Regression analysis for appraisal adjustments

What the model estimates

A multiple regression fits sale price against the property characteristics you supply — gross living area, pool presence, garage capacity, and whatever else your market supports. The fitted coefficient on each characteristic is the market's indicated contribution of one additional unit of that characteristic, with the other modeled characteristics held constant. A GLA coefficient of $45 means that, across the sales in the set, an extra square foot of living area is associated with about $45 of sale price once pool and garage differences are accounted for.

"Held constant" is the part that paired sales cannot deliver at scale, and it is the reason regression is worth the extra step: it separates elements that move together in the real market.

What the data has to look like

• One competitive market area. Mixing distinct submarkets pushes location differences into the other coefficients.
• A bounded time window. A twelve-month window is common; if the market moved materially inside it, account for time.
• Enough sales per variable. Every additional variable needs sales to support it. A handful of sales with five variables produces coefficients that look precise and mean nothing.
• Arm's-length, verified sales. Distressed and non-market transfers distort coefficients more than they distort a single grid.
• Clean characteristic data. MLS GLA and garage fields are frequently wrong; a mis-keyed square footage moves the coefficient.

Reading the diagnostics

A coefficient on its own tells you nothing about whether the data supports it. CompShield reports the diagnostics alongside every model so you can judge that yourself before adopting any rate.

• Sample size and usable records. The number of sales that actually entered the model after exclusions, with every excluded row and its reason listed. A rate derived from eight usable sales is a different animal from one derived from eighty.
• R² and adjusted R². The share of the variation in sale price the model explains. Adjusted R² penalizes adding variables that do not earn their place, so it is the more honest of the two. High R² is not a licence to adopt a coefficient, and a modest R² does not invalidate one — it tells you how much of the price movement the modeled characteristics account for.
• Standard error and t-statistic. The standard error is how much the estimated rate would be expected to move from sample to sample. The t-statistic is the estimate divided by that error — a rough measure of how firmly the data separates the coefficient from zero.
• p-value. The probability of seeing an association this strong if the characteristic truly had no effect on price in this data. A small p-value (commonly below 0.05) says the relationship is unlikely to be noise. It says nothing about whether the size of the coefficient is reasonable, and nothing about whether the data represents the subject's market.
• 95% confidence interval. The range the true rate plausibly occupies given this sample. A GLA estimate of $45 with an interval of $38–$52 is a usable indication; the same $45 with an interval of $2–$88 is not, even though both report the same point estimate. Read the interval before the estimate.
• VIF (multicollinearity). How much a variable overlaps with the others. When larger homes in a set almost always have three-car garages, the model struggles to attribute price to one rather than the other, and both coefficients become unstable.
• Residuals and influential sales. Sales the model prices badly. A single unusual transaction can drag a coefficient on its own, so the outlier rows are surfaced by address for you to verify or exclude.

When the diagnostics fail the reliability screen — too few records per variable, an interval too wide to be meaningful, severe collinearity — CompShield says the data does not provide reliable support rather than printing a number anyway. Screens are statistical only; they are not a finding that the dataset represents the subject's competitive market.

Limitations to state plainly

Regression describes association within the data supplied, not causation, and it cannot see anything you did not give it — condition, view, functional utility, quality of finish. A coefficient outside a credible range is a data problem or a specification problem, not a market finding, and the appraiser should say so rather than apply it. A regression that disagrees with a clean paired sale deserves scrutiny in both directions.

Documenting it in the workfile

A reviewer should be able to reconstruct the analysis from the addendum alone. That means stating the data source and search criteria, the time window and market area, the variables modeled, the resulting rates, the adjustment applied to each comparable, the gross adjustment percentage, and the reconciliation to a point indication. CompShield produces exactly that narrative from the analysis it runs, so the write-up and the math cannot drift apart.

Compare with paired sales analysis or see the GLA adjustment derivation.