You run the RESET test on a regression of wages on years of education and experience. The F-test for Ŷ² and Ŷ³ is rejected at the 1% level. What is the correct interpretation?
AThe original regression has perfect multicollinearity and must be re-estimated
BThe linear model likely has functional form misspecification — the relationship may be nonlinear or missing interaction terms
CYears of education and experience are jointly insignificant predictors of wages
DThe model has heteroskedastic errors and requires robust standard errors
RESET rejection means that powers of the fitted values (Ŷ², Ŷ³) have additional predictive power beyond what the linear model already captures. Since Ŷ is a linear combination of the regressors, Ŷ² implicitly tests all quadratic and interaction terms simultaneously. Rejection signals that the true relationship involves nonlinearity (e.g., wage returns to education may be convex) or missing interactions. It says nothing about multicollinearity (A), the significance of individual predictors (C), or heteroskedasticity (D) — those require separate diagnostics.
Question 2 Multiple Choice
When running the RESET test for a regression Y = β₀ + β₁X₁ + β₂X₂ + u, what additional regressors are added to the augmented regression?
AX₁² and X₂² — squares of the original predictors
BX₁², X₂², and X₁X₂ — all quadratic and interaction terms
CŶ² and optionally Ŷ³ — powers of the fitted values from the original model
Dû² and û³ — powers of the residuals from the original model
RESET adds powers of the fitted values Ŷ — specifically Ŷ² and optionally Ŷ³ — not powers of the original regressors. This is RESET's elegance: since Ŷ is a linear combination of all regressors, Ŷ² implicitly expands into all squared terms and pairwise products simultaneously, testing broadly for nonlinearity with just one or two added variables. Adding squares of individual regressors (A, B) would be a targeted test, not a general screening test. Using residuals (D) confuses RESET with other diagnostic procedures.
Question 3 True / False
Failing to reject the RESET null hypothesis proves that the model's functional form is correctly specified.
TTrue
FFalse
Answer: False
Failure to reject is not proof of correct specification — it is only evidence that this test did not detect a problem. RESET has limited power against certain misspecifications, such as omitted variables that enter linearly or misspecification in the error distribution. As with all hypothesis tests, failing to reject can reflect a Type II error (missing a real problem) rather than absence of a problem. The correct interpretation: 'RESET found no evidence of nonlinear functional form,' not 'the model is correctly specified.'
Question 4 True / False
RESET rejection identifies which specific regressor is causing functional form misspecification.
TTrue
FFalse
Answer: False
This is RESET's key limitation. Because Ŷ² combines all regressors nonlinearly, rejection could mean any of several things — one regressor needs a quadratic term, two regressors interact, the dependent variable should be transformed, or other issues. RESET is a screening test that signals something is wrong but gives no guidance on what to fix. After rejection, diagnosing the specific problem requires substantive economic reasoning and further targeted tests. RESET detects; it does not diagnose.
Question 5 Short Answer
Why does RESET add powers of the fitted values Ŷ rather than powers of each individual regressor directly?
Think about your answer, then reveal below.
Model answer: Using Ŷ² and Ŷ³ is a parsimonious way to test for many types of nonlinearity simultaneously with just one or two added variables. Since Ŷ = β̂₀ + β̂₁X₁ + β̂₂X₂ + ..., Ŷ² expands algebraically into a sum of all squared terms and pairwise cross-products of the regressors. Adding Ŷ² therefore implicitly tests all quadratic and interaction effects at once, using a single degree of freedom in the F-test. Adding powers of each regressor individually would require many parameters, diluting the test's power and requiring more degrees of freedom.
The tradeoff is diagnostic resolution: the compression of all nonlinear terms into Ŷ² makes the test powerful and parsimonious, but at the cost of ambiguity when it rejects. RESET tells you that something nonlinear is missing; finding out which something requires substantive judgment.