Goldfeld–Quandt test

In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups, and hence the test is sometimes called a two-group test. The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt. Both a parametric and nonparametric test are described in the paper, but the term "Goldfeld–Quandt test" is usually associated only with the former.

In the context of multiple regression (or univariate regression), the hypothesis to be tested is that the variances of the errors of the regression model are not constant, but instead are monotonically related to a pre-identified explanatory variable. For example, data on income and consumption may be gathered and consumption regressed against income. If the variance increases as levels of income increase, then income may be used as an explanatory variable. Otherwise some third variable (e.g. wealth or last period income) may be chosen.

The parametric test is accomplished by undertaking separate least squares analyses on two subsets of the original dataset: these subsets are specified so that the observations for which the pre-identified explanatory variable takes the lowest values are in one subset, with higher values in the other. The subsets needs not be of equal size, nor contain all the observations between them. The parametric test assumes that the errors have a normal distribution. There is an additional assumption here, that the design matrices for the two subsets of data are both of full rank. The test statistic used is the ratio of the mean square residual errors for the regressions on the two subsets. This test statistic corresponds to an F-test of equality of variances, and a one- or two-sided test may be appropriate depending on whether or not the direction of the supposed relation of the error variance to the explanatory variable is known.

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