Cornell (1988) presented the original example of mixture experiment for producing vinyl for automobile seat covers. The data is shown in Table 11.14, and the variable names are the same as those given in Section 11.8.

(a) Given that this is a cross between an extreme vertices design (plus the overall centroid appropriate for tting a Schee linear model in the mix-

ture components) and a 22 factorial in the process variables, what is the appropriate model for this data?

(b) Fit the model by least squares using the R lm function.

(c) In this experiment, the runs were not made in a completely random or-

der, but rather randomized within whole plots and run as a split-plot experiment. Ret the model using the lmer in the R package lme4 in-

cluding a random term for whole plots like the example shown in Section 11.8. Is there any dierence in the parameter estimates you get in (b)

and (c)? What does this imply?