Sum of Squares in Generalised Factorial Designs

When fitting a model that contains factors raised to powers higher than 1, it is common practice to combine the terms into a single term. The basic mle for combining the terms is to ignore any powers on the factors and see what the corresponding interaction is, for example, if we have the following set of 

Run Percent carbonation (x ) Line speed (X3) Operating pressure (X2) Deviation from expected height (inches)  

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