Use the EEw1s2 function in the daewr package to create a estimation- equivalent split-plot design. (a) Call

Question:

Use the EEw1s2 function in the daewr package to create a estimation-

equivalent split-plot design.

(a) Call the function with no arguments to see the list of designs available.

(b) Create the design for one whole plot factor and two sub-plot factors, with seven whole plots and two sub-plots per whole plot (do not randomize the order).

(c) In the BYU Department of Chemistry and Biochemistry, experiments were run to study the process of making Alumina (Al2O3|a catalyst support) in the lab. Three factors were varied (batch mixing time, l-

tration time, and packing density prior to calcination). The experiments were run using the split-plot design you created in (a). Mixing time was the whole plot factor and several batches were mixed at each of three mixing times. Each batch was split in two after mixing and each half was ltered and packed according to the plan you created with s1=ltration time and s2=packing density. Surface area is one of the characteris-

tics of Alumina that was sought to be controlled. The resulting surface area measurements for the 14 half batches (in the order generated by the EEw1s2 function are: 186.8782, 131.9686, 210.127, 187.2568, 140.336, 163.783, 171.3387, 171.0459, 170.2234, 217.1703, 202.6545, 191.1687, 137.4807, 143.1752. Fit the general quadratic model to this data by REML using the lmer function in the lme4 package and by least squares using the rsm function in the rsm package. Are the resulting coecients the same using the two methods?

(d) Using the lmer function perform a full and reduced model test to see if any of the factors can be dropped from the model. Can any factors be dropped from the model to reduce the dimensions from 3 to 2?

(e) Make contour plots of the prediction equation for surface area at the stationary point for any factors not on the axis. image text in transcribed