4. Recode the Bath categorical variable to create two dummy variables B2 and Bh as following: B2 will be an indicator variable for an extra full bath and Bh will be an indicator variable for an extra half bath. For example, any home with at least one-half bath Bh will be equal to 1 and zero otherwise. If a home has at least 1 full additional bath, then B2 should be equal to 1 and zero otherwise. Note that, for homes with both an additional half bath and an additional full bath, both Bh = 1 and B2 = 1. a. What proportion of variance in the price of the house can be explained by the combination of Bh and B2 variables? b. Is this proportion of variance statistically significant at .05 level of significance? In other words, is the overall model statistically significant at .05 level of significance? Justify your answer. c. Find the corresponding regression equation. Does each variable (Bh and B2) significantly predict the price of the house? Justify your answer and report coefficients and p values for each variable. d. What is the predicted price for the house that has an extra full bath? e. What is the predicted price for the house that has an extra half bath?

Id	Price ($ thousands)	SqFt	Baths	Bedrooms	Garage
1	53,072	928	1	1	0
2	63,158	758	1	2	0
3	64,903	903	1	2	0
4	70,175	1508	1	3	0
5	76,991	1032	2	3	0
6	87,709	1093	1	3	0
7	95,044	1289	2	4	0
8	51,680	1365	1	3	1
9	72,990	699	1	2	1
10	73,106	765	1	2	1
11	73,609	781	1	2	1
12	74,023	914	1	2	1
13	81,283	928	1	3	1
14	82,635	938	1	2	1
15	85,195	1108	1.5	3	1
16	84,655	1038	1	2	1
17	89,541	1295	2	3	1
18	92,898	1023	1	3	1
19	94,609	1562	1	3	1
20	115,336	1585	1.5	3	1
21	120,177	1575	2.5	3	1
22	64,815	849	1	3	2
23	74,973	2186	1.5	4	2
24	77,068	1403	1.5	3	2
25	81,839	792	1	2	2
26	84,771	869	1	2	2
27	84,593	1354	1	3	2
28	89,633	1508	1	3	2
29	86,802	1205	1	2	2
30	89,339	879	1	2	2
31	89,172	1111	2	3	2
32	93,770	1228	1.5	3	2
33	95,989	1354	1.5	3	2
34	99,990	1296	2	3	2
35	105,347	1605	1.5	3	2
36	114,753	1635	1.5	3	2
37	124,711	1621	2.5	3	2
43	79,827	1601	1	3	3
44	128,894	2296	2.5	3	3