statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, the Ramsey Regression Equation Specification Error Test (RESET) test is a general

specification A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard. There are different types of technical or engineering specificati ...

test for the

linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is call ...

model. More specifically, it tests whether non-linear combinations of the fitted values help explain the

response variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or deman ...

. The intuition behind the test is that if non-linear combinations of the

explanatory variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...

s have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

or another non-linear functional form. The test was developed by

James B. Ramsey James Bernard Ramsey (1937 - 2021) was an American econometrician. He was a professor of economics at New York University, and was chair of the economics department between 1978 and 1987. Ramsey received his B.A. in mathematics and economics fro ...

as part of his Ph.D. thesis at the

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

in 1968, and later published in the ''

Journal of the Royal Statistical Society The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founded ...

'' in 1969.

Technical summary

Consider the model :

\hat=E\=\beta x.

The Ramsey test then tests whether

(\beta x)^2, (\beta x)^3, \ldots ,(\beta x)^k

has any power in explaining . This is executed by estimating the following

y=\alpha x + \gamma_1\hat^2+ \cdots +\gamma_\hat^k+\varepsilon,

and then testing, by a means of a

F-test An ''F''-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model th ...

whether

\gamma_1~

through

~\gamma_

are zero. If the null-hypothesis that all

\gamma~

coefficients are zero is rejected, then the model suffers from misspecification.

Technical summary

See also

References

Further reading