Problem 4

To examine the effects on the housing prices, we estimated the following regression. 

where price = the housing price, SIZE = size measured in square feet, ROOMS = the number of rooms, and Z denotes other control variables. Below are the summary statistics of the variables and the estimation results of the above regression.

(a) Write the estimated equation.

(b) State whether the following statement is True, False, or Uncertain. And explain why. "It is believed that the more rooms a house has, the higher its price is. However, the coefficient estimate for ROOMS is negatively significant. Therefore, the above estimation results are wrong and do not make sense."

(c) What is the net effect of SIZE on the housing price? Calculate the range of the net effect.

(d) Re-express the estimated equation in (a) using the centered variables at their sample means, e.g., using (SIZE−1052) and (ROOMS−3.4).