विधियों की तुलना करें

	विषमता के लिए ब्रुश-पेगन परीक्षण	साधारण न्यूनतम वर्ग (OLS) समाश्रयण	भारित न्यूनतम वर्ग (Weighted Least Squares - WLS)
क्षेत्र	अर्थमिति	अर्थमिति	सांख्यिकी
परिवार	Regression model	Regression model	Regression model
उद्भव वर्ष	1979	2019	1935
प्रवर्तक	Trevor Breusch & Adrian Pagan	Wooldridge (textbook treatment); classical least squares	Alexander Craig Aitken
प्रकार	Lagrange-multiplier test for heteroskedasticity	Linear regression	Weighted linear estimator
मौलिक स्रोत	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.
उपनाम	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
संबंधित	3	5	3
सारांश	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.