Glejser test

In statistics, the Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser (fr: Herbert Glejser), regresses the residuals on the explanatory variable 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 and find the sample residuals ei.

Step 2: Regress the absolute value |ei| on the explanatory variable that is associated with the heteroscedasticity.



\begin{align} \end{align} $$
 * e_i| & = \gamma_0 + \gamma_1 X_i + v_i \\[8pt]
 * e_i| & = \gamma_0 + \gamma_1 \sqrt{X_i} + v_i \\[8pt]
 * e_i| & = \gamma_0 + \gamma_1 \frac 1 {X_i} + v_i

Step 3: Select the equation with the highest R2 and lowest standard errors to represent heteroscedasticity.

Step 4: Perform a t-test on the equation selected from step 3 on γ1. If γ1 is statistically significant, reject the null hypothesis of homoscedasticity.

Software Implementation
Glejser's Test can be implemented in R software using the  function of the   package. It can also be implemented in SHAZAM econometrics software.