This cone-like shape is a very common case of heteroscedasticity. Interpretationįor the Sugar content variable, the residuals / Age chart shows a relatively homogeneous distribution of residuals along the Age variable.įurthermore, 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.įor the Size variable, the residuals / Age chart shows that residuals clearly become more variable as the fruits grow older. Repeat the same procedure with the Residuals(Size) column selected in the Residuals box. The results of this first analysis are displayed in a new sheet. Check the White test checkbox and launch the analysis by clicking on the OK button. Select the Residuals(Sugar) column in the Residuals box, and the Age column in the explanatory variables box. Open the XLSTAT menu and click on Time / Tests for heteroscedasticity. Performing Breusch-Pagan and White heteroscedasticity tests in XLSTAT Therefore, if the p-value associated to a heteroscedasticity test falls below a certain threshold (0.05 for example), we would conclude that the data is significantly heteroscedastic. Ha (alternative hypothesis): data is heteroscedastic. H0 (null hypothesis): data is homoscedastic. Heteroscedasticity tests imply the two following hypotheses. Breusch-Pagan and White heteroscedasticity tests: what hypothesis are we testing? We will use the Breusch-Pagan and White heteroscedasticity tests to show how these tests work in two extreme situations: homoscedasticity and strong heteroscedasticity. This is a typical case of heteroscedasticity. Compare babies to adults: babies have relatively “standard” heights whereas adult heights are very variable. Very often, the size of an organism is more variable with age. If that is the case, we speak about heteroscedasticity. Technically, we are asking if regression residuals are heterogeneously distributed along the explanatory variable. The aim of this tutorial is to check if the variability of a dependent variable (for example: sugar content or size) changes with an explanatory variable (age) in a linear regression. To see how we technically generated the data, please go to the last section of this tutorial.

The first regression (sugar content) presents homoscedasticity whereas the second (size) is strongly heteroscedastic. Residuals of the two regressions are displayed in the dataset. We used sugar content and size as dependent variables in the first and in the second regression, respectively. Two simple linear regressions were carried out considering age as the explanatory variable. The data correspond to an experiment aiming at testing the effect of age (measured in days) on sugar content and on size of a new fruit variety. Dataset for running Breusch-Pagan and White heteroscedasticity tests in XLSTATįor this tutorial we use an artificial dataset we built on purpose to compare a homoscedastic model to another one with strong heteroscedasticity. This tutorial will help you run and interpret heteroscedasticity tests - Breusch-Pagan & White tests - in Excel using the XLSTAT software.

P value with xlstat