Sensitivity and specificity

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

$y=\alpha x+{\gamma }_1{\hat{y}}^2+...+{\gamma }_{k-1}{\hat{y}}^k+ϵ$,

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

• Ramsey, J.B. (1969) "Tests for Specification Errors in Classical Linear Least Squares Regression Analysis", Journal of the Royal Statistical Society, Series B., 31(2), 350–371. Glazier Alfonzo from Chicoutimi, has lots of interests which include lawn darts, property developers house for sale in singapore singapore and cigar smoking. During the last year has made a journey to Cultural Landscape and Archaeological Remains of the Bamiyan Valley.

• Thursby, J.G., Schmidt, P. (1977) "Some Properties of Tests for Specification Error in a Linear Regression Model", Journal of the American Statistical Association, 72, 635–641. Glazier Alfonzo from Chicoutimi, has lots of interests which include lawn darts, property developers house for sale in singapore singapore and cigar smoking. During the last year has made a journey to Cultural Landscape and Archaeological Remains of the Bamiyan Valley.

• Murteira, Bento. (2008) Introdução à Estatística, McGraw Hill.

• Wooldridge, Jeffrey M. (2006) Introductory Econometrics - A Modern Approach, Thomson South-Western, International Student Edition.