3. The C.F. Eye Care Company manufactures intraocular lenses that replace the human lens following cataract surgery.An experimenter is considering conducting an experiment to investigate a critical quality characteristic of the lenses using a 2³ factorial design with one run at each corner of the cube.All three factors are quantitative.

a. What model can the experimenter fit to the data from this experiment?

b. Suppose that the experimenter was interested in testing for curvature.What changes to the design would you recommend to the experimenter?

c. If curvature is significant, you need to add ____________ more runs, and these runs should be located _____________________________________________.

d. If the experimenter makes the modification to the design that you suggest in part (b) and (c) above, and curvature is statistically significant, then a model of higher-order than the one in part (a) can be considered.Write down this model.

e. You cannot fit this model using the original design from part (a).Why?

f. Suppose that at the start of the experiment you suspected that the model in part (d) would probably be required to adequately explain the response. Explain why the sequential strategy of experimentation used in this exercise is superior to running one single comprehensive experiment with all three factors at three levels.