With reference to the example of the (2^{3}) design on page ({ }^{* * *}), express the

Question:

With reference to the example of the $2^{3}$ design on page ${ }^{* * *}$, express the total sum of squares as the sum of the contributions from each of the seven treatments plus the error sum of squares.

This decomposition is the basis for the analysis variance and it is summarized in the first column of the ANOVA table.

Sum of squares for any treatment in a $2^{3}$ design is ( estimated effect $)^{2} 2 \times r$. Refer to Exercise 13.32 for the total and error sum of squares.]

Data From Exercise 13.32

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