The diagonal elements of the hat matrix are often used to

Chapter 12, Problem 83E

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The diagonal elements of the hat matrix are often used to denote leverage- that is, a point that is unusual in its location in the \(x\) -space and that may be influential. Generally, the \(i\) th point is called a leverage point if its hat diagonal \(h_{i i}\) exceeds \(2 p / n\), which is twice the average size of all the hat diagonals. Recall that \(p=k+1\).
(a) Table
 contains the hat diagonal for the wire bond pull strength data used in Example  Find the average size of these elements.
(b) Based on the preceding criterion, are there any observations that are leverage points in the data set?

Equation Transcription:

     

   

Text Transcription:

x

i

hii    

2p/n  

p=k+1

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