Question

A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055x1 - 3.6x2, where x2 is a dummy variable that represents whether the house in on a busy street or not. Here x2 = 1 means the house is on a busy street and x2 = 0 means it is not. Based on this information, which of the following statements is true? And why?

a) On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.

b) On average, homes that are on busy streets are worth $3.6 more than homes that are not on busy streets.

c) On average, homes that are on busy streets are worth $3.6 less than homes that are not on busy streets.

d) On average, homes that are on busy streets are worth $3600 more than homes that are not on busy streets.

Answer 1

a) On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.

Explanation:

For the same home (x1 is the same), x2 = 1 if it is on a busy street and x2 = 0 if it is not on a busy street. If x2 = 1, the value of 't' decreases by 3.6 when compared to the value of 't' for x2=0. Since 't' is given in thousands of dollars, when a home is on a busy street, its value decreases by 3.6 thousand dollars.

`t(x1, 0)= 24.6 + 0.055x1\\t(x1, 1) = 24.6 + 0.055x1 - 3.6\\t(x1, 1) = t(x1, 0) - 3.6`

Therefore, the answer is a) On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.