# Fitting of the parameters of non-linear regression

I can fit the data with non-linear function, namely Mechanistic Growth curve from the JMP library. See the example of the fit in the next figure. The fit equation is BA = a(1 - b e-c *PA).

BA represents a parameter within sheet metal forming domain. I also now that this fit depends on the three parameters: P1 - tooling dimension, P2 - tooling dimension, and P3 - plate thickness. Is it possible to couple the parameters of the fit curve (a, b, and c) and (P1, P2, and P3)? I want to have equation in a form of BA = a(P1, P2, P3)(1 - b(P1, P2, P3) exp-c(P1, P2, P3)*PA).

What I've done so far is, I obtained the a, b, and c for every possible combination of P1, P2, and P3. P1, P2, and P3 are not nominal parameters, however I've done full factorial analysis for all available tooling dimensions and thicknesses.

I don't see where I should go further. Is there a way to obtain this kind of equation or during the non-linear fit or after obtainment of parameters?

• A little more explanation of the context might help here. Why do you want to go further? Have you any notion of the form e.g. $a(P_1,P_2,P_3)$ might take? – Scortchi - Reinstate Monica Jun 1 '16 at 14:44
• The idea is to get the formula where a user enters the P1, P2, and P3 and as a result receives the value of BA. It's difficult to say the form of the a(P1, P2, P3), that's what I want to know in the end. – Vitalii Vorkov Jun 1 '16 at 15:00
• I meant to say to edit the question to include more information. Presumably there's an error term you haven't mentioned. And from your talking of "every possible combination" I'd guess that $P_1$, $P_2$, & $P_3$ are categorical variables (so with plenty of data the saturated model might be just what you want if prediction's the aim). What are the 10, 20, & 30, 40 lines on your graph? It's best to be explicit about these things - & probably wouldn't hurt to come out with it & say just what BA, PH, &c. in fact represent. – Scortchi - Reinstate Monica Jun 1 '16 at 15:37
• I included a bit more information, can you give a hint? Or point a possible direction? I'm not a statistician, but a mechanical engineer. – Vitalii Vorkov Jun 9 '16 at 7:51
• (+1) Thanks! Your use of "parameter" seems rather broad to a statistician: I'd suggest (1) "BA represents a parameter [...]" - "response" or "dependent variable" - what you're trying to predict from the other variables; & (2) "the three parameters: P1 [...]" - "predictors" or "dependent variables" - what you're using to predict BA. (I nearly made these edits myself but was afraid of inadvertently changing your meaning.) And you still haven't explained what the different lines on the graph are. In analogous situations I've had a theory to suggest a functional form for $a(P_1,P_2,P_3)$, &c ... – Scortchi - Reinstate Monica Jun 9 '16 at 15:32