Weighted least squares

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

Related Topics:
Linear regression - Least squares - Minimization

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

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

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

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

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: w_i = 1/sigma^2.

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