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Suppose that we wish to solve a [[linear model]] using [[linear least squares]]. The model can be written as
:<math>\mathbf{y} = X \boldsymbol \beta + \boldsymbol \varepsilon,</math>
where ''X'' is a matrix of explanatory variables (the [[design matrix]]), '''''β''''' is a vector of unknown parameters to be estimated, and '''''ε''''' is the error vector.
The estimated parameters are
:<math>\hat \boldsymbol \beta = \left(X^\top X \right)^{-1} X^\top \mathbf{y},</math>
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