1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.5. Quantitative Techniques 1.3.5.18. Yates Algorithm


For Orthogonal Designs, Parameter Estimates Don't Change as Additional Terms Are Added  In most cases of leastsquares 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 2^{3} 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 parameter estimates are the leastsquares coefficient estimates for progressively more complicated models.  
Example Prediction Equation 
We use the parameter estimates derived from a leastsquares analysis for the
eddy current
data set to create an example prediction equation.
Parameter Estimate   Mean 2.65875 X1 1.55125 X2 0.43375 X1*X2 0.06375 X3 0.10625 X1*X3 0.12375 X2*X3 0.14875 X1*X2*X3 0.07125 A prediction equation predicts a value of the reponse variable for given values of the factors. The equation we select can include all the factors shown above, or it can include a subset of the factors. For example, one possible prediction equation using only two factors, X1 and X2, is: \( \hat{Y} = 2.65875 + 1.55125 \cdot X_1  0.43375 \cdot X_2 \) The leastsquares parameter estimates in the prediction equation reflect the change in response for a oneunit change in the factor value. To obtain "full" effect estimates (as computed using the Yates algorithm) for the change in factor levels from 1 to +1, the effect estimates (except for the intercept) would be multiplied by two. Remember that the Yates algorithm is just a convenient method for computing effects, any statistical software package with leastsquares regression capabilities will produce the same effects as well as many other useful analyses. 

Model Selection 
We want to select the most appropriate model for our data while
balancing the following two goals.
