Dear Simon,
> -Original Message-
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
On
> Behalf Of Simon Bonner
> Sent: October-11-09 2:33 PM
> To: Peng Yu
> Cc: r-h...@stat.math.ethz.ch
> Subject: Re: [R] Why H1=1? (H's the hat matrix)
&g
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...
ected onto itself.
Regards,
John
> -Original Message-
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
On
> Behalf Of Peng Yu
> Sent: October-11-09 2:03 PM
> To: r-h...@stat.math.ethz.ch
> Subject: [R] Why H1=1? (H's the hat matrix)
>
>
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 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 =
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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