Long shot: How to use numpy.polyfit to reproduce Vec Quadratic() results?

[#1]

Apologies for the transgression, which is; ironically; a direct result of my personal progress in JSL.

A very helpful computer scientist in my organization is trying to translate something initially written in JSL to Python. Specifically, the challenge is how to reproduce what the JSL function 'Vec Quadratic()' is doing? See also the attached example table .

Background:

The JSL application to be translated creates formula columns for the confidence and prediction intervals. The formulas are then used to calculate the values of the confidence and prediction intervals for some user specified value of x, aka independent variable.

Questions:

• Is numpy.polyfit (https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html) the right choice for this?
• If it is, anyone who knows how to use numpy.polyfit to reproduce the results for Lower & Upper 95% Mean & Indiv columns in the attached table or can point us into the right direction?

Screenshots for orientation:

• What we want to achieve in Python (results inside the red frame)
  

• How the columns shown above were generated
  

[#2]

... you notice that it has some issues with matrix manipulations

after adjusting the brackets, you get:

import numpy as np

s = np.array( [[1.,3.,5.],[3.,2.,6.], [5.,6.,1.] ])
x = np.array( [[1.,3.,5.],[2.,4.,6.] ])

res= x @ (s @ x.T)
print(res)
print(res.diagonal())

... which fits to

Names Default To Here( 1 );
exS = [1 3 5, 3 2 6, 5 6 1];
exX = [1 3 5, 2 4 6];

Print(r= exX * exS * exX`);

tmp=as list(r);
print(tmp[1][1],tmp[2][2])

[#3]

@Ressel  I think the confusing part of your request is that Vec Quadratic() is simply performing matrix math as described by the Scripting Index.  The results of Vec Quadratic() is simply the output of matrix operations.

The formulas themselves, which give the 95% values, are generated by the Fit Y by X platform. 'Fit y By X' is also what is responsible for creating the plot.  So the question as I understand it, is more accurately; How do I do a Bivariate Fit of y By x with confidence levels in Python or numpy? 

I think the Vec Quadratic() is the wrong focus since it didn't create the formula or the constants, it's just a mathematical operation in the generated formula.

[#4]

@Paul_Nelson, this is correct, which I only figured out later (and shamelessly exploited to accept my own answer as solution). With regards to this as well as the exact phrasing of the question, I honestly didn't have it in me. The more one learns ... Thank you very much for sharing & have a good weekend.
(P.s.: As a sophisticated, statistical software company you'd almost count on engineers without computational talent being part of the business model. For better or worse.)

[#5]

I applaud the openness of Jmp for Python
As @Paul_Nelson  mentions - now with Jmp18, if a functionality is missing in JMP, every user can easily grab it from Python - with 2-3 lines of code. amazingly useful!

On the other hand, some Wikipedia knowledge about matrix manipulation, DOEs, regression, neural networks, etc. is nothing to worry about being "stolen".

With the "functionality" coming from state-of-the-art, up-to-date Python packages, it will be the "soft skills", the absence of bugs, the intuitive interface, the superior user experience that will speak for JMP and separate it from the competition:

Re: Wish list - new Label: user experience 

[#6]

Moreover, I think it's only natural that users getting into data analytical & automation work via JMP are unlikely to have a firm grasp of Python, or any other programing & scripting language for that matter. JMP is proactively trying to recruit this type of user and makes it (I think) easy to step into scripting in JSL. Once the user develops and learns, though, this can be expected to trigger the wish for additional knowledge, at least in some cases and after the initial barrier of understanding a few basic, computational concepts is overcome. Of course the first intuition for this kind of user will be to ask the community for help, especially after the advertised Python integration in JMP 18. Finally, the fact that a professional data scientist is tasked with copying what a lay statistician has developed in JMP for use in an actual business setting speaks for itself. Although, I might be getting it all wrong.