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Mathematically, the Fit Two Level Screening platform takes the n values in the response vector and rotates them into n new values. The rotated values are then mapped by the space of the factors and their interactions.
Contrasts = T’ × Responses
In the above equation, T is an n by n orthonormalized set of values starting with the intercept, main effects of factors, two-way interactions, three-way interactions, and so on, until n values have been obtained. Since the first column of T is an intercept, and all the other columns are orthogonal to it, these other columns are all contrasts, that is, they sum to zero. Since T is orthogonal, it can serve as X in a linear model. It does not need inversion, since T’ is equivalent to T-1 and (T’T)T’. The contrasts are the parameters estimated in a linear model.

Help created on 3/19/2020