Post-regression prediction of independent variable

[filipepaula]

I have fitted a 2nd degree polynomial non-linear function to data. Specifically, data is from an immunoassay where dosage produces an OD (measured response).
Is it possible to predict concentration values based on that model, starting from ODs?

Meaning, is it possible to predict X values based on a regression model of Y(X), like an inverse function?

[Carlo Lazzaro]

Filipe:
it is not clear (to me, at any rate) what you're intended to achieve.
As I can get your query, I do not think that what you have in mind can be accomplished without reversing the predictor and the dependent variable as they are currently plugged in your regression model.
Anyway, providing more details (as per FAQ) about your query would be a wise step to take. Thanks.

[Marcos Almeida]

You unfortunately didn't provide the commands and output of your model.

That said, if I understood well your query, yes, in general terms, it is possible, although the participation of the necessary inverse function in your model was not clear to me.

Please check whether the example 1 applies to your needs (http://www.stata.com/manuals13/rfp.pdf)

Hopefully that helps.

P.S.: crossed with Carlo's excellent advice.

[Phil Bromiley]

Let me expand a bit on Marcos' and Carlo's comments. When you regress y on x, you get a estimate based on minimizing the squared errors in that equation (y= b0 + b1 x + e). This should generally give you a parameter on x that is pretty good at predicting y. But, what you appear to want is to predict x and x-squared from y. Here, as Carlo points out, you would normally regress x on y and x-squared on y and then use those parameters to predict x and x-squared from y.

As Marcos points out, you probably can use the parameters from your regression of y on x and x-squared to calculate a predicted x and x-squared, but that is not likely to be the best prediction of those variables that you can get from y.