Linear Least Squares (mathematics) - Weighted Linear Least Squares

Weighted Linear Least Squares

See also: Least squares#Weighted least squares See also: Weighted mean

In some cases the observations may be weighted—for example, they may not be equally reliable. In this case, one can minimize the weighted sum of squares:

where wi > 0 is the weight of the ith observation, and W is the diagonal matrix of such weights.

The weights should, ideally, be equal to the reciprocal of the variance of the measurement. The normal equations are then:

This method is used in iteratively reweighted least squares.

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