Dale, a quick response before my 2:00 class.
What does your correspondent want the SE _of_?
It rather looks as though the question dealt with the SE of a single
(new) observation at a particular value of (X1, X2, ...). If this
is indeed the question, Draper & Smith deal with it in their section
on the uncertainty about predicted values (of, in general, n observations
at a particular spot in the space of the predictors; if n = 1 we have
the case I mentioned above). Sorry, my copy is 60 miles away just now,
can't give you a page reference.
I believe D&S's formulae are based on an assumption that the
residuals are homoscedastic. If this is not the case in the querent's
data, either (a) the problem is somewhat more complicated, or (b) a
nonlinear transformation of the response variable (probably) or the
predictor(s) (maybe) or both (maybe) might be in order. (Notice that
(b) does not necessarily negate (a) ! )
OTOH, if I've mis-guessed what the querent's question was,
perhaps others will mis-guess it too: in which case a clarification
of the query might be helpful.
-- Don.
On Wed, 12 Apr 2000, Dale Glaser wrote:
> A colleague sent the following to me at work today and after perusal of
> various texts (Neter et al, Pedhazur, Cohen, etc.) I am unable to give
> anything but an opinion.......here is what he sent:
>
> "Can you answer me the following question. It concerns what is the
> appropriate standard error (SE) from a curve fitting program when what one
> wants to plot is derived from a COMBINATION of certain parameters, each of
> which has its own SE, specifically,
> I fit parabolas to some data, sensitivity (y) as a function of pupil
> position (x)
> y = ax^2 + bx + c
> >From trivial Calculus, the peak of this function is at -b/2a
>
> Now, I have seperate SEs for a, b and c from the fits.
> What is the best SE to use for -b/2a ? For example, do the SEs add?"
>
> At first he proposed an equation that took the square root of the variance
> of the estimates, i.e., sqrt(SE^2 lin + SE^2 quad). My feeling was that
> given the partialed nature of standard errors in a multiple regression
> context, it may be misleading to add the respective standard errors, e.g.,
> SE for the linear component + SE for the quadratic component, etc.,
> especially given the collinearity (if centering not performed) of the terms.
> However, I also understand that variance components can be additive. Anyway,
> if anyone has a general opinion I would be most appreciative as I am a bit
> stumped on this one...............thank you...........dale glaser
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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