Question

Suppose we have the following regression:

housingprice = β0 + β1size + (β2size)² + β3bedrooms + β4pool + β5view + β6pool×view + U,

where pool is a dummy variable of the house has a pool and the view is a dummy variable of the house has a nice view. Suppose the size of the house increases from 1000 sqft to 1100 sqft, the number of bedrooms increases from 2 two 3, dummy pool goes from 0 to 1, but the dummy view goes from 1 to zero, then, what is the expected change of price in terms of β0,··· ,β6?

Answer 1

Given

housingprice = β0 + β1*size + β2*(size)² + β3*bedrooms + β4*pool + β5*view + β6*pool×view + U

Initially, for size = 1000, bedrooms = 2, pool = 0, view = 1, we get the following housing price:

housingprice1 = β0 + β1*1000 + β2*(1000)² + β3 * 2 + β4 * 0 + β5 * 1 + β6* 0×1 + U

= β0 + β1*1000 + β2*(1000)² +  β3 * 2 + β5 + U

Now, for size = 1100, bedrooms = 3, pool = 1, view = 0, we get the following housing price:

housingprice1 = β0 + β1*1100 + β2*(1100)² + β3 * 3 + β4 * 1 + β5 * 0 + β6* 1×0 + U

= β0 + β1*1100 + β2*(1100)² + β3 * 3 + β4 * 1 + U

Hence, change in housing price

= β0 + β1*1100 + β2*(1100)² + β3 * 3 + β4 * 1 + U - (β0 + β1*1000 + β2*(1000)² +  β3 * 2 + β5 + U)

= β1*100 + β2*2,10,000 +  β3 + β4 - β5