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least squares, method of

least squares, method of A method of estimating parameters in a model by minimizing the sum of squares of differences between observed and theoretical values of a variable. If yi, i = 1,…,n,

is a sample of n observations, and μi is a set of theoretical values corresponding to a set of unknown parameters, θ, and a set of known associated observations, xi, then the criterion to be minimized with respect to variations in θ is the sum of squares, Σ(yi – μi)2

The values of θ at which the minimum occurs are known as least squares estimates.

The method of weighted least squares is used when each observation is associated with a weight, wi (see measures of location), and the criterion to be minimized is Σwi(yi – μi)2

See also likelihood, regression analysis.

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