Ms Jenny Wong is a property agent dealing with rental of private property in Singapore. She wanted to examine what the key factors affecting the rent of private property are. She recorded the following data for her most recent 105 transactions:

RENT: Monthly rent of property (S$)

SIZE: Build-up area (sq ft)

TIME: Walking time to the nearest MRT station (minutes)

POOL: 1 means the property has a swimming pool

0 means the property does not have a swimming pool

The dataset can be found in the TOA Data File 'Question_4' worksheet. The RENT is the dependent variable and the other variables are independent variables.

(a) Describe the relationship between RENT and the three (3) independent variables by writing down the linear equation. Interpret the coefficients to show how each of the independent variables impacts the rent. You are required to present the whole regression output table.

(b) Jenny wants to estimate the rent for a particular property in which the build-up area is 4,500 sq ft, the walking time to the nearest MRT station is 15 minutes, and it has a swimming pool. What is your estimate of the rent?

(c) Interpret the adjusted coefficient of multiple determination. Explain what the implication in this case is. (5 marks) (d) Execute appropriate hypothesis tests to advise Jenny on which variable(s) is/are statistically significant at the 5% significance level. Write down your steps in detail.

No.	Rent	Size	Time	Pool
1	15600	4600	17	0
2	10800	4200	19	1
3	14400	4600	12	1
4	12900	4400	16	1
5	8400	4200	28	1
6	14700	4200	12	0
7	19500	5000	15	1
8	16200	4200	9	1
9	13200	4600	18	0
10	15990	4800	13	1
11	17550	4200	14	1
12	12540	3400	8	1
13	16248	5000	7	1
14	14766	4200	18	1
15	11664	4600	11	1
16	16878	4200	16	1
17	10362	4400	16	0
18	12450	4600	21	0
19	11934	4400	10	0
20	12558	3800	15	0
21	15138	5200	8	1
22	11574	3800	14	0
23	12558	4200	20	1
24	20718	5200	9	1
25	19578	4200	11	1
26	10386	4400	21	0
27	11220	3800	26	1
28	15432	4200	9	1
29	13980	4400	14	1
30	10824	4000	11	1
31	14040	3400	19	1
32	12426	4000	11	1
33	14862	4800	16	1
34	9972	4000	16	0
35	10626	3800	10	1
36	10962	4000	14	0
37	12960	4600	19	1
38	18726	5200	7	1
39	11988	4200	19	1
40	16392	4400	16	1
41	12360	4200	9	0
42	13932	3800	16	0
43	11898	4200	19	0
44	12306	4000	20	0
45	10536	4600	24	0
46	18468	4800	21	0
47	16152	4400	8	1
48	13488	4400	17	1
49	10296	4000	16	0
50	13008	4400	15	1
51	11556	4400	14	0
52	14184	4400	20	1
53	10344	4400	23	1
54	15084	3800	12	1
55	14760	4600	7	1
56	8844	3400	12	0
57	10560	4400	15	1
58	13704	4600	17	1
59	9990	3200	19	0
60	11364	4400	24	1
61	18726	4800	13	1
62	17388	4000	21	1
63	16194	4400	11	0
64	9258	4000	13	1
65	13326	4200	9	1
66	12582	4400	13	0
67	11454	4400	18	0
68	15258	5000	15	0
69	12450	4200	10	0
70	12582	4400	19	0
71	17640	4200	13	1
72	10578	4000	17	0
73	17658	4800	8	1
74	13440	3800	6	0
75	7500	3800	18	1
76	14208	5200	17	0
77	9846	4600	19	1
78	13068	5000	12	1
79	11532	4800	16	1
80	7554	4800	28	1
81	13254	4600	12	0
82	17670	5400	15	1
83	14676	4600	9	1
84	11940	5000	18	0
85	14400	5200	13	1
86	15792	4600	14	1
87	11286	3800	8	1
88	14622	5400	7	1
89	13290	4600	18	1
90	10500	5000	11	1
91	15192	4600	16	1
92	9324	4800	16	0
93	11202	5000	21	0
94	10740	4800	10	0
95	11298	4200	15	0
96	13626	5800	8	1
97	10416	4200	14	0
98	11298	4600	20	1
99	18648	5800	9	1
100	17622	4800	11	1
101	10740	4800	8	1
102	11298	4200	14	0
103	13626	5800	20	1
104	10416	4200	9	1
105	11298	4600	11	1