Can you include X1/X2 in a model when you've already included X1 and X2?

#1
Can you include X1/X2 in a model when you've already included X1 and X2? For example, I am trying to predict housing prices. X1=square feet and X2=lot size. I want to see how much of the lot isn't being used as a proxy for how big the front and back yard are. Thus, I want to use X1/X2 since this is my only data. Can I include X1/X2 when I have already included X1 and X2?
 
#3
Yes. It's not that different from an interaction term.
Thank you. Quick question: Let's say you have the following output:

HousePrice=150,000+20Square_feet+5Lot_size-7Square_feet/Lot_size

Let's say you want to predict the effect on house price of an increase in square feet of 100. For "-7Square_feet/Lot_size" would you divide 100 by the average lot size? If not, how would you predict the change in house price?
 

Jake

Cookie Scientist
#4
Just like in models with an interaction term, in this situation you can plug in any value of lot_size that you're interested in. The sample mean of lot_size is a very common and reasonable choice. But there may be other values of lot_size that are of a priori interest as well.
 
#5
Just like in models with an interaction term, in this situation you can plug in any value of lot_size that you're interested in. The sample mean of lot_size is a very common and reasonable choice. But there may be other values of lot_size that are of a priori interest as well.
Thank you so much!