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I want to simulate responses for fractional factorial design.

As an input for simulation I want to use estimated effect sizes of main factors and some interactions.

I know there is a formula for calculating effects from obtained responses:

"For each of the main effects, the estimated effect consists of the mean at the high level of the factor minus the mean at the low level of the factor."

Here is the screenshot of fractional factorial design from a book:

enter image description here

And here is formulas for calculation of effects when responses are known:

enter image description here

But I want inverse:

  1. Input values of estimated main effects and interactions (A B C AB AC 1 etc.)
  2. Derive a simulated responses for all rows (a, b, ab..) so that they lead to that predefined effects.

Could you help me please how to approach this problem?

R or JMP code would be extremely helpful.

After all I want to use derived responses in this SAS JMP code for simulation binomial responses. Also I will use it with higher number of factors.

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