R help - Nov 2008 - function for simultaneous confidence interval of regression coefficients

List,

Would someone be so kind as to point me to a function that will calculate
simultaneous confidence intervals of regression coefficients based upon
their distribution as (under the assumption of normal errors, with
\mathbf{X} as the design matrix):

$\hat{\mathbf{\beta}} \sim N(\mathbf{\beta},
\sigma^2(\mathbf{X}^T\mathbf{X})^{-1})$.


'confint' calculates individual coefficients so far as I can tell, but I
need simultaneous CIs based on the confidence ellipse/ F distribution.
Inverting the ellipse gives this equation:

\mathbf{\hat{\beta}} \pm
\sqrt{\mathrm{diag}(s^2(\mathbf{X}^T\mathbf{X})^{-1}) \times p \times F_{p,
n-p, .95}}

Thanks, and sorry for such a dumb question.  Either I am not searching for
the right thing or this hasn't already been addressed in the lists (perhaps
because it is so easy).

Kyle

	[[alternative HTML version deleted]]

see
?coef  # extract the estimates
?vcov  #  extract their covariance matrix
?qf  # get the F quantile of interest

Also, you may be interested in

?car::ellipse
?ellipse::ellipse.lm
?gmodels::glht.test

hth,

Kingsford Jones


On Sat, Nov 29, 2008 at 4:30 PM, Kyle Matoba <kylematoba at gmail.com>
wrote:
> List,
>
> Would someone be so kind as to point me to a function that will calculate
> simultaneous confidence intervals of regression coefficients based upon
> their distribution as (under the assumption of normal errors, with
> \mathbf{X} as the design matrix):
>
> $\hat{\mathbf{\beta}} \sim N(\mathbf{\beta},
> \sigma^2(\mathbf{X}^T\mathbf{X})^{-1})$.
>
>
> 'confint' calculates individual coefficients so far as I can tell,
but I
> need simultaneous CIs based on the confidence ellipse/ F distribution.
> Inverting the ellipse gives this equation:
>
> \mathbf{\hat{\beta}} \pm
> \sqrt{\mathrm{diag}(s^2(\mathbf{X}^T\mathbf{X})^{-1}) \times p \times F_{p,
> n-p, .95}}
>
> Thanks, and sorry for such a dumb question.  Either I am not searching for
> the right thing or this hasn't already been addressed in the lists
(perhaps
> because it is so easy).
>
> Kyle
>
>        [[alternative HTML version deleted]]
>
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