Continuation of Exercise 15.20. Suppose that a colleague suggests that you put the additional 4 runs at the center of the design region (assume that the three factors are continuous so that this is possible). What do you think about this suggestion? Does it improve the precision of estimation of the model parameters as much as replication of the factorial runs?

Data From Exercise 20

Suppose that you plan to run a \(2^{3}\) factorial experiment with 8 runs. You discover that your budget has been increased so that you can perform an additional 4 runs. Where would be the best places to run these additional 4 trials if you want to both get a model-independent estimate of error and reduce the variances of the model parameter estimates as much as possible? Restrict your choices to replicating some of the original 8 runs.