This exercise is based on Section 5.2 of Box et al. [2005]. An experiment for optimizing response yield (y) in a chemical plant operation was conducted. The three factors considered are temperature $(\mathrm{T})$, concentration (C), and catalyst type (K). The order of the runs (run) was randomized. The levels for the factors are listed below.

Factor	Level
$\overline{\text { T. Temperature }\left({ }^{\circ} \mathrm{C}\right)} 1$	$60(-1), 180(+1)$
C. Concentration (%)	$20(-1), 40(+1)$
K. Catalyst	$\mathrm{A}(-1), \mathrm{B}(+1)$

The data are available in the chemplant data frame.

glimpse (chemplant, $\mathrm{n}=3$ )

a. State the design.

b. Use $\mathrm{R}$ to calculate all the factorial effects.

c. Which factors have an important effect on yield? Explain how you arrived at your answer.

Data from Section 5.2

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## Rows: 16 ## Columns: 5 3, 7, 13, 4, 16, 1, 1, 1, 1, 1, 10, 12~ 1, 1,~ ~ ## $ run 6, 2, 1, 5, 8, 9, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 59, 74, 50, 69, 50, 81, 46, 79, 61, 70, 5~ ## $ T ## $ C ## $ K ## $ y -~