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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} = \mathbf{X \beta} + \mathbf{ \
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
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