4 Data was collected from a random sample of 220 home sales from a community in

Question

4 Data was collected from a random sample of 220 home sales from a community in 2017 Let P denote the selling price (in $1000), Bdr denote the number of bedrooms, Hsize denote the size of the house (in square feet), Age denote the age of the house (in years), Poor denote a dummy variable that is equal to 1 if the condition of the house is reported as "poor" and is zero otherwise, and View denote a dummy variable that is 1 if the house has a view of a nearby mountain range and is zero otherwise. An estimated regression yields the following fitted regression line: P = 119.2 + 0.485Bdri + 0.156Hsizei + 0.090Agei-18.8Peorit 25.5Viewi -0.005(Hsize,* Poor0.005(Hsize, * Viewi) a) Suppose that a homeowner of a 2500 square foot house removes a row of tall trees that is blocking the view of the mountains from the house. What is the regression's prediction for the increase in the value of the house? b) Consider a house that has a view of the mountains and is in poor condition. Suppose the homeowner adds 100 square feet to the house. What is the regressions prediction for the increase in the value of the house?

Explanation / Answer

a) The value of the house in this case will change only by the view and the product of view and Hsize will change and the view

as the mountain view in dummy variable has value 1 in case of mountain range so the value will increase by 25.5*1 +0.005(2500*1) = 25.5+12.5 = 38

in thousand dollars the value will increase by $38000

b) Since the house is in poor condition the value of dummy variable is 1 and for mountain ranges the value of view is also taken as 1

also the Hsize increases by 100

so the total change in regression would be by keeping everything else the same (all other regressors same )

100*0.156-0.005(100*1)+0.005(100*1) = 15.6

so the value of the house increases by $15600

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