Covariance Matrix for Unstandardized Regression Coefficient Estimates

[cristiano1974]

Dear listers,
 I'd like to understand how to interpret the coefficients of variance-covariance matrix obtained from linear regression.

Is there any paper about it?

Any help would be really appreciated.

Thanks

Cristiano.

[Bruce Weaver]

cristiano74 wrote

Dear listers,
 I'd like to understand how to interpret the coefficients of
variance-covariance matrix obtained from linear regression.
Is there any paper about it?

Any help would be really appreciated.

Thanks

Cristiano.

If you're talking about the covariance matrix for the  regression parameters, which is via "COVB ('savfile'|'dataset')", the numbers on the main diagonal give the variances of the regression coefficients.  The square roots of those variances are the standard errors shown in your table of regression coefficients.  The off-diagonal terms are covariances between pairs of regression coefficients.  If you would rather see them as correlations, use "CORB ('savfile'|'dataset')" instead of "COVB ('savfile'|'dataset')".

[cristiano1974]

Thanks Bruce,

 but if I have the covariance beetween the regression coefficients'work' and 'education' of 0.4, what I can say? It's quite different from Pearson's coefficient, isn't it?

Thanks again for your collaboration.

C.

On Fri, Jan 15, 2010 at 4:27 PM, Bruce Weaver <[hidden email]> wrote:

cristiano74 wrote:
>
> Dear listers,
>  I'd like to understand how to interpret the coefficients of
> variance-covariance matrix obtained from linear regression.
> Is there any paper about it?
>
> Any help would be really appreciated.
>
> Thanks
>
> Cristiano.
>
>

If you're talking about the covariance matrix for the  regression
parameters, which is via "COVB ('savfile'|'dataset')", the numbers on the
main diagonal give the variances of the regression coefficients.  The square
roots of those variances are the standard errors shown in your table of
regression coefficients.  The off-diagonal terms are covariances between
pairs of regression coefficients.  If you would rather see them as
correlations, use "CORB ('savfile'|'dataset')" instead of "COVB
('savfile'|'dataset')".



-----
--
Bruce Weaver
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http://sites.google.com/a/lakeheadu.ca/bweaver/
"When all else fails, RTFM."

NOTE:  My Hotmail account is not monitored regularly.
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[Bruce Weaver]

cristiano74 wrote

Thanks Bruce,
 but if I have the covariance beetween the regression coefficients'work' and
'education' of 0.4, what I can say? It's quite different from Pearson's
coefficient, isn't it?

Thanks again for your collaboration.

C.

Covariances are not in standardized units, so the are not restricted to the range -1 to 1, and the value changes when you change units of measurement.  That makes interpretation of a number like 0.4 difficult.  You might be better working off with the corresponding correlation matrix if you want to interpret things in that way.  

I think the only time I've used the covariance matrix for the parameters has been if I wanted to test the difference between a couple parameters.  The covariance between the two is needed to work out the standard error  of the difference between 2 parameters.  

  Variance error of difference = Var(parameter 1) + Var(parameter 2) - 2*Cov(1,2)
  SE of difference = SQRT(variance error of difference)

[Hector Maletta]

Besides what Bruce says, note that correlation coefficients equal the
covariance divided by a product of functions of the relevant standard
deviations (sqrt of 1-SD), therefore one can easily transform one matrix
into the other.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Bruce Weaver
Sent: 15 January 2010 16:29
To: [hidden email]
Subject: Re: Covariance Matrix for Unstandardized Regression Coefficient
Estimates

cristiano74 wrote:

>
> Thanks Bruce,
>  but if I have the covariance beetween the regression coefficients'work'
> and
> 'education' of 0.4, what I can say? It's quite different from Pearson's
> coefficient, isn't it?
>
> Thanks again for your collaboration.
>
> C.
>
>

Covariances are not in standardized units, so the are not restricted to the
range -1 to 1, and the value changes when you change units of measurement.
That makes interpretation of a number like 0.4 difficult.  You might be
better working off with the corresponding correlation matrix if you want to
interpret things in that way.

I think the only time I've used the covariance matrix for the parameters has
been if I wanted to test the difference between a couple parameters.  The
covariance between the two is needed to work out the standard error  of the
difference between 2 parameters.

  Variance error of difference = Var(parameter 1) + Var(parameter 2) -
2*Cov(1,2)
  SE of difference = SQRT(variance error of difference)



-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/
"When all else fails, RTFM."

NOTE:  My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.
--
View this message in context:
http://old.nabble.com/Covariance-Matrix-for-Unstandardized-Regression-Coeffi
cient-Estimates-tp27175862p27182427.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

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[hidden email] (not to SPSSX-L), with no body text except the
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