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EDIT: Given the suggestion of Bill Huber I plan to look at bounds on the errors-in-variables regression by regression both y on x and x on y. … So I will give them both analyses and request at least that they tell the FDA that in addition to do the bootstrap I did inverse regression and bounded the Deming regressions which I think is more appropriate …

Examples of such techniques include Sliced Inverse Regression, Principal Hessian Directions, Sliced Average Variance Estimation, Kernel Sliced Inverse Regression, Principal Components Regression, etc. … Is this SDR/DRR + Regression on a low-dim dataset faster than only regression on a high-dim dataset? …

The usual solution in such cases is "inverse regression" (as described, for instance, in Draper & Smith, Applied Regression Analysis (Second Edition), section 1.7). … Otherwise, these components of variance may need explicitly to be modeled and estimated in the inverse regression analysis. …

There is a relatively simple resolution of this problem: compute a “fiducial limit” based on “inverse regression” [Draper & Smith 1981]. … References Draper, NR and H Smith, 1981: Applied Regression Analysis, Second Edition. John Wiley & Sons, New York. …

Finally, the results of such measurements should be expressed using methods of "inverse regression," or a generalization thereof, as explained in a summary by Lavagnini & Magno writing in Mass Spectrometry …

I was trying to write an answer for this question: Selection of data range changes coefficients too much in lmer (inverse regression) Basically the OP has lots of data of Amplification vs Voltage (see … If I invert the two variables in the regression, does it mean I need to build an errors-in-variables model? …

A problem which you might encounter is regression attenuation or regression dilution. … Except for possibly making some inverse regression ill-posed due to crossing some asymptote or creating negative values in roots logs etcetera. …

Magno, “A statistical overview on univariate calibration, inverse regression, and detection limits: application to gas chromatography/mass spectrometry technique”, Mass Spectrometry Reviews 26 (2007) 1 …

Given we're trying to find an interval for a particular $x$, another way to look at the problem is as a kind of inverse regression problem, but there are some details to sort out here. … A reference: Florenz Plassmann and Neha Khanna (2007) Assessing the Precision of Turning Point Estimates in Polynomial Regression Functions Econometric Reviews, vol. 26, issue 5, pages 503-528 The 2003 …

This is sometimes called an 'inverse regression' problem. … It's probably worth your time to google on this; or rather on one of these: inverse regression -sliced --- (because this avoids some not-so-relevant hits) inverse regression calibration Your problem …

This is what I mean by inverse regression. However I've seen since been playing with some toy models and I'm starting to see that the 'wrong' method produces much better predictions. … Are there other situations where inverse regression actually outperforms? …

There is a special case: sliced inverse regression, where principal components are done on subsets of the data formed by values of the outcome variable. …

In a multivariate context, that is with at least X or Y being a random vector, are there formulae or theorems that link (even remotely) the forward and inverse regression, $\text{E}(X|Y)$ and $\text{E} … *Note : this question is related to dimension reduction trhough the sliced inverse regression technique. …

I mentioned in the comments that you might like to look at inverse regression, but the particular form of your function may preclude getting far with that. …

I have been working on an inverse regression addon for SPSS and using this paper heavily: I. Lavagnini, F. … Magno, A statistical overview on univariate calibration, inverse regression, and detection limits: Application to gas chromatography/mass spectrometry technique., Mass spectrometry reviews 26, 1-18 (2007 …