🏠 Automated Property Valuation Model — Live Regression

R² is the fraction of the variance in comparable sale prices that the fitted regression explains, calculated as 1 minus the ratio of the sum of squared residuals to the total sum of squared deviations from the mean price. An R² of 0.85 means 85% of the price variation across comparables is accounted for by the five features in the model; the remaining 15% is attributed to noise, unmeasured features, or genuine randomness in how buyers value a specific property. Because this simulation generates comparables from a true underlying model plus random noise, R² here is a direct, tunable measure of how much of that noise you have injected.

Ordinary least squares picks each coefficient to best explain the price variation attributable to that feature after accounting for all the others, so a feature that moves price a lot per unit change (like an extra 1,000 sq ft) naturally gets a larger coefficient than one with a smaller typical price effect (like one point of a 1–10 condition score), even if both are equally "important" in a statistical sense. The bar chart in this simulation lets you compare the fitted coefficients against the true generating coefficients, and watch the fitted values converge toward the true ones as more comparable sales are added and estimation noise shrinks.

A confidence interval (what this simulation displays) bounds the uncertainty in the model's estimate of the average price for properties with the subject's exact features — it narrows toward zero as more comparable data arrives, because with infinite data you would know that average exactly. A prediction interval instead bounds where one actual sale price is likely to fall, which must also account for the irreducible noise in individual transactions (buyer whims, negotiation, timing) and therefore never shrinks below roughly the residual standard deviation, no matter how much data you collect. AVMs quote something closer to a prediction interval in production because clients care about a single sale price, not an average.

AVMs struggle with unique or unusual properties that fall outside the range of nearby comparable sales, with fast-moving markets where recent comparables are already stale, and with features that are hard to quantify numerically, such as kerb appeal, a recent renovation's finish quality, or a noisy road. They also inherit any bias present in historical sales data — if certain neighbourhoods were historically under- or over-valued for non-market reasons, a naively trained AVM will project that pattern forward. This is why regulators generally require a human valuation, not an AVM alone, for high-stakes decisions like mortgage lending above a certain loan size.