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→Uncorrelated residuals: I suspect that what was intended was that the _errors_, rather than the residuals, are uncorrelated. |
→Correlated residuals: ditto: _errors_, not _residuals_ |
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The hat matrix has a number of useful algebraic properties.<ref>Gans, P. (1992) ''Data Fitting in the Chemical Sciences,'', Wiley. ISBN 978-0-471-93412-7</ref><ref>Draper, N.R., Smith, H. (1998) ''Applied Regression Analysis'', Wiley. ISBN 0-471-17082-6</ref> Practical applications of the hat matrix in regression analysis include [[Leverage (statistics)|leverage]] and [[Cook's distance]], which are concerned with identifying observations which have a large effect on the results of a regression.
==Correlated
The above may be generalized to the case of correlated
:<math> \hat{\boldsymbol{\beta}} = \left(X^\top \Sigma^{-1} X \right)^{-1} X^\top \Sigma^{-1}\,\mathbf{y}, </math>
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the hat matrix is thus
:<math> H = X \left(X^\top \Sigma^{-1} X\right)^{-1} X^\top \Sigma^{-1}, \, </math>
and again it may be seen that ''H''<sup>2</sup> =
== See also ==
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