# Follow-up: [R] Inverse prediction with R?

Martyn Plummer plummer at iarc.fr
Tue Feb 22 15:08:54 CET 2000

```My \$0.02.

If y ~ a + b * (x - xbar) where xbar is the mean of the observed x values,
then a 95% confidence region for x given a new value of y may be obtained
by solving the inequality

abs (y - ahat - bhat * (x - xbar)) /
sqrt (Var(ahat) + (x - xbar)^2 * Var(bhat)) <= 1.96

where ahat, bhat are your estimates of a and b.  If b is significantly
different from 0 at the 5% level then this is a (usually rather skew)
interval, otherwise it may be the whole real line or two intervals.

As Brian says, this is the calibration problem. Most of the literature on
it comes from technometrics, whic isn't my field.  I found the following
review useful when I looked into this some years ago.

Osborne, C. Statistical Calibration: A Review, Intenational Statistical
Review, 51, 309-336, 1991.

Martyn
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