قارن الطرق

	المربعات الصغرى الموزونة غير الخطية (NWLS)	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	1960s–1980s (formalized in applied econometrics)	2019	1935
صاحب الطريقة	Extension of Gauss-Newton nonlinear least squares with Aitken-type weighting	Wooldridge (textbook treatment); classical least squares	Alexander Craig Aitken
النوع	Nonlinear regression estimator	Linear regression	Weighted linear estimator
المصدر التأسيسي	Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson Education. ISBN: 978-0134461366	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	NWLS, nonlinear weighted least squares, weighted nonlinear regression, heteroscedasticity-corrected nonlinear regression	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	Nonlinear Weighted Least Squares combines the flexibility of nonlinear regression with the variance-stabilizing power of observation-level weights. It minimises a weighted sum of squared residuals around a user-specified nonlinear mean function, making it the method of choice when the relationship is inherently nonlinear and error variance differs across observations.	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.