A useful application of multiple regression analysis is Hedonic modeling. Hedonic models seek to explain the price of a goodsuch as a housein terms of its attributes (e.g., number of bedrooms, square footage, or distance from the nearest toxic waste dump). Consider the following Hedonic model of home sale prices: Pricei = 0 + 1(Square footage)i + 2Bathroomsi + 3Bedroomsi + ui. Using data from 37 home sales, you estimate the model and obtain 0 = 90000, 1 = 1100,2 = 16000, 3 = 35000, SE(1) = 650. (a) Interpret each coefficient. (b) What is the model's forecasted sale price for a 2500-square-foot home with 3 bedrooms and 2.5 bathrooms? (c) In a remodeling frenzy, a homeowner adds an additional bedroom and an additional bath-room by splitting up existing rooms. What is the forecasted change in the price of her home? (d) A homeowner adds a 450-square-foot bedroom and a 75-square-foot bathroom by extending the footprint of his home into an area that used to be a driveway. What is the forecasted change in the price of his home? (e) Conduct two-sided tests of the hypothesis that square footage has no effect on sale price at the 10, 5, and 1 percent levels. (f) Construct a 95 percent confidence interval for 1.