Your question sounds as though you're really interested in the precision
with which a predicted value can be estimated. If that is what you had
in mind, consult a good text on regression (Draper & Smith, e.g.) and
look in the index, or the Table of Contents, for "Variance of Y-hat" or
"precision of predicted value" or "confidence limits for the true mean
value of Y". The formula involves X'CX where X is the vector of values
of the predictor for these unknown observations, X' is its transpose,
and C is the variance-covariance matrix among all the predictors.
It thus includes the effect of the leverage of this point on the
uncertainty in the predicted value Y-hat.
If you want a discussion of leverage per se, as a concept and as a
figure of speech, ask again. -- DFB.
On Wed, 11 Feb 2004, Rajarshi Guha wrote:
> I know that when I create a multiple linear regression model I can
> evaluate leverage values for the points used to create the model.
>
> >From what I understand leverage gives an indication of how much a
> given observation affects the coefficients in the model. Thus when I
> use the model to predict values for some unknown observations (ie
> observations not used to create the model) calculating leverage values
> for these observations does not make sense - is this correct?
It makes sense; but whether it is useful for what you want to do with
it is another question. The leverage value for each observation is
inherent in its X coordinates, and thus implicitly present, whether you
find it convenient to calculate a formal leverage value or not.
> If the above is true is there any measure that I could use (apart from
> R2 values or residuals) that I can use to obtain some indication of
> how the good the coefficients are when predicting unknown observations
> (sort of a 'reverse leverage' value)?
I would have thought (as I wrote above) that your underlying question
was less about the precision of the coefficients ("how good the
coefficients are") than about the precision of the predictions you want
to make for these unknown observations. -- D.
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816
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