Park Glejser Test: Numerical Example

To detect the presence of heteroscedasticity using the Park Glejser test, consider the following data.


The step by step procedure of conducting Park Glejser test:

Step 1: Obtain estimate the regression equation

$$\hat{Y}_i = 19.8822 + 4.7173X_i$$

Obtain the residuals from this estimated regression equation:


Take the absolute values of these residuals and consider it as your dependent variables to perform the different functional forms suggested by Glejser.

Step 2: Regress the absolute values of $\hat{u}_i$ on the $X$ variable that is thought to be closely associated with $\sigma_i^2$. We will use the following function forms.

 Functional FormResults
1)$|\hat{u}_t| = \beta_1 + \beta_2 X_i +v_i$

$|\hat{u}_i| = 5.2666-0.00681X_i,\quad R^2=0.00004$

$t_{cal} = -0.014$

2)$|\hat{u}_t| = \beta_1 + \beta_2 \sqrt{X_i} +v_i$

$|\hat{u}_i| = 5.445-0.0962X_i,\quad R^2=0.000389$

$t_{cal} = -0.04414$

3)$|\hat{u}_t| = \beta_1 + \beta_2 \frac{1}{X_i} +v_i$

$||\hat{u}_i| = 4.9124+1.3571X_i,\quad R^2=0.00332$

$t_{cal} = -0.12914$

4)$|\hat{u}_t| = \beta_1 + \beta_2 \frac{1}{\sqrt{X_i}} +v_i$

$\hat{u}_i| = 4.7375+1.0428X_i,\quad R^2=0.00209$

$t_{cal} = 0.10252$

Since none of the residual regression is significant, therefore, the hypothesis of heteroscedasticity is rejected. Therefore, we can say that there is no relationship between the absolute value of the residuals ($u_i$) and the explanatory variable $X$.

Error Variance is Proportional to Xi: Park Glejser Test

How to perform White General Heteroscedasticity?

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

You may also like...

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

x Logo: Shield Security
This Site Is Protected By
Shield Security