Regression in Adjustment Support
~11 min read · Read slope, intercept and R² well enough to support (or reject) an adjustment.
Regression fits a line through the market: price as a function of square footage and friends. Read the slope as a per-unit adjustment, R² as explanatory power — and respect the limits: extrapolation, omitted variables, and correlation masquerading as causation.
The model
Simple linear regression: Price = intercept + slope × variable. The slope (coefficient) is the marginal price change per unit — a $128/sq-ft coefficient IS a market-extracted GLA adjustment. The intercept anchors the line (rarely meaningful alone — 'price at zero square feet' is arithmetic, not real estate). Multiple regression adds variables (GLA, lot, age, baths), each coefficient holding the others constant — closer to how adjustments actually work, and the engine inside AVMs.
- Slope = per-unit contributory value
- Intercept anchors, seldom interprets
- Multiple regression = simultaneous adjustments
Reading the fit
R² (0–1): the share of price variation the model explains — 0.85 means 85% explained, 15% left to everything unmodeled. Higher is better but context rules: 0.6 may be strong for heterogeneous markets. Beware small samples (a line through five points fits anything), outliers dragging the slope, and multicollinearity in multiple regression (bedrooms and GLA overlapping scrambles the individual coefficients even when predictions hold).
- R² = explained share of variation
- Sample size and outliers police the slope
- Collinear variables blur coefficient meaning
The limits
No extrapolation: the model speaks only inside the data's range — a line fit on 1,400–2,600 sq ft homes says nothing about 4,000. Omitted variables bias what remains (leaving out condition loads its effect onto whatever correlates with it). Correlation ≠ causation — the model describes association. In practice: regression SUPPORTS adjustments and sanity-checks the grid; it does not replace comp selection, verification, or judgment.
Worked example
From 38 tract sales: Price = 96,400 + 131 × GLA, R² = 0.81. The appraiser's subject is 2,150 sq ft; comps differ from the subject by ±300 sq ft. A reviewer asks: (a) the supported GLA adjustment; (b) predicted price for the subject; (c) whether the model can value a 4,200 sq ft custom home on acreage.
(a) The slope: $131/sq ft — a market-extracted GLA adjustment, applied to comp differences (a comp 300 sq ft larger adjusts −$39,300), with R² = 0.81 saying GLA alone explains four-fifths of price variation in this tract — strong support. (b) 96,400 + 131 × 2,150 = 96,400 + 281,650 = $378,050 — a useful benchmark beside the grid, not a substitute for it. (c) No: 4,200 sq ft on acreage sits far OUTSIDE the data range and product type — extrapolation plus omitted variables (lot, quality) make the model silent there; that home needs its own comps. Slope for adjustments, R² for confidence, range for humility.
Common exam pitfalls
Extrapolating beyond the sample's range.
The model describes its data — predictions outside the observed range are fiction with decimals.
Reading high R² as proof of the right model.
R² measures fit, not truth — omitted variables and collinearity hide inside good-looking fits.
Replacing the grid with the equation.
Regression supports adjustments and cross-checks value; comp selection and verification remain the appraisal.
Slope is the adjustment, R-squared is the confidence, the data's range is the fence — stay inside it.
Recap
- Price = intercept + slope × variable; slope = per-unit value
- Multiple regression holds other variables constant
- R² = share of variation explained
- Watch samples, outliers, collinearity
- Never extrapolate; correlation isn't causation
- A support tool for adjustments, not a substitute appraisal
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