Should coefficient on interaction term be positive or negative? I have the following model for housing prices

price = $\beta_0$ + $\beta_1$ sqrft + $\beta_2$ bedrooms + $\beta_3$ sqrft $\times$ bedrooms + $\beta_4$ bathroom,

where sqrft is square feet.

I am confused regarding the interaction term. Should $\beta_3$ be positive or negative? I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct?
I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct?


As @emeryville said, if your question is about what the result should look like, different people may have different theories.  I think one can make a reasonable argument that going from 1 bedroom (small house) to 2 bedrooms should have a larger impact on the price than going from say 5 bedrooms (large house) to 6 bedrooms because the marginal value of adding an extra bedroom is larger in that case.

This is maybe outside the scope of your question, but based on the wording of your question, it sounds like you have a hypothesis which may not be supported by the results of your model.  So I just want to add that this could mean that your theory was wrong, but it could also mean other things, like that there is some outlier in the dataset that greatly influences the results, or that the model was misspecified in that it does not accurately reflect the true relationship between your variables.  If your estimated result was a negative $\beta_{3}$, but the true of value of that parameter is positive, that could mean that you have some omitted variables that resulted in a biased coefficient.  For example, perhaps the neighborhood location is associated with whether the effect of adding a bedroom is higher or lower for larger houses (and location is also correlated with price).  In a downtown location, both price and size could depend on different factors than a house in a suburb and the value of additional bedroom could be different.  So you would need to add location to the regression equation to obtain an unbiased $\beta_{3}$ coefficient.