 |
S.O.S. Mathematics CyberBoard
|
| View previous topic :: View next topic |
| Author |
Message |
bluesilver
S.O.S. Oldtimer
Joined: 12 Sep 2004
Posts: 184
|
 Posted: Fri, 20 Oct 2006 18:28:27 UTC Post subject: covariance matrix |
 |
|
I have the question regarding the calculation of the covariance matrix that is used in multiple linear regression models. Suppose that B is the vector of regression coefficients, X is the matrix of the levels of the regressor variables, and σ^2 is the unknown variance of errors. Then X' is the transpose of X, (X'X)^-1 is the inverse of X'X. Then the covariance matrix is
Cov(B) = σ^2 (X'X)^-1
OK, that is what I see in the textbook. So, my question is: can I use the unbiased estimator of σ^2 (i.e., the residual mean square) instead of σ^2 to calculate the covariance matrix above? If not, please tell me of other methods of calculating the covariance matrix. |
|
| Back to top |
|
 |
royhaas
Member of the 'S.O.S. Math' Hall of Fame
Joined: 23 Jun 2003
Posts: 2023
Location: San Antonio,Texas USA
|
| Posted: Fri, 20 Oct 2006 19:24:50 UTC Post subject: |
|
|
Yes, use the MSE. Note that in linear regression the X matrix is treated as a constant, so there are no problems. The MSE will have n-p degrees of freedom for a matrix of column rank p.
_________________
Live long and prosper. |
|
| Back to top |
|
|
Bilbo
Member of the 'S.O.S. Math' Hall of Fame
Joined: 14 Jan 2006
Posts: 690
Location: Yountville, California
|
| Posted: Fri, 20 Oct 2006 19:28:04 UTC Post subject: Re: covariance matrix |
|
|
| bluesilver wrote: | I have the question regarding the calculation of the covariance matrix that is used in multiple linear regression models. Suppose that B is the vector of regression coefficients, X is the matrix of the levels of the regressor variables, and σ^2 is the unknown variance of errors. Then X' is the transpose of X, (X'X)^-1 is the inverse of X'X. Then the covariance matrix is
Cov(B) = σ^2 (X'X)^-1
OK, that is what I see in the textbook. So, my question is: can I use the unbiased estimator of σ^2 (i.e., the residual mean square) instead of σ^2 to calculate the covariance matrix above? If not, please tell me of other methods of calculating the covariance matrix. |
Using an estimate of  provides an estimate of the covariance matrix, not the covariance matrix itself. But estimate is all you can do. |
|
| Back to top |
|
|
bluesilver
S.O.S. Oldtimer
Joined: 12 Sep 2004
Posts: 184
|
| Posted: Fri, 20 Oct 2006 19:28:25 UTC Post subject: |
|
|
| Great. Thank you. I'm just curious - are there also other methods, or there is only one method of calculating the covariance matrix? |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
FAQ 
Search 
Memberlist 
Usergroups
Register
Profile 
Log in to check your private messages 
Log in 
