In: Statistics and Probability
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 |