Question

You are trying to determine how the price (in 1000s) of a home is related to square feet (sqft), the number of bathrooms (bath), and how nice the house (nice). Nice is a integer from 1 to 7 where 7 is considered very nice. You estimated the following regression equation with your 80 home sample

Price_i = 25.00 + 0.06 sqft_i + 10.04 bath_i + 10.04 nice_i

b. If is costs $32,500 to increase the nice rating from 5 to 7, what percentage of this increase can a customer expect to recoup when selling the home?

c. If is costs $20,000 to increase the nice rating from 2 to 4, what percentage of this increase can a customer expect to recoup when selling the home?

d. Considering your answers to (b) and (c). Can you see a problem with the "nice" rating

How to solve this question

Answer 1

b. When the rating is 5, the component 10.04 nice_i becomes 10.04*5 = 50.2. When the rating is 7, the new value becomes 10.04*7 = 70.28. Because prices are in 1000s, we see that the price is increased by (70.28*1000 – 50.2*1000) = 20080. Now if the cost of increasing the rating is 32500, the consumer can recoup 20080*100/32500 = 61.78%  

c. When the rating is 2, the component 10.04 nice_i becomes 10.04*2 = 20.08. When the rating is 4, the new value becomes 10.04*4 = 40.16. Because prices are in 1000s, we see that the price is increased by (40.16*1000 – 20.08*1000) = 20080. Now if the cost of increasing the rating is 20000, the consumer can recoup 20080*100/20000 = 100.4%  

d. Considering your answers to (b) and (c), we acknowledge that an increase in the rating from 2 to 4 and from 5 to 7 is earning the same profit. But a higher rating is not resulting in profits while a lower rating is giving profit, resulting in an incentive to keep the ratings low.