45, 92, -51, 89, -75, 0, 14, 46, -20, -90, -83, 82, 29, -32, 68, 55, 41, -85, 56, 97, -11, -25, -28, 65, 61, 54, -36, -24, 98, 49, 19, 3, -94, -46, 26, 92, -72, -29, 93, 71, 15, 3, -89, -66, -85, -42, 83, 43, 27, 76, 71, 62, 44, 9, 2, 40, 8, 78, -6, -61, -93, 28, -46, -48, 25, -34, -91, 73, 90, 77, -5, 98, 1, -5, -85, 63, -15, 57, 20, 71, -67, -60, -46, -71, -9, 62, 99, 80, -15, 53, 29, 52, -91, -78, -77, -57, 21, -74, 46, -11, 74, -21, -48, -7, -56, 54, 8, -51, -61, -46, 79, 42, 97, 61, 40, -99, -13, 55, -53, -71, 80, 31, -35, 77, 89, -2, 75, 59, -66, 87, 23, 48, 80, -28, 86, 54, 37, -41, 95, -87, 79, -49, 8, -95, 66, 79, -38, 75, 49, -30, 7, -46, -44, 43, -26, -63, 23, 77, -8, 36, 83, 10, 12, -34, 32, -63, -32, 47, -5, 53, 66, 32, 14, 24, 28, 57, -48, -89, -51, -26, -21, -37, -41, -17, -40, 19, 25, 89, -11, 92, -43, -50, 53, -36, 50, -12, 68, -28, 18, 62, -48, -86, 87, -80, 58, 73, -93, 81, -86, 26, 3, 51, 74, 37, 45, 85, 12, 49, 93, -93, -5, 61, -64, -48, -11, 68, -36, -83, -18, 30, -53, -88, 6, 43, -38, 50, -28, 91, 49, 21, 86, -15, -18, 2, 0, 55, -73, 85, -49, -18, -90, 89, 79, -21, 23, 38, 43, 83, 72, 63, 14, -35, 81, -2, -71, 70, 51, -26, -20, 74, 10, -37, 61, -29, -62, 18, -46, 75, 98, 18, -4, 25, 13, 70, -34, 79, 16, -55, -7, -56, -55, 79, 29, 13, -31, -12, -29, -33, 12, 17, -5, -59, -12, 76, -6, -4, -5, -90, -45, -33, -14, -56, 64, -99, -65, -98, -97, 35, -50, -63, 8, -7, -46, 3, -69, 24, -23, -6, 78, -21, 2, -99, -29, 75, 40, -30, -40, 10, -41, -65, -42, -88, -8, -32, -2, -39, -95, -73, 32, 99, -35, -88, 81, -32, -19, 58, 83, -73, -23, 1, -34, -40, -39, 35, -52, -24, 57, -44, 2]

2 large retail companies (W and T) are compared on a Census variable, percent of people who own their home within 3 square miles of the store. The percent that own their home for W is:

84, 79, 73, 81, 74, 77, 64, 78, 78, 78, 61

Percent for T is:

58, 61, 57, 62, 61, 59, 56, 64, 61, 70

- Try the jackknife bootstrap and find the estimate of difference in percentage owning their home between the two companies as to central tendency. Use lambda=.05

2 large retail companies (W and T) are compared on a Census variable, percent of people who own their home within 3 square miles of the store. The percent that own their home for W is:

84, 79, 73, 81, 74, 77, 64, 78, 78, 78, 61

Percent for T is:

58, 61, 57, 62, 61, 59, 56, 64, 61, 70

- Try the jackknife bootstrap and find the estimate of difference in percentage owning their home between the two companies as to central tendency. Use lambda=.05

1.         Suppose that the relationship between the price of steel and the quantity of steel demanded is as follows:

                                 Price             Quantity

                                   $1                       8

                                    2                      7

                                    3                      6

                                    4                      5

                                    5                      4

                                    6                      3

            a.         Calculate the arc elasticities between each of the prices in the above demand curve (i.e. between $1 and $2, between $2 and $3, etc.)

            b.         Draw a graph showing the above demand curve and label the elasticities you just calculated between each price.

            c.         Calculate the total revenue (expenditures) at each price.  Note the change in TR as price increases.

            d.         Generalize from the above -- what is the relationship between price elasticity and total revenue (expenditures).

The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. Suppose the following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.

(a)

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

(b)

Use Fisher's LSD procedure to determine where the differences occur. Use α = 0.05.

Find the value of LSD for each pair of divisions. (Round your answers to two decimal places.)

