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The Hat Matrix in Regression and ANOVA

David C. Hoaglin and Roy E. Welsch
The American Statistician
Vol. 32, No. 1 (Feb., 1978), pp. 17-22
DOI: 10.2307/2683469
Stable URL: http://www.jstor.org/stable/2683469
Page Count: 6
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The Hat Matrix in Regression and ANOVA
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Abstract

In least-squares fitting it is important to understand the influence which a data y value will have on each fitted y value. A projection matrix known as the hat matrix contains this information and, together with the Studentized residuals, provides a means of identifying exceptional data points. This approach also simplifies the calculations involved in removing a data point, and it requires only simple modifications in the preferred numerical least-squares algorithms.

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