Consider the data in Exercise 14-97. Use only the first eight rows of data from the 2³factorial design and assume that the experiment was conducted in blocks based on seed type.

(a) Analyze the factorial effects and comment on which effects are important.

(b) Develop a regression model to predict the response in terms of the actual factor levels.

(c) Does a residual analysis indicate any problems?

Exercise 14-97

An article in European Food Research and Technology [€œFactorial Design Optimisation of Grape (Vitis vinifera) Seed Polyphenol Extraction€ (2009, Vol. 229(5), pp. 731€“742)] used a central composite design to study the effects of basic factors (time, ethanol, and pH) on the extractability of polyphenolic phytochemicals from grape seeds. Total ployphenol (TP in mg gallic acid equivalents/100 g dry weight) from three types of grape seeds (Savatiano, Moschofilero, and Agiorgitiko) were recorded. The data follow.

Ethanol (%) Time (H) Run pH TP Moschofilero Savatiano Agiorgitiko 13,320 1 40 2 1 13,127 8,673 13,596 8,925 40 2 5 4,370 3 40 1 10,714 12,047 8,049 4 40 5 10,730 11,299 5,315 2 12,149 9,700 9,384 2 10,910 7,107 8,290 1 11,620 8,755 7,905 9,757 8. 60 5 9,792 9,347 9,748 9. 40 13,593 7,253 10 60 4. 3 13,459 8,727 8,390 11,980 7,164 7,611 11 50 12 50 6. 3 10,338 5,928 7,292 13 50 13,992 12,200 8,305 14 50 13,450 10,552 8,380 8,792 15 50 3 11,745 9,284 16 50 4 3 12,267 9,084 8,302