XLSTAT: Breusch-Pagan & White Heteroscedasticity Tests in Excel

 

Background

Heteroscedasticity tests imply the two following hypotheses.

• H0 (null hypothesis): data is homoscedastic.

• Ha (alternative hypothesis): data is heteroscedastic.

If the p-value associated to a heteroscedasticity test falls below a certain threshold (0.05 for example), we can conclude that the data is significantly heteroscedastic.

 

Dataset for Example

The attached data is an artificial dataset which tests the effect of age on sugar content and fruit size via two linear regressions. The sugar content regression shows homoscedasticity; the size regression shows strong heteroscedasticity. 

The Sugar content variable is created as twice the Age plus a random normal error, representing independent and identically distributed residuals. For Size, residuals are Age multiplied by the random error, making them clearly dependent.

The goal is to check if residual variability changes with age (heteroscedasticity). Breusch-Pagan and White tests are used to compare homoscedastic and heteroscedastic cases.

 

Setting Up

• Open XLSTAT.

• Click on the Forecasting/ Time series analysis menu and select the Tests for heteroscedasticity feature.

In the General tab:

• Select the Residuals(Sugar) column in the Residuals box, and the Age column in the explanatory variables box.

• Check the White test checkbox.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet

Repeat the same procedure with the Residuals(Size) column selected in the Residuals box.

 

Interpreting the Results

For the Sugar content variable, the residuals / Age chart shows a relatively homogeneous distribution of residuals along the Age variable.

Furthermore, both tests show high p-values (0.322 for the Breusch-Pagan test and 0.296 for the White test) suggesting that we cannot reject the null hypothesis that the residuals are homoscedatstic

For the Size variable, the residuals / Age chart shows that residuals clearly become more variable as the fruits grow older. This cone-like shape is a very common case of heteroscedasticity.

Both tests yield p-values well below 0.05, leading us to reject the null hypothesis of homoscedastic residuals, consistent with the chart.