Use $\mathrm{R}$ to calculate the three-way interaction effects from the experiment in Example 6.2 . Interpret these interaction terms.

Data from Example 6.2

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Example 6.2 (Silk Study). Silk fibroin is a protein that has many biomedical applications. Bucciarelli et al. [2021] used a 24 factorial design to study extrac- tion of silk fibroin from silk filament. The design was replicated three times. The four factors considered are described in Table 6.4. The number of baths is a discrete variable. Time, temperature, and salt concentration are all continuous variables. The +1 and -1 levels correspond to the two levels of each factor used in the study. Weight loss and amount of sericin were used to determine the effectiveness of the process. The 24 different extractions (experimental runs) are listed in Table 6.5. Each extraction required degumming in a boiling bath for 30 minutes, rinsing three times with distilled water at room temperature then drying for two days. The order of the preparation was randomized to mediate the effect of humidity and temperature.