Different results when forcing a quadratic model in fit model platform vs a simple square transformation

[#1]

Hello Community,

I have a question regarding a comparison of results between the results of a 2nd degree polynomial and a square transformation. To make things simple I created some mock data I'm gonna attach to this message, but here below a screenshot:

For the polynomial approach, I did it on "fit model" platform and ticked "no intercept" option and also unticked "center polynomials" in the model specification options in the red arrow the option  (option I discovered thanks to a similar discussion: Solved: Fit Model: Square Transformation vs 2nd Order Polynomial - JMP User Community ). Then, I created a model of A as a function of B and B square and then force the model to be just A as a function of B square. and I exported these results.

Concerning the square transformation approach, I just created another column ("B square" in the screen capture below) with B squared. The results are not the same as you can see here below :

When I open the formulas :

Prediction formula from the fit model approach: 

Formula from column with square transformation:

As you can see, the results are not the same because of the multiplicative factor "0.0129..." with the fitting model approach.

Could you please help me in understanding why in the fit model platform despite my efforts to force a model of A as a function of B square, there is always a multiplicative factor that is presente in the prediction equation ? What is behind this ?

Thanks.

[#2 · Accepted solution]

Hi @Julianveda : Your first formula (with the 0.0129) is there to predict A as a function of B (A=0.0129*B*B, based on the model you specified) . The other formula (B*B) is just B*B; so they shouldn't match.    

[#3]

Thank you @MRB3855 , I see your point. I got confused when exploring the functionality "center polynomials" from the discussion in the link I shared.