4. Process Modeling 4.4. Data Analysis for Process Modeling 4.4.3. How are estimates of the unknown parameters obtained? 4.4.3.2. Weighted Least Sum of Squares
	As mentioned in Section 4.1, weighted least sum of squares (WLSS) regression is useful for estimating the values of model parameters when the data points being used differ in quality from one another on average. As suggested by the name, parameter estimation by the method of weighted least sum of squares is closely related to parameter estimation by "regular", "unweighted" or "equally-weighted" least sum of squares.
General WLSS Criterion	In weighted least squares parameter estimation, as in regular least squares, the unknown values of the parameters, , in the regression function are estimated by finding the numeric values for the parameters that minimize the sum of the squared deviations between the observed responses and the functional portion of the model. Unlike least squares, however, 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. The weighted least sum of squares criterion that is minimized to obtain the parameter estimates is
Some Points Mostly in Common with Regular LSS (But Not Always!!!)	Like regular least squares estimates: The weighted least squares estimates are denoted by to emphasize the fact that the estimates are not the same as the true values of the parameters. are treated as the variables in the optimization while values of the response and predictor variables and the weights are treated as constants. The parameter estimates will be functions of both the predictor and response variables and will generally be correlated with one another. (WLSS estimates are also functions of the the weights, .) Weighted least squares minimization is usually done analytically for linear models and numerically for nonlinear models.