Following from Pregibon 1981 the hat matrix is defined by HW12XXTWX 1 XTW12 ½613. 1 Hat Matrix 11 From Observed to Fitted Values The OLS estimator was found to be given by the p 1 vector b XT X 1XT y. In statistics the projection matrix sometimes also called the influence matrix or hat matrix maps the vector of response values dependent variable values to the vector of fitted values or predicted values.
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