I learned 20+ years ago when I started appraisal that linear regression simply does not work for homes in urban areas of Northern California.
This is what a true regression model will look like for GLA:
1. A base amount that represents the starting point for GLA, assuming your smallest home is a certain size such as 800sf.
2. A segmented linear regression is invariably the best representation for price increases or decreases. This has linear segments between so-called "knots" or change points. For example, assuming the minimum GLA is 800sf, $300/sf from 800-1500sf, $250/sf from 1500-2500sf, $200/sf from 2500-5000sf and $0/sf for over 5000sf. In this case the knots are 1500sf, 2500sf and 5000sf.
3. The model in #2 would look like this Value(GLA) = $240,000 + max(0,GLA-800) x $300 - max(0,GLA-1500) x $50 - max(0, GLA-2500) x $50 - max(0,GLA-5000) x $200
4. By the way the function max(x,y) means that you take the value of x if it is larger than y, otherwise y. So, max(0, -$200) is just 0 or in other words max(0,y) only take the value of y if it is positive.
5. For the given model, we add $300 for each square foot of GLA above 800sf - out to infinity. Then we subtract $50/sf for each sf above 1500sf out to infinity, then subtract another $50/sf for each sf over 2500sf out to infinity then subtract $200/sf for each sf over 5000sf out to infinity.
You can do this in Excel. If we put the GLA in column 1 the function for the value would be:
=240000+MAX(0,A2-800)*300-MAX(0,A2-1500)*50-MAX(0,A2-2500)*50-MAX(0,A2-5000)*200
GLA | GLA Value Contribution |
800 | $240,000 |
1,000 | $300,000 |
1,500 | $450,000 |
1,600 | $475,000 |
2,400 | $675,000 |
2,500 | $700,000 |
2,600 | $720,000 |
3,200 | $840,000 |
4,000 | $1,000,000 |
4,900 | $1,180,000 |
5,000 | $1,200,000 |
5,100 | $1,200,000 |
5,200 | $1,200,000 |
And in the Sales Grid we would have (in this kind of sales grid, there is an extra column for variable "Value Contribution" and the adjustments are simply Subject_Value_Contribution - Comparable_Value_Contribution:
Subj GLA | Value Contrib. | Comp GLA | Value Contrib | Adjustment |
4000 | $1,000,000 | 3200 | $840,000 | $160,000 |
By the way, if there is really no demand for homes over a certain size in a market area, the value contribution for the extra GLA may actually decrease above a certain size. I have seen this for example, where heating costs are high --- necessitating closing off parts of the house. Then throw in additional maintenance costs - making the extra GLA of such homes a liability for many. And some women have a very negative view of having to clean those superfluous areas of the home.