Ramsey RESET Test

Overview

1. Procedure

1. Estimate the OLS model: $Y=X\beta +u$.
2. Calculate the fitted values: $\hat{Y}$.
3. Create auxiliary regression: Add powers of fitted values (${\hat{Y}}^2,{\hat{Y}}^3,\dots$) as new predictors to the original model.$$Y=X\beta +{\gamma }_1{\hat{Y}}^2+{\gamma }_2{\hat{Y}}^3+v$$
4. Test Significance: Test if ${\gamma }_1={\gamma }_2=0$ using an F-test.

2. Interpretation

• Null Hypothesis ($H_0$): The model is correctly specified.
• Alternative ($H_1$): The model is misspecified.

Significant Result: Indicates that non-linear combinations of the predictors help explain the response, suggesting that terms (like squares or interactions) are missing from the original model.

3. Python Implementation Example

import statsmodels.stats.diagnostic as dg

# Results: [F-Stat, p-value, df_num, df_denom]
reset = dg.linear_reset(model, power=2, test_type='fitted')
print(f"RESET p-value: {reset.pvalue:.4f}")

4. Related Concepts

• Multiple Linear Regression - Model being tested.
• Log Transformations - Potential fix for non-linearity.