Create an 8-run, 25-2 fractional factorial design and, again as in Exercise 19.15, pretend that the experimenter has used this design instead of the full one. Extract from the full 32-run data table, the results corresponding to the 8 runs indicated in the 25-2  design.

(i) Determine the design resolution and alias structure. Can any  two-way  interactions be determined independently without confounding? What does this imply in terms of what can be truly estimated from this much reduced set of results?

(ii) Repeat the entire Exercise 19.14. How do the estimates of the main effects compare to the ones obtained from the full data set?

(iii) If the experimenter had only been interested in determining which of the 5 factors has a signi?cant effect on the response, comment on the advan- tages/disadvantages of the quarter fraction, 8-run design versus the full 32-run experimental design.