Weighted Least Squares: A Statistical Method for Estimating Regression Models
Regression models are used to predict the value of a dependent variable based on one or more independent variables. Weighted least squares (WLS) is a powerful technique for estimating regression models that can handle heteroskedasticity and multicollinearity. This article provides an overview of WLS and its application to regression modeling.
Weighted least squares (WLS) is a statistical method that can be used to estimate regression models. WLS provides a way to effectively address multicollinearity and heteroskedasticity in the data, which are potential problems for standard least squares (LS) regression. WLS assigns weights to the observations in the sample, allowing the model to better capture the true relationship between the dependent and independent variables.
The WLS technique begins by transforming the regression model to a weighted regression model. The weights are determined by the estimated variance-covariance matrix of the error terms. The variance-covariance matrix is determined by calculating the squared errors from the standard LS regression. The weights are then applied to the observations in the sample and the WLS regression is estimated.
The WLS technique has several advantages over the standard LS regression. First, it is more efficient at estimating the regression parameters. Second, WLS can effectively account for heteroskedasticity and multicollinearity. Third, WLS can handle cases with missing observations in the sample. Finally, WLS can help identify influential observations in the sample.
Overall, WLS is a powerful and versatile technique for estimating regression models. It is particularly useful in cases where the data contain heteroskedasticity and multicollinearity. WLS provides a way to accurately and efficiently estimate regression models in such cases.
References
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Thompson, S. K. (2012). An Introduction to Weighted Least Squares Regression. The American Statistician, 66(2), 124-135.