Critical Inquiry Exam 2 Practice 2026 - Free Practice Questions and Study Guide

Heteroscedasticity means the spread of the errors changes with the level of the explanatory variables. The Breusch-Pagan test is built to detect exactly this: it takes the residuals from your regression, squares them, and then regresses those squared residuals on the original predictors (and sometimes their powers or cross-products). If the predictors help explain why the residuals vary, you’ll see a significant relationship, which shows up as a large R-squared in this auxiliary regression. The test uses that R-squared to form a statistic that follows a chi-square distribution under homoscedasticity, giving you a formal decision rule.

This approach is standard in regression because it ties the variance structure directly to the variables in your model, unlike some other tests. The Durbin-Watson test, for instance, targets autocorrelation in residuals rather than changes in variance over the data. The Shapiro-Wilk test checks whether residuals are normally distributed, not whether their spread changes with predictors. Levene’s test compares variances across groups, which is a different setup than regression-based heteroscedasticity.