Data was collected from a random sample of 300 home sales from a community in 20
ID: 1105321 • Letter: D
Question
Data was collected from a random sample of 300 home sales from a community in 2003. Let P denote the selling price (in $1000), Bdr denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet) Lsize denote the lot size (in square feet), and Age denote the age of the house (in years). An estimated regression yields the following fitted regression line: B = 150 + 30Bdrit 32Bathit 0.15Hsize, + 0.0025Lsizei-15Agei (a) (4 points) Suppose that a homeowner converts part of an existing family room in her house into a new bathroom. What is the regressions prediction for the increase in the value of the house? Be careful of units. (hint: the size of the house doesnt change.)Explanation / Answer
(a)
Coefficient of Bathi in the regression equation is 32, which means that as 1 more bathroom is added, value (price) of the house increases by $32,000.
Increase in value of house = $32,000
(b)
Coefficient of Bdri in the regression equation is 30, which means that as 1 more bedroom is added, value (price) of the house increases by $30,000. When 2 bedrooms are added,
Increase in value of house = $30,000 x 2 = $60,000
Coefficient of Hsizei in the regression equation is 0.15, which means that as size of house increases by 1 square foot, value (price) of the house increases by $150 (= 0.15 x $1,000), therefore when size of house increases by 160 square feet,
Increase in value of house = $150 x 160 = $24,000
Total increase in value = $(60,000 + 24,000) = $84,000
(c)
Coefficient of Agei in the regression equation is -15, which means that as homeowner sells the house after 1 year, value (price) of the house decreases by $15,000.
Decrease in value (price) of house = $15,000
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