قارن الطرق

	اختبار بروش-بيجان للتباين غير المتجانس	الانحدار المربعات الصغرى الموزون (WLS)	اختبار وايت لعدم تجانس التباين
المجال	الاقتصاد القياسي	الإحصاء	الاقتصاد القياسي
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1979	1935	1980
صاحب الطريقة	Trevor Breusch & Adrian Pagan	Alexander Craig Aitken	Halbert White
النوع	Lagrange-multiplier test for heteroskedasticity	Weighted linear estimator	General test for heteroskedasticity
المصدر التأسيسي	Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294.	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.	White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
الأسماء البديلة	BP test, Breusch-Pagan-Godfrey test, Lagrange multiplier test for heteroskedasticity, Breusch-Pagan değişen varyans testi	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares	White's general heteroskedasticity test, White değişen varyans testi
ذات صلة	3	3	3
الملخص	The Breusch-Pagan test, introduced by Trevor Breusch and Adrian Pagan in 1979, is a Lagrange-multiplier test for heteroskedasticity — the condition where the variance of a regression's errors changes with the explanatory variables. It works by regressing the squared OLS residuals on candidate variables and checking whether they explain any of the residual variation, signalling that the constant-variance assumption is violated.	Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated.	The White test, introduced by Halbert White in 1980, is a general test for heteroskedasticity that makes no assumption about its functional form. It regresses the squared OLS residuals on the regressors, their squares, and their cross-products, so it can detect heteroskedasticity related to any of these terms. The same 1980 paper introduced the heteroskedasticity-consistent ('White') standard errors that are the standard remedy when the test rejects.