the hat matrix can be used to define the [[degrees of freedom (statistics)#Effective degrees of freedom|effective degrees of freedom]] of the model.
SomeThe otherhat propertiesmatrix ofhas thea hatnumber matrixof areuseful summarized inalgebraic 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 anlysis 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.
