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.

Data from Excel:

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

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?