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Weighted least squares

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Weighted least squares is a method of regression, similar to least squares in that it uses the same minimization of the sum of the residuals:

 S = \sum_{i=1}^n (y_i - f(x_i))^2.

However, instead of weighting all points equally, they are weighted such that points with a greater weight contribute more to the fit:

 S = \sum_{i=1}^n w_i(y_i - f(x_i))^2.

Often, wi is given as the inverse of the variance, giving points with a lower variance a greater statistical weight:

 w_i = 1/\sigma_i^2.
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