# Multivariate Regression on House Prices

I am trying to run a Multivariate Regression Model where I am trying to explain House Prices by some given data such as the number of baths, location of the house, square feet and so on.

While playing with the variables I decided to model the price per square feet variable to explain the House Price (obviously just a linear modification of the variable I am trying to explain). Running the Regression on this, all my previous variables that were significant all became insignificant (all p-values above 0,10). Nonetheless my adjusted R-Squared skyrocketed up to 0,98. I obviously have a gut-feeling that this result is wrong and may be prone to multicollinearity or some other statistical sin I am not aware of. I would like to understand if this result is viable or not and why?

• I think it would help us give an answer if you could tell us exactly what are the independent variables Commented Jan 2, 2018 at 11:13

That said, if all your houses had the same area, then price and price per unit area would be just be the same variable, up to a constant factor, and regression on price and price per unit area would give you $R^2$ of 1.