Linganisha mbinu

	Kipimo cha Breusch-Pagan cha Usumbufu wa Kigezo (Heteroskedasticity)	Weighted Least Squares (WLS)
Nyanja	Ekonometriki	Takwimu
Familia	Regression model	Regression model
Mwaka wa asili	1979	1935
Mwanzilishi	Trevor Breusch & Adrian Pagan	Alexander Craig Aitken
Aina	Lagrange-multiplier test for heteroskedasticity	Weighted linear estimator
Chanzo asilia	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.
Majina mbadala	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
Zinazohusiana	3	3
Muhtasari	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.