Intercept of a parabola

[#1]

Hi,

While using JMP's "Fit Y by X" platform to fit data with a quadratic model, I observed that the intercept obtained using JMP’s centered polynomial notation for a parabola differs from the intercept obtained using the standard (uncentered) ( y = ax^2 + bx + c ) format. Based on my understanding, the intercept represents the value of ( Y ) when ( x = 0 ), and I don't see why these values should differ according to the notation used.

I have attached an example using the equation ( y = 203x^2 - 3x + 1000 ). The uncentered model correctly indicates that the intercept is 1000, whereas the centered notation shows the value -125875, a significantly different result.

I have tried to find an explanation for this discrepancy in JMP's help documentation and within the community forums, but I have been unsuccessful so far. Therefore, I would appreciate it if someone could clarify what I might be missing here.

Many thanks,

Paulo

[#2]

The Fit Y by X default option is a centered polynomial fit centered around the mean (xavg) of the X factor.

Uncentered polynomial (what you are looking for): y = ax^2 + bx + c

Centered polynomial: y = A(x-xavg)^2 + Bx + C = Ax^2 - 2A*xavg*x + Bx + A*xavg^2 + C

So comparing term for term:
a = A

b = -2A*xavg + B

c = A*xavg^2 + C

So you can use these formulas to calculate the uncentered fit coefficients, or fit an uncentered polynomial from Fit Special.

[#3]

Thanks, @Mark_Zwald.