On Aug 30, 2012, at 12:08 AM, m4n14ccc wrote:
Hey
I have a little problem here:
I have an experimental space, lets say [-1,+1]^2, and I fit a second
order
model above it. Regarding the whole experimental space the regression
function maps within [-3,+4], which means nothing else than
f^-1([-3,+4])=[-1,+1]
Now for example the question is: What is f^-1([-1,+2])=?
Is there any inverse function available in order to get the argument
of a
regression function f?
In a general sense such a problem is ill-defined mathematically
because the inverse of a second order quadratic (my assumption
regarding what you meant by "second order") will not necessarily be a
function in the mathematical sense of being one-to-one. You could
first plot and then see if it makes sense to fit a surface to the
point set generated by:
sapply( seq(-1, 1, by=0.01) , f)
(Which could then be limited in your more restricted domain.) You
could then predict those elements in seq(-1, 1, 0.01) which had
corresponding images in f(seq(.)).
It would be more productive if you assembled a test case in R code.
--
David Winsemius, MD
Alameda, CA, USA
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