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STAT 350: Lecture 9

Here is an example of some of the matrix algebra I was doing in class. Consider the weighing design where two objects of weights tex2html_wrap_inline63 and tex2html_wrap_inline65 are weighed individually and together. The resulting design matrix is

displaymath67

So

displaymath69

and

displaymath71

The hat matrix is

displaymath73

which is

displaymath75

Notice that the trace of H is 2 which is the number of parameters in tex2html_wrap_inline79 .

You can also check that H is idempotent.

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Richard Lockhart
Mon Mar 3 13:01:03 PST 1997