Question

P-20 + 50 size + 10 nbed + 15 nbath +e. a) Suppose you know that a house has size = 1.6, nbed - 3, and nbath - 2. What is the expected value of this house? (b) Suppose you know that a house has size 2.6, nbed - 3, and nbath - 2. What is the expected value of this house? (c) Having seen the above predicted model a builder decides to increase the value of his home and changes the original size =1.6, nbed = 3, and nbath =2 home into a size =1.6, nbed = 20, and nbath - 2 home. What is the expected value of this refurbished home? Does this seem logical? What might be the issue/problem with this new evaluation?

Answer 1

(a) We have price of house (value of house) as P

P = 20 + 50 size + 10 nbed + 15 nbath +e

Now expected value of P,

E(P) = 20 + 50 E( size) + 10 Enbed) + 15 Enbath) + Ele) since, E(e) = 0, we will get E(P) = 20 + 50E( size) + 10 Enbed) + 15E( nbath)

and we know that

size = 1.6, nbed = 3 and nbath =2 then expected value of house is,

EP) = 20 + 50 x 1.6 + 10 x 3 + 15 x 2 = 160

(b) Now we have size = 2.6 and everything else is same then,

EP) = 20 + 50 x 2.6 + 10 x 3 + 15 x 2 = 210

(c) Now builder has decided to increase the value of home by increasing nbed to  20 and keeping everything else same then,

EP) = 20 + 50 x 2.6 + 10 x 20 + 15 X 2 = 380

Value of the house has increased in model with in reality this is completely illogical, because it is impossible to build a new house with 20 beds using the same space as with the 2 beds. we can not do this without increasing the size of house.