In statistics, the Glejser test for

heteroscedasticity In statistics, a sequence (or a vector) of random variables is homoscedastic () if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The s ...

, developed in 1969 by Herbert Glejser, regresses the residuals on 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 ...

that is thought to be related to the heteroscedastic variance. After it was found not to be asymptotically valid under asymmetric disturbances, similar improvements have been independently suggested by Im, and Machado and Santos Silva.

Steps for using the Glejser method

Step 1: Estimate original regression with

ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the ...

and find the sample residuals ''e''_''i''. Step 2: Regress the absolute value , ''e''_''i'', on the explanatory variable that is associated with the heteroscedasticity. :

, e_i, & = \gamma_0 + \gamma_1 \frac 1 + v_i \end

Step 3: Select the equation with the highest ''R''² and lowest standard errors to represent heteroscedasticity. Step 4: Perform a t-test on the equation selected from step 3 on ''γ''₁. If ''γ''₁ is statistically significant, reject the

null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...

of homoscedasticity.

Software Implementation

Glejser's Test can be implemented in R software using the glejser function of the skedastic package. It can also be implemented in

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econometrics software.

References

{{Reflist Statistical tests Statistical hypothesis testing