Factorial design dispersion matrix

The determinant (X X) = S which is the minimum value. The eigenvalues of the dispersion matrix are all equal and the variance of all estimated model parameters are / 8. The parameters are independently estimated and the dispersion matrix is a diagonal matrix (the covariances of the models parameters are zero). This means that parameters estimated from a two-level factorial design are independently estimated, with equal and maximum precision. 

We consider one of these designs, 2 full-factorial, fractional-factorial or Plackett-Burman design, of N experiments. The postulated model of p coefficients consists of a constant term, main effects and possibly first-order interactions. All diagonal coefficients (coefficients of variance) in the dispersion matrix are equal to l/N and all non-diagonal terms are zero. 

The VIF equal 1 for all coefficients, confirming the orthogonality of the design. The determinant of the dispersion matrix is N , which is the smallest possible value for N experiments in a cubic domain of limits 1. 2-level factorial and Plackett-Burman designs allow the best and most precise estimates of coefficients. 

TABLE 7 Dispersion Matrix of the NASA Factorial Design ... 

---