Weighting Least Square Regression - Arizona Department of Health Services
Weighted Least Square Regression
Definition
Each term in the weighted least squares criterion includes an additional weight, that determines how much each observation in the data set influences the final parameter estimates and it can be used with functions that are either linear or nonlinear in the parameters.
Section 4.4.3.2
Weighted Least Square Regression
One of the common assumptions underlying most process modeling methods, including linear and nonlinear least squares regression, is that each data point provides equally precise information about the deterministic part of the total process variation.
In other words, it is assumed that the standard deviation of the error term is constant over all values of the predictor or explanatory variables. This assumption, clearly does not hold, even approximately, in every modeling application.
Ref: NIST, Section 4.1.4.3
Weighted Least Square Regression
One of the common assumptions underlying most process modeling methods, including linear and nonlinear least squares regression, is that each data point provides equally precise information about the deterministic part of the total process variation.
In other words, it is assumed that the standard deviation of the error term is constant over all values of the predictor or explanatory variables. This assumption, clearly does not hold, even approximately, in every modeling application.
Ref: NIST, Section 4.1.4.3
In a weighted fit, less weight is given to the less precise measurements and more weight to more precise measurements when estimating the unknown parameters in the model.
Using weights that are inversely proportional to the variance at each level of the explanatory variables yields the most precise parameter estimates possible.
Ref: NIST, Section 4.1.4.3
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