Question

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

Answer 1