Parameter Estimates As Terms Are Added
In most cases of least squares fitting, the model coefficients for previously added terms change depending on what was successively added. For example, the X1 coefficient might change depending on whether or not an X2 term was included in the model. This is not the case when the design is orthogonal, as is a 23 full factorial design. For orthogonal designs, the estimates for the previously included terms do not change as additional terms are added. This means the ranked list of effect estimates simultaneously serves as the least squares coefficient estimates for progressively more complicated models.
Read more about this topic: Yates Analysis
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