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The diagonal elements of the hat matrix are the [[leverage (statistics)|leverage]]s, which describe the influence each observed value has on the fitted value for that same observation.
If the vector of observed values is denoted by '''y''' and the vector of fitted values by <math>\hat{\mathbf{y}}
:<math>\hat{\mathbf{y}} = \mathbf{H y}.</math>
As <math>\hat{\mathbf{y}}</math> is usually pronounced "y-hat", the hat matrix is so named as it "puts a hat on '''y'''".
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