The article ??An Application of Fractional Factorial Designs?? (M. Kilgo, Quality Engineering, 1988:19??23) describes a 2^5??1design (half-replicate of a 2⁵design) involving the use of carbon dioxide (CO₂) at high pressure to extract oil from peanuts. The outcomes were the solubility of the peanut oil in the CO₂(in mg oil/liter CO₂), and the yield of peanut oil (in percent). The five factors were A: CO₂pressure, B: CO₂temperature, C: peanut moisture, D: CO₂flow rate, and E: peanut particle size. The results are presented in the following table.

a. Assuming third-and higher-order interactions to be negligible, compute estimates of the main effects and interactions for the solubility outcome.

b. Plot the estimates on a normal probability plot. Does the plot show that some of the factors influence the solubility? If so, which ones?

c. Assuming third- and higher-order interactions to be negligible, compute estimates of the main effects and interactions for the yield outcome.

d. Plot the estimates on a normal probability plot. Does the plot show that some of the factors influence the yield? If so, which ones?

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Treatment Solubility Yield Treatment Solubility Yield 29.2 63 d ade bde abd e 22.4 23 a 23.0 21 37.2 74 b 37.0 36 31.3 80 abe 139.7 99 48.6 33 23.3 24 cde 22.9 63 асе 38.3 66 acd 36.2 21 bce 42.6 71 bcd 33.6 44 abc 141.4 54 abcde 172.6 96