We are talking about SCA, so throw out the cost data except possibly for new construction. I was just in an AI conference yesterday that had a couple of high-volume real estate agents discussing real estate along the California Central Coast. In Carmel, new construction SFR costs $4,500/sf for many homes. The agent said he recently sold a 2,500 sf home for $10.5M in Carmel. Santa Cruz - Monterey/Carmel real estate has been booming since the pandemic. Many wealthy people from Silicon Valley started moving in that direction. He said people see a house, fall in love with it, and are often willing to pay whatever it takes to get it (more or less).
The set of good sales comparables is usually very limited, so you have to deal with large differences and a number of differences that all interrelate. It is a complex dynamic, and it is very, very difficult to deal with features in isolation. GLA interacts with room counts with lot size with location and so on. If you adjust one up or down - you need to adjust all the others. It is a situation where all the impact of all features on sale price have to be handled as a whole. Paired sales treats these features in isolation, under the assumption they do not interact with other features. That is a MAJOR failure of paired sales. Linear Regression assumes that a given features impact on price is constant throughout its range of value. That is absolutely not the case, especially if we have to expand outward from the subject beyond its original subdivision (if it were even part of some subdivision originally). Of course in older areas with many updates, you can have major differences from one house to the next neighboring house.
The only thing that works consistently and is NOT a black-box approach (such as Random Forest, Neural Networks, ...) is MARS (aka "earth"). Earth can be used to increase your understanding of a neighborhood or market area. It will tell you that, for example, The value of a bathroom, if a house has more than 3 bathrooms, is impacted by whether or not the house has an ADU. Yes, it can tell you that and give you an approximate value for the combination of ADU and bathroom count as an adjustment to the value contribution on top of the contribution from the total bathroom count. It is that precise. I can say, I can go into a completely new market area, run Earth and walk away with a better knowledge of market value in that area, than an appraiser who has been working there for 20 years.
In the SF Bay Area, the value contribution of GLA changes as you go up in value - and usually at specific points or "knots." So you may have $700/sf up to 1200sf, then $750/sf for each additional square foot up to 2500/sf, then something like $500/sf for each additional square foot over 2500 sf and up to 4000 square foot and then have it level off beyond 4000 sf or even drop off. You may get a nice R2 of 0.80 or higher from such a model. On the other hand, a linear regression model may do no better than 0.40 or 40%.
You see, in real estate, at least in a large mixed Metro area like the SF Bay Area, there are many different neighborhoods, which are either mostly custom-built or originate from older subdivisions with houses that have been updated over many years. There is certainly no single underlying parametric distribution like the normal distribution. No - the variances in property values change over all feature ranges. The most you can do is just fit a model to the whole mess - a model that is good at replicating previous sale prices and does good on tests for robustness on the value of unknown sales ( We do this 100 times: Randomly divide our 200 sales into 10 partitions of 20 sales, then randomly choose 9 out of the ten partitions to build a new Earth (aka MARS) model to test on the remaining 10th partition and see how close it comes to estimating the sale prices in that 10th partition. Then, choose the best model - or average the best models into one. )