Don't try to manipulate data in order to get desired (orpublished) results.

Contact the autors. Tell them what you tried and what your problem is. Provide thesource and the data you used and the analysis you did. Ask if the data and analysis is correct or if you missed something. Ask for everything required to reproduce their result. Maybe there is a mistake in the data set you have or in the way you analyze the data -- or that the authors did not correctly describe the complete analysis or that they made a mistake somewhere.

Yes, I agree with Jochen Wilhelm

Jochen Wilhelm@ is totally right, on a more general case (not here, where the only eay is the one suggested by Jochen) you should desire to look at a subset of a data set obeyng a given functional relation (i.e. a model). This is a sort of classification (or discriminant anallysis depending on the context) that instead of being based on the distribution of satistical units in a mutivariate space, relies on the relative adherence of each point to an a priori model we presume to fit the data (the model could derive from a training set or from literature). This approach is called SIMCA and is very useful in many occasions, you could find the essential here: https://en.wikipedia.org/wiki/Soft_independent_modelling_of_class_analogies

or here:

https://mdatools.com/docs/simca.html

As a rule of thumb, you can not go so far away from the used data -to build the,model- for neither estimation nor forecasting. When your recorded data are from 40 BC, you can not find reasonable estimation for a very far year like 2000 BC using regression analysis. You need more advanced models.

Just for the heck of it are you sure regression is what you should use and not calibration they're completely different because the regression predictor is measured without but calibration is not. Thus that error must be taken into account for calibration or as it's sometimes called inverse regression. Google these terms to get a full description of the methods. The Longnecker and Ott book see attached screenshot had a very good section on calibration methods. The book edition is in the z-library google instructions. Best, wishes, David Booth

Thank you for your quick answers.

I totally agree with Jochen Wilhelm : data are data and we should not make them fit our beliefs. To contact the authors would be the best way to clarify this situation.

I had a discussion with one of my research colleagues and there was a little trick that I did not noticed at first that explains the difference I obtained and why the authors did not report confidence intervals so I finally got my answer.

Babak Jamshidi : I know that it would be litigious to use a fitted model to estimate parameters that are well beyond the intervals of the subset used during the fitting process. However, I wonder how to estimate the error rate/deviation of estimations when the model is used slightly above its upper or lower limit.

For instance, if I take the following relation (with N = 103, RSE = 0.181 and CF = 1.02), how could I correct the estimated height if I measure a P. officinalis that is more than 50 meters (because they generally never exceed 35m in height) ?

By Excel programme

@Mathis, If you don't have any information about a region you can't predict very well what happens there can you? David Booth

David Eugene Booth : No, I cannot use local allometric equation to predict tree height if I am in a completely different ecosystem. I agree, that makes sense.

This equation was developed from field data here, in Guadeloupe (French West Indies), and is used to predict tree height when it was not measured during field sampling.

@Mathis what I meant was if as @Babek said without data at the nearby heights you wish to predict then you have no reliable data to use to make your prediction. This is called extrapolation and is very dangerous to use. Best wishes, David Booth