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Fit Spline By Group: Save Spline Coefficients to Column?

Hi all--having an issue.  I am using Fit Y by X to fit 5,000 separate regressions.  I hold control, select red drop-down arrow, and Fit->Flexible, Fit->Spline and select, say, 0.1.   This fits a spline to all 5,000 graphs with lambda of 0.1.  I have 28 X values in each of 5,000 graphs, and I understand there are 4 different spline coefficients (A, B, C, D).

I understand if I just had 1 regression, I could select "Save Coefficients" and a nifty Bx5 matrix, (where B is a subset of my X values) table will pop out with each row as an B value and columns 2-5 as the values of my spline function, for each discrete value of B.

However, when I do this fitting "By Group" with 5,000 regressions, I get 5,000 of these tables as outputs!   I would like a way to either:

1) Get 1 table that contains all of the knot spline function values for all values of B (ie  for all "By: Groups" (instead of 5000 separate tables)

Or:

2) Be able to get Spline value A from spline function as its own column in the original datatable, get Spline value B from spline function as its own column in original datatable, etc. where spline values A, B, C, D pertain to the correct discrete B value and the correct By: Group

I know if I just I hit Ctrl and "Save Predicteds" after Fit Y by X, there will be a column saved to the original datatable with ~5000 formulas (JMP says "Huge formula with 5000 items).   It is a conditional formula that looks for the By: Group, then does Spline Eval(X, [28x5]) for each group.   Is there a way I can use this script and do find/replace to extract the Spline Coefficient?  Maybe there is some unique JSL thing to do?  How do I get these darn coefficients???

I also understand there is a Spline Coef(x, y, lambda) thing in JSL but I don't understand jsl syntax at all and am dimwitted in programming, in general.

Thanks for any advice and your time.