Functional Form Misspecification and the RESET Test

A regression assumes the relationship between predictors and outcome takes the form you wrote down — usually linear. If the true relationship actually curves, or the predictors interact, a plain linear fit will systematically miss that shape no matter how much data you add, and the coefficients it reports will be biased in a way that ordinary significance tests won't flag. The Ramsey RESET test (Regression Equation Specification Error Test) is a simple, general check for exactly this kind of functional-form misspecification, without requiring you to guess which specific nonlinear term is missing.

The test works by refitting the same regression with extra terms added: the model's own fitted values, squared and cubed. If the original linear specification were correct, those powers of the fitted values should have no explanatory power left to add — they're just polynomials in a linear combination of the same predictors already in the model. If they turn out to be jointly significant, that's evidence the true relationship isn't simply linear in the original predictors, even though RESET doesn't say which nonlinear term (a square term, a log, an interaction) is missing — only that something is.

For example, regressing a stock's return on a single "value" score, a RESET test finding the squared fitted value highly significant would suggest the true relationship is concave or convex rather than a straight line — prompting a check for whether the value effect is actually strongest only at extreme scores.