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I am running a regression to test how different attributes affect house prices. These attributes have been separated into three categories that are: structural factors (number of room, size, square feet, type of home), external factors (garden, balcony, lot size), and locational factors (these are dummies for where the home is located). So I ran 2 different regressions, one where the price was the dependent variable, and one where the price per square meter. And then ran multiple regression where I only used the independent variables for each category to see how what the results for R2 were. These were the results I got for each category:

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The results are as expected, the structural variables have the highest R2, and highest impact on price. However, in the regression where the dependant variable was the price per m2, the R2 for locational variables was higher than the structural. Does anyone know how I could explain this change, and what the cause of that could be? I appreciate any answers and suggestions.

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  • $\begingroup$ It seems that the price and structural factors also depend on size (total meters) so their significance is probably being overestimated, like a confounding variable (size). When you subtract the size factor from the price (by using "price per m2"), you are cleaning that overfit and/or levelling the explanatory power of the other variables (locational and external). The second model should be used. In addition, some countries use "price per m2" as the indicator of price in the real estate sector. $\endgroup$
    – Lima_Institute_of_Econometrics
    Commented May 23, 2022 at 19:24

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In this case the price per M2 will vary depending on how expensive an area is. For example, if you purchase a property at, say, Manhattan, the price is going to be a lot higher than purchasing a similar property on a different place (Queens or other, cheaper locations). This is something that typically happens on for example California, where properties in Los Angeles or San Diego are a lot more expensive than bigger (and in many cases better) properties in other States, sold by a lower price.

In this case, what might be happening is that, because you are controlling for the price per area, it doesn't matter which ammenities your property have. This implies that even if you have many ammenities, the relative change in price for each unit of area is more affected by where it is located than by what are the charateristics of the state.

I hope this clarifies a bit.

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