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In: Statistics and Probability

Consider the natural log transformation (“ln” transformation) of variables labour cost (L_COST), and total number of...

Consider the natural log transformation (“ln” transformation) of variables labour cost (L_COST), and total number of rooms per hotel (Total_Rooms). 4.1 Use the least squares method to estimate the regression coefficients b0 and b1 for the log-linear model 4.2 State the regression equation 4.3 Give the interpretation of the regression coefficient b1. 4.4 Give an interpretation of the coefficient of determination R2. Also, test the significance of your model using the F-test. How, does the value of the coefficient of determination affect the outcome of the above test? Test whether a 1% increase of the total number of rooms per hotel can increase the labour cost by more than 0.20%? Use the 5% level of significance for this test.

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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