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In: Statistics and Probability

Forecasting labour costs is a key aspect of hotel revenue management that enables hoteliers to appropriately...

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 line3.4 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%) 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

STARS Total_Rooms Region_ID ARR_MAY ARR_AUG L_COST
5 412 1 95 160 2.165.000
5 313 1 94 173 2.214.985
5 265 1 81 174 1.393.550
5 204 1 131 225 2.460.634
5 172 1 90 195 1.151.600
5 133 1 71 136 801.469
5 127 1 85 114 1.072.000
4 322 1 70 159 1.608.013
4 241 1 64 109 793.009
4 172 1 68 148 1.383.854
4 121 1 64 132 494.566
4 70 1 59 128 437.684
4 65 1 25 63 83.000
3 93 1 76 130 626.000
3 75 1 40 60 37.735
3 69 1 60 70 256.658
3 66 1 51 65 230.000
3 54 1 65 90 200.000
2 68 1 45 55 199.000
1 57 1 35 90 11.720
4 38 1 22 51 59.200
4 27 1 70 100 130.000
3 47 1 60 120 255.020
3 32 1 40 60 3.500
3 27 1 48 55 20.906
2 48 1 52 60 284.569
2 39 1 53 104 107.447
2 35 1 80 110 64.702
2 23 1 40 50 6.500
1 25 1 59 128 156.316
4 10 1 90 105 15.950
3 18 1 94 104 722.069
2 17 1 29 53 6.121
2 29 1 26 44 30.000
1 21 1 42 54 5.700
1 23 1 30 35 50.237
2 15 1 47 50 19.670
1 8 1 31 49 7.888
1 20 1 35 45 0
1 11 1 40 55 0
1 15 1 40 55 3.500
1 18 1 35 40 112.181
3 23 1 40 55 0
4 10 1 57 97 30.000
2 26 1 35 40 3.575
5 306 2 113 235 2.074.000
5 240 2 61 132 1.312.601
5 330 2 112 240 434.237
5 139 2 100 130 495.000
4 353 2 87 152 1.511.457
4 324 2 112 211 1.800.000
4 276 2 95 160 2.050.000
4 221 2 47 102 623.117
4 200 2 77 178 796.026
4 117 2 48 91 360.000
3 170 2 60 104 538.848
3 122 2 25 33 568.536
5 57 2 68 140 300.000
4 62 2 55 75 249.205
3 98 2 38 75 150.000
3 75 2 45 70 220.000
3 62 2 45 90 50.302
5 50 2 100 180 517.729
4 27 2 180 250 51.000
3 44 2 38 84 75.704
3 33 2 99 218 271.724
3 25 2 45 95 118.049
2 42 2 28 40 0
2 30 2 30 55 40.000
1 44 2 16 35 0
3 10 2 40 70 10.000
2 18 2 60 100 10.000
1 18 2 16 20 0
2 73 2 22 41 70.000
2 21 2 55 100 12.000
1 22 2 40 100 20.000
1 25 2 80 120 36.277
1 25 2 80 120 36.277
1 31 2 18 35 10.450
3 16 2 80 100 14.300
2 15 2 30 45 4.296
1 12 2 40 65 0
1 11 2 30 50 0
1 16 2 25 70 379.498
1 22 2 30 35 1.520
4 12 2 215 265 45.000
4 34 2 133 218 96.619
2 37 2 35 95 270.000
2 25 2 100 150 60.000
2 10 2 70 100 12.500
5 270 3 60 90 1.934.820
5 261 3 119 211 3.000.000
5 219 3 93 162 1.675.995
5 280 3 81 138 903.000
5 378 3 44 128 2.429.367
5 181 3 100 187 1.143.850
5 166 3 98 183 900.000
5 119 3 100 150 600.000
5 174 3 102 211 2.500.000
5 124 3 103 160 1.103.939
4 112 3 40 56 363.825
4 227 3 69 123 1.538.000
4 161 3 112 213 1.370.968
4 216 3 80 124 1.339.903
3 102 3 53 91 173.481
4 96 3 73 134 210.000
4 97 3 94 120 441.737
4 56 3 70 100 96.000
3 72 3 40 75 177.833
3 62 3 50 90 252.390
3 78 3 70 120 377.182
3 74 3 80 95 111.000
3 33 3 85 120 238.000
3 30 3 50 80 45.000
3 39 3 30 68 50.000
3 32 3 30 100 40.000
2 25 3 32 55 61.766
2 41 3 50 90 166.903
2 24 3 70 120 116.056
2 49 3 30 73 41.000
2 43 3 94 120 195.821
4 9 3 100 180 0
2 20 3 70 120 96.713
2 32 3 19 45 6.500
2 14 3 35 70 5.500
2 14 3 50 80 4.000
1 13 3 25 45 15.000
1 13 3 30 50 9.500
2 53 3 55 80 48.200
3 11 3 95 120 3.000
1 16 3 25 31 27.084
1 21 3 16 40 30.000
1 21 3 16 40 20.000
1 46 3 19 23 43.549
1 21 3 30 40 10.000

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