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The '''hat matrix''', '''H''', is used in [[statistics]] to relate [[errors]] in [[residuals]] to [[observational error|experimental errors]]. Suppose that a [[linear least squares]] problem is being addressed. The model can be written as
:<math>\mathbf{y^{calc}=Jp}</math>
where '''J''' is a matrix of coefficients and '''p''' is a vector of parameters. The solution to the un-weighted least-squares equations is given by
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