# 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 *y _{i}*,

*i*= 1,…,

*n*,

is a sample of

*n*observations, and μ

*is a set of theoretical values corresponding to a set of unknown parameters, θ, and a set of known associated observations,*

_{i}*x*, then the criterion to be minimized with respect to variations in θ is the sum of squares, Σ(

_{i}*y*– μ

_{i}*)*

_{i}^{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,

*w*(see measures of location), and the criterion to be minimized is Σ

_{i}*w*(

_{i}*y*– μ

_{i}*)*

_{i}^{2}

See also likelihood, regression analysis.

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