Homes sold recently in Mid City Home 7 11 12 14 17 19 20 24 25 30 31 32 33 34 44 45 50 51 56 57 66 71 78 81 82 83 86 88 95 96 98 100 104 108 109 113 114 117 119 123 124 125 Price $758,000 $662,500 $615,000 $631,500 $735,500 $557,000 $836,000 $530,500 $782,000 $940,000 $910,000 $561,500 $675,000 $698,000 $770,000 $832,500 $537,500 $755,500 $628,500 $704,500 $555,500 $833,500 $882,500 $717,000 $921,500 $824,000 $941,500 $862,500 $803,000 $762,500 $634,000 $855,000 $1,056,000 $670,000 $585,000 $618,000 $578,500 $997,500 $751,000 $724,000 $598,500 $739,500 SqFt 1830 2030 1870 2150 2190 1700 1920 1820 2210 2040 2250 1930 2250 2280 1920 1940 1700 2100 1720 2190 1450 1950 2280 2190 2140 2050 2250 1880 2150 1970 2000 2080 2440 1890 1990 1940 2000 2290 1950 2060 1900 2160 Bedrooms Bathrooms 3 3 3 2 2 2 3 3 3 3 2 2 3 3 3 2 4 3 4 3 4 3 2 2 3 3 5 3 3 2 3 3 3 2 3 2 2 2 3 2 2 2 3 3 4 3 3 3 4 3 2 2 4 3 3 3 4 3 2 2 2 2 3 3 4 3 3 2 3 3 2 2 3 2 5 4 3 2 2 2 3 3 4 3 Offers 3 3 2 5 4 1 2 3 2 1 3 2 3 4 1 2 3 3 2 3 1 3 3 4 2 1 2 1 3 1 1 2 3 1 3 2 3 1 3 1 3 3 Brick Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Neighborhood East North North West North North East West North East East West North North North East West North North North West East East North East East East East East East North East East North North North West East West North North North Continue to analyze the file Mid City.xlsx that contains data on 128 recent sales in Mid City. For each sale, the file shows the neighborhood (east, west, or north) in which the house is located, the number of offers made on the house, the square footage, whether the house is made primarily of brick, the number of bathrooms, the number of bedrooms, and the selling price. Neighborhoods east and west are more traditional neighborhoods, whereas neighborhood north is a newer, more prestigious neighborhood. Question #1 Now, suppose it is conjectured that the brick premium varies by neighborhood. To account for this conjecture, we will need to augment our model with interaction variables. Before doing so read chapter 10-6b as an introduction to interaction variables. Now augment Model B with interaction terms as follows: Price = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West + b8BrickYes*East + b9BrickYes*West Let us refer to this model as Model C. For simplicity, let S = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers. As a result, your answers to each of these will include \"S\" plus a selection of the regression coefficients from b5,...,b9. In particular ask yourself what the values of the dummy variables and interaction terms are for each of the different types of houses. To get you started with have provided the first few answers. What is the price of a non-Brick house in the North? _______S______________ What is the price of a Brick house in the North? _______S+b5______________ What is the brick premium in the North? _b5_(the difference between a brick and a non-brick house)__________ What is the price of a non-Brick house in the East? ___S + b6 East_______ What is the price of a Brick house in the East? S+b5 BrickYes+ b6 East + b8 BrickYes * East What is the brick premium in the East? _ b5 BrickYes+ b8 BrickYes * East What is the price of a non-Brick house in the West? _S + b7 West_ What is the price of a Brick house in the West? S + b5 BrickYes + b7 West + b9BrickYes * West What is the brick premium in the West? _ b5 BrickYes + b9 BrickYes * West Provide an economic interpretation of b8. Hint: this has to do with how brick houses in the east compare with brick houses in the north. Provide an economic interpretation of b9. Hint: this has to do with how brick houses in the west compare with brick houses in the north. Run Model C using StatTools. You need to first create the interaction variables using "Data Utilities", and the dummy variables (again using "Data Utilities" if you do not have them from Assignment 2). Then add all the requested variables as independent variables, and designating Price as the dependent variable. Attach the regression output as Exhibit 1. Use this output, what is the brick premium in the North? $_____ East? $_____ West? $_____ Question #2 Run the following regression as Model D: Log(Price) = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West Recall that for our purposes, \"Log\" refers to natural logarithms. Include the StatTools output as Exhibit 2. Estimate the price of a 1720 sq ft. brick house in the North that has 3 bedrooms, 2 bathrooms and has had 1 offer made on it. From the output, it is seen that b7 = _______________. Provide an economic interpretation. Suppose a homeowner adds an extension to her house in the form of a 400 sq ft. bedroom. According to Model D, what is the increase in the predicted selling price of her house? Be careful with the units! \f