Ramsey RESET test

The Regression Equation Specification Error Test ( RESET) test of Ramsey ( 1969) is a test in statistics to verify the model specification in the context of linear regression. It checks whether non-linear combinations of the explanatory variables have an influence on the declared variable. If the non-linear combinations of the explanatory variables have an impact, then the linear model specification should be reconsidered. But mis-specification as the Non consider relevant variables, structural breaks, homoskedasticity, etc. can be displayed by the test. One advantage of the RESET test is that no explicit alternative model must be specified; the disadvantage that it provides but also no evidence of a "correct" specification.

Mathematical formulation

In the linear model, the following model specification is assumed

And it is estimated

The test checks whether a non-linear model of the form

Not have a greater explanatory power than the linear model.

The hypotheses are

The test statistic is

With

  • The coefficient of determination of the linear model,
  • The determination of the non- linear model,
  • The sample size,
  • The number of explanatory variables and
  • The number of additional parameters in the non-linear model.

If the coefficients of the linear regression in the nonlinear model re-estimated and they differ significantly from the estimated coefficients in the linear model, so this is also an indication of a misspecification.

The RESET test can also be extended to generalized linear models.

Example

In the Boston Housing data, the average purchase price of houses per district ( medv ) is a function of the proportion of the lower class population ( lstat ) estimated using a simple linear regression. The regression line in the scatter plot clearly shows that the relationship between the two variables is not linear.

The RESET test (with and ) gives the following result:

RESET test data: LinReg RESET = 83.4103, df1 = 2, df2 = 502, p- value < 2.2e -16 As the chart already suggests the null hypothesis significance level is discarded because the value is less than, for example by

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