232803_en-US

liliconcom

Fit Model - "Polynomial to Degree" Question

Hello,

 

I am trying to find an easier way to construct my model. In the past I learned that a 4th order polynomial typically conforms well to parameters on a wafer surface. What I would like to do, is to find the 4th order polynomial for a temperature that was measured with an KLA i4 wafer depending on its X- and Y-coordinates. The model should have individual and mixed (crossed) factors of X and Y up to the 4th degree. When I use the "Macro" function in "Fit Model" I do not get the mixed terms (I tried the other options as well).

 

Example of using "Polynomial to Degree":

X_Coord
Y_Coord
X_Coord*X_Coord
Y_Coord*Y_Coord
X_Coord*X_Coord*X_Coord
Y_Coord*Y_Coord*Y_Coord
X_Coord*X_Coord*X_Coord*X_Coord
Y_Coord*Y_Coord*Y_Coord*Y_Coord

 

What's missing, are the mixed (crossed) terms:

X_Coord*Y_Coord

X_Coord*X_Coord*Y_Coord
X_Coord*Y_Coord*Y_Coord

X_Coord*X_Coord*X_Coord*Y_Coord
X_Coord*X_Coord*Y_Coord*Y_Coord
X_Coord*Y_Coord*Y_Coord*Y_Coord

 

I can obviously can add them one at a time, but that seems error-prone.

Any suggestions of how to do this?

 

Re: Fit Model - "Polynomial to Degree" Question

Fourth order polynomials and interactions with third order are not common, so you should use caution that you're not overfitting your data, but if you want to do this it's not too hard with a minimal number of clicks.

 

As you've already seen you can use the Polynomial to Degree macro to get up to the fourth order polynomials. Then select all of the X effects up to third order and then the Y column in the columns list and then Cross. Finally select all of the Y effects up to third order and then the X column in the columns list and then Cross.

 

That will get all of the effects you're looking for.