In: Statistics and Probability
Consider the natural ln 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. 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?
4.4.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 |