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

2009-10-11 Thread John Fox
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

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

2009-10-11 Thread 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...

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

2009-10-11 Thread John Fox
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) > >

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

2009-10-11 Thread Gabor Grothendieck
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 =

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

2009-10-11 Thread Peng Yu
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! __ R-help@r-project.org mailing list https: