The Breusch-Pagan test is a statistical procedure for testing whether the variance of errors in a regression model depends on values of the explanatory variables. It fits an auxiliary regression of squared OLS residuals on the predictors, computes a test statistic as N×R² from that auxiliary regression, and compares it to a chi-squared distribution with k degrees of freedom. Parameters: the test operates on OLS residuals from a fitted regression model, uses a chi-squared reference distribution, and requires normally distributed errors for the exact test (robust variants exist for non-normal errors). Persistence mechanism: implemented in all major statistical software packages (R, Python statsmodels, Stata) and codified in regression analysis textbooks. [formal: breusch-pagan | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
breusch-pagan test
The Breusch-Pagan test is a statistical procedure for testing whether the variance of errors in a regression model depends on values of the explanatory variables. It fits an auxiliary regression of squared OLS residuals on the predictors,…
Definition
Why it is in scope
A human-made statistical test for detecting heteroscedasticity (non-constant variance of errors) in regression models. It works by regressing squared residuals on explanatory variables and testing whether they explain significant variation — built to persist through statistical practice and software implementation.
Names and aliases
- breusch-pagan testen · CANONICAL
Relations from this entry
- cmskmodwa04zunobpymq3i7ifINSTANCE_OF →
The Breusch-Pagan test is a statistical test for heteroscedasticity in regression models. It IS a specific kind of regression diagnostic: a formal hypothesis test that determines whether grouped variance in the errors is related to the predictors.
- cmsm60g0j00jt1q13798ptex4INSTANCE_OF →
The Breusch-Pagan test is a specific kind of statistical test used to detect heteroscedasticity in regression residuals. It follows the standard structure: null hypothesis of homoscedasticity, a chi-squared test statistic, and a decision rule. A competent speaker would call it 'a statistical test.' Specific→general.
- cmsdai2d503n23vv3e00xn5baDEPENDS_ON →
The breusch-pagan test detects heteroscedasticity in regression residuals. Its entire operational framework is regression — remove regression and the test has no residuals to analyze. This passes the Law 8 removal test.
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- Created
- Aug 8, 2026, 11:17 PM UTC
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- 42c7d62dcb0fdadb9019236d1113952e7fa22aa14cb04614b751c7e0d31feb95