North and South LSD = North and West LSD = South and West LSD =

Find the pairwise absolute difference between sample attendance means for each pair of divisions. (Round your answers to the nearest integer.)

x_N − x_S=

x_N − x_W=

x_S − x_W=

For this assignment, write a program that will generate three randomly sized sets of random numbers using DEV C++

To use the random number generator, first add a #include statement for the cstdlib library to the top of the program:

#include <cstdlib>

Next, initialize the random number generator. This is done by calling the srand function and passing in an integer value (known as a seed value). This should only be done ONE time and it MUST be done before actually getting a random number. A value of 1 (or any integer literal) will generate the same sequence of "random" numbers every time the program is executed. This can be useful for debugging:

srand(1);

To get a different series of random numbers each time the program is run, the actual time that the program is run can be passed as the seed value for the random number generator. This is done as follows:

srand(time(0));

If the time function is used, make sure to include the ctime library as well.

Note: the two srand instructions that are listed above are simple examples of how to use the instruction. In a program, only one version will be used.

Now that the random number generator has been initialized, a random number can be generated by calling the rand function:

num = rand();

The above line of C++ code will generate a "random" integer between 0 and RAND_MAX and saves the value in an integer variable named num. RAND_MAX is a pre-defined constant that is equal to the maximum possible random number. It is implementation dependent but is guaranteed to be at least 32,767.

Modulus division can be used to restrict the "random" integer to a smaller range:

num = rand() % 7;

will produce a value between 0 and 6. To change the range to 1 through 7, simply add 1:

num = rand() % 7 + 1;

To get random values that are within a specified range that starts at a value other than 0 or 1:

num = minimum_value + (rand() % (maximum_value - minimum_value + 1));

So, to get values within the range 3 - 17:

num = 3 + (rand() % (17 - 3 + 1));

Run 1 (using srand(5);) on Windows PC

There are 59 numbers in the first set of numbers.

 93 55 49 60 30 27 49 72 40 14 21 33 76 26  7 63  7 50 31 17
 92 93 11 36 49 52 83 22 31 51 69 59 10 53 15 22 87 83 34 86
  6 54 85 15 19 60 15 46 12 84  5 91 59 33 99 70  4 17 36

There are 235 numbers in the second set of numbers.

 66 38  1 36 10 89 90 93 51  6 35 50 68 46 82 75 35 82 60 53
 40  9 53 85 90 16 39 93 63 85 86 84 17 58 78 60 19 67 85  0
 26 71 80 74 78 85 43 73 33 29 39 56 61 75 92 83 55 86 19 66
 70 86 21 75 46 58 72  2 51 47 82 16 17 91 16 68 41 25  9 86
 51 33 67 89 61 46 73 82 24 91 49 43 54 27 32 72 76 96 16 97
 97  5 73 27 58 86 52 68  7 68 59 61 98  2 25 86 75 16 93 89
 32 82 68 74 21 71 20 67 94 58 30 70  0 72 24 95 86  8 87 36
 77 71 14 26 46  8 76  2 50 55 19 24 46 16 34 71 33 71 60 25
 58  5 93 11 86 34 72 32 33 80 42 30  0 10 38 58 67 98 45 26
 24 24 28 84 36 17  0  4 60 95 69 60 55 69 42 40 26 93 32 53
  0 28 64 74 75 17 30 72 30 54 48 37  8 39  4 44 65 81  5 43
 28 98 67 63 69 14 68 63 80 73 89 58 17 82 22

There are 205 numbers in the third set of values.

 81 40 35 33 69 58 56 79 66  0  2 24 65 35 50 84  7 26 85 35
 88 75 24 58 16 20 38 23 18  7 44 52 16 82 36 47 22 31 30 21
 78 59 54 88  0 17 90 81 87 73 59 58 60 94 49 92 22 29 81  1
 97 39 49 71 59 32 90 36 55 33 25 97 40 23 34 81 66 29 38 88
 35 88  2 55  5 45 44 94 34 83 26 91 16 85 10 64  1 66 28 96
 66 87 18 34 60 53 83 90 23 12 65 84 71 75 98 31 35  5 29 22
 72 51 22 37 38 51 62 26 56 12 23  1 22 27 76 85 34 61 92 48
 68 42 32 78 95 54  6 32 67 26 51 62 36 25 93 59 54 51 25 45
 15 54 55 73 19 51 24 36  2 79 19 97 23 66 91  5 91  1 27 20
 47 55 15 62 42 13 70 94 58 98 17  6 18 23 75 11 52 28 45 30
 89 95 32 95 49