# Ramsey RESET test

In statistics, the Ramsey Regression Equation Specification Error Test (RESET) test (Ramsey, 1969) is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the fitted values help explain the response variable. The intuition behind the test is that if non-linear combinations of the explanatory variables have any power in explaining the response variable, the model is mis-specified.

## Technical summary

Consider the model

$\hat{y}=E\{y|x\}=\beta x.$

The Ramsey test then tests whether $(\beta x)^2, (\beta x)^3...,(\beta x)^k$ has any power in explaining $y$. This is executed by estimating the following linear regression

$y=\alpha x + \gamma_1\hat{y}^2+...+\gamma_{k-1}\hat{y}^k+\epsilon$,

and then testing, by a means of a F-test whether $\gamma_1~$ through $~\gamma_{k-1}$ are zero. If the null-hypothesis that all $\gamma~$ coefficients are zero is rejected, then the model suffers from mis-specification.

## References

• Murteira, Bento. (2008) Introdução à Estatística, McGraw Hill.
• Wooldridge, Jeffrey M. (2006) Introductory Econometrics - A Modern Approach, Thomson South-Western, International Student Edition.