[R] Why H1=1? (H's the hat matrix)

[Simon Bonner]

Another, less geometric, way to think about this:

The fitted response for a linear model is a weighted average of the
observed responses. The i-th row of the hat matrix list the coefficients
of the average for the i-th fitted value. These values sum to 1 for each
row, and so H %*% 1=1.

Cheers...

-  
Simon Bonner
Post-Doctoral Fellow
Department of Statistics, UBC

www.simon.bonners.ca


On Sun, 2009-10-11 at 14:09 -0400, Gabor Grothendieck wrote:
> H projects vectors onto the range of X so any vector already in the
> range of X gets projected onto itself.
> 
> On Sun, Oct 11, 2009 at 2:03 PM, Peng Yu <pengyu.ut at gmail.com> wrote:
> > Suppose I have the following hat matrix:
> >
> > H=X(X'X)^{-1}X'
> > X is a n by p matrix, where n >= p and X_{i,1} = 1
> >
> > I'm wondering why H1 = 1. (Here, 1 is column vector, whose each
> > element is the number 1)
> >
> > Thank you!
> >
> > ______________________________________________
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> >
> 
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.
>