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For the case of linear models with [[independent and identically distributed]] errors in which '''V''' = σ<sup>2</sup>'''I''', this reduces to ('''I''' - '''H''')σ<sup>2</sup><ref name="Hoaglin1977"/>.
For [[linear models]], the [[trace (linear algebra)|trace]] of the hat matrix is equal to the [[rank (linear algebra)|rank]] of '''X''', which is the number of independent parameters of the linear model.
For other models such as LOESS that are still linear in the observations '''y''',
the hat matrix can be used to define the [[degrees of freedom (statistics)#Effective degrees of freedom|effective degrees of freedom]] of the model.
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