Hat matrix

In statistics, the projection matrix ${\displaystyle \mathbf {P} }$, sometimes also called the influence matrix or hat matrix ${\displaystyle \mathbf {H} }$, maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on each fitted value. The diagonal elements of the projection matrix are the leverages, which describe the influence each response value has on the fitted value for that same observation.

If the vector of response values is denoted by ${\displaystyle \mathbf {y} }$ and the vector of fitted values by ${\displaystyle \mathbf {\hat {y}} }$,

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