Regressions
You can achieve what you want (and very accurately too) by using multivariate regression, as I suggested in my earlier post.
Ah, yes and no. We are getting into apples and oranges discussions.
The OP queried simulation of existing and approved AFM/POH data. For this sort of stuff, the aim must be to replicate the approved data to a very high level of precision and accuracy, lest the legal/regulator censure machine strike thee down. When I first started playing with such things back in the late 60s/early 70s, computing was in its public infancy and available multivariate analyses didn't cut the mustard from the point of both accuracy and precision. I revisited those techniques, again, late 70s/early 80s with a similar observation. Hence my comment regarding multivariate analyses. Caveat - for simple graphical data, multivariate analysis often will provide acceptable results so the OP's cited example may well suit that technique. For more complex presentations, it all gets a tad difficult to achieve acceptable accuracy and precision.
Your story is somewhat different. For reasons which totally elude me, you appear to have a significantly modified aircraft for which the AFM/POH performance data was not updated. It is usual for any mod work to be accompanied by updated performance supplement information if such changes are other than trivial. For instance, I can recall several multis for which the MTOW figure was reduced due to WAT limit constraints associated with aerial forests. As a sideline interest, perhaps you can provide further information on this aspect of your post - if appropriate, to me by PM for my interest.
Effectively, you are working to your own defacto design standards, are the arbiter of accuracy and precision, and the arbiter of end product acceptability. Therefore, you can do the work however you might choose. In such a situation, clearly, the use of multivariate analysis can be made to be fine.
I remember doing least squares regression by hand
Dear, oh dear ... bragging, again .. ah, the memories of machine code and assembler programming .... I couldn't do that stuff these days if my life depended on it.