Does RESET find the correct model?

No. It tests selected additions against the current specification.

Must the additions be powers of fitted values?

No. Implementations offer other variants, which should be named.

Does a large p-value prove linearity?

No. Power depends on the sample and the departures the selected augmentation can detect.

AI Glossary / Statistics and probability / Intermediate

Ramsey RESET test

Definition

The Ramsey RESET test is a regression diagnostic that looks for neglected nonlinear structure by adding functions of the original model's fitted values or explanatory variables and testing whether their coefficients are jointly zero. RESET stands for regression equation specification error test. A significant result challenges the adequacy of the specified regression under the test's assumptions. It does not identify a unique missing variable or prove which alternative model is correct.

What it means

A straight-line regression may leave predictable structure in its errors even when its coefficients appear plausible. RESET asks whether selected nonlinear additions provide evidence against the original specification. In a common version, those additions are squared and cubed fitted values.

The test is a diagnostic alarm with a defined scope. Rejection can motivate investigation of transformations, interactions, omitted structure, or other specification problems. Failure to reject means the chosen test did not find sufficient evidence; it does not certify the model, establish causal validity, or guarantee accurate future forecasts.

How it works

Fit the original regression using the intended observations and record its fitted values. Choose the augmentation in advance where practical. For the familiar fitted-value version, add selected powers such as the square and cube of those fitted values to the original explanatory variables, retaining the original terms.

Fit the augmented model on the same observations. Test the joint null hypothesis that all added coefficients equal zero. The comparison requires identifiable added columns: powers that duplicate existing terms or are linearly dependent cannot supply the assumed number of independent restrictions.

Classical implementations can express the comparison as an F-type statistic; software also offers Wald formulations and covariance estimators appropriate to different error assumptions. Heteroskedasticity or dependent observations require attention to the covariance and reference distribution rather than blindly applying the ordinary homoskedastic formula. Record the powers, augmentation type, covariance method, sample, and test result so another analyst can reproduce the diagnostic.

Three practical examples

1. A retailer checks whether a linear sales model leaves evidence of nonlinear price effects before trusting its demand projections.

2. A facilities team tests a regression of energy use on weather variables, then investigates whether seasonal interactions could explain a diagnostic rejection.

3. A credit analyst uses RESET as one part of regression review, alongside residual plots and validation on later observations, without treating it as a test of causal assumptions.

Think of it this way

Think of testing a shelf with additional pressure at selected points. Movement tells you the current construction deserves inspection, but it does not tell you which screw is loose. No movement under those particular checks does not prove the shelf will withstand every possible load.

Worked example

Consider an original teaching comparison with 50 observations. The original regression has three estimated coefficients, including its intercept, and residual sum of squares SSE_R = 120. An augmented regression adds two independent columns and has five coefficients in total, with SSE_U = 80. These are stipulated model summaries for illustrating the calculation.

Under the conventional nonrobust comparison, the two added restrictions give numerator mean square (120 - 80)/2 = 20. The augmented residual degrees of freedom are 50 - 5 = 45, giving residual mean square 80/45, approximately 1.77778.

The F-type statistic is therefore 20/(80/45) = 11.25, with the conventional reference degrees of freedom 2 and 45. A reported p-value would require the chosen reference procedure and its assumptions; the number alone is not a probability that the original model is wrong.

If an analyst instead uses a heteroskedasticity-robust covariance estimator, the test is based on that coefficient covariance. It should not be reconstructed from this simple difference in residual sums of squares. The calculation also assumes both models use exactly the same observations.

Illustrative case study

In a fictional delivery company, an analyst fits delivery time using distance and parcel count. RESET rejects the original specification. A residual plot suggests that long routes behave differently during busy periods.

The team examines route characteristics and constructs a revised model using operationally meaningful terms. It evaluates that model on a later period, checks residual behavior again, and compares errors for short and long routes. The manager records RESET as the reason for further investigation, rather than claiming that the test proved congestion was the missing cause. The revised model must still demonstrate practical improvement.

Common misconceptions and mistakes

Do not describe rejection as proof of a specific omitted variable. Several departures can create similar diagnostic signals. Do not interpret non-rejection as evidence that every relevant variable is present or that endogeneity is absent.

Adding more powers indiscriminately can consume degrees of freedom and create numerical instability. Repeatedly changing the test until a preferred result appears undermines its interpretation. A model with good in-sample fit can still fail a specification diagnostic, and a model that passes can still predict poorly. The test is also not a general substitute for checking dependence, influential observations, measurement quality, or the substantive plausibility of the regression.

Business use

RESET supports model governance by making one aspect of specification review explicit and reproducible. It is useful when a regression informs forecasts, resource planning, or performance comparisons. Pair the result with residual graphics, domain knowledge, and evaluation data. Decide whether discovered structure is large enough to affect decisions, rather than responding only to a statistical threshold.

Check your understanding

The original model uses 100 rows, but the augmented model drops five rows. Can their residual sums of squares be inserted directly into the same nested comparison?

Answer: No. Refit both on a common sample before making that comparison; otherwise the difference mixes changed observations with changed specification.

Related terms

Nonlinear regression
Wald test
Model validation
Model specification
residual analysis
omitted variable
F-test
heteroskedasticity

Learn next

Learn nested regression comparisons and residual plots, then study robust covariance estimation. Practice distinguishing evidence against a specification from evidence supporting a particular replacement model.

Sources

Statsmodels, linear_reset documentation and implementation notes: https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.linear_reset.html

The primary software documentation specifies augmentation alternatives, the joint coefficient test, and covariance options. The numerical comparison and fictional case are original teaching illustrations.

Previous: RAMnets Next: Rand index