قارن الطرق

	اختبار بروش-بيجان للتباين غير المتجانس	انحدار المربعات الصغرى العادية (OLS)	الانحدار المربعات الصغرى الموزون (WLS)
المجال	الاقتصاد القياسي	الاقتصاد القياسي	الإحصاء
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1979	2019	1935
صاحب الطريقة	Trevor Breusch & Adrian Pagan	Wooldridge (textbook treatment); classical least squares	Alexander Craig Aitken
النوع	Lagrange-multiplier test for heteroskedasticity	Linear regression	Weighted linear estimator
المصدر التأسيسي	Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
الأسماء البديلة	BP test, Breusch-Pagan-Godfrey test, Lagrange multiplier test for heteroskedasticity, Breusch-Pagan değişen varyans testi	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
ذات صلة	3	5	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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.