4. Fractionation experiment, continued The fractionation experiment was described in Exercise 3, where the response PCE was used. Consider here, instead, the analysis of “Yield”.

(a) Fit the first-order model for the response variable “Yield” based on the initial first-order 24 factorial design, shown as the first 16 runs in Table 16.24. Conduct the corresponding analysis of variance.

(b) At the design center point, three additional observations were collected, for which the sample variance was s2 0 = 0.090. Test the first-order model for lack of fit, using a 5% level of significance. (Hint: Since the factorial points include no replication, msPE = s2 0 , and ssE based on all 19 runs is equal to ssE from the factorial portion of the design plus (n0 − 1)s2 0 .)

(c) Based on the results of parts

(a) and (b), what subsequent experimentation would you recommend?