Coteron, Sanchez, Martinez, and Aracil ("Optimization of the Synthesis of an Analogue of Jojoba Oil Using a Fully Central Composite Design," Canadian Journal of Chemical Engineering, 1993) studied the relationship of reaction temperature $x_{1}$, initial amount of catalyst $x_{2}$, and pressure $x_{3}$ on the yield of a synthetic analogue to jojoba oil. The following table summarizes the experimental results.

$x_{1}$	$x_{2}$	$x_{3}$	$y$
-1	-1	-1	17
1	-1	-1	44
-1	1	-1	19
1	1	-1	46
-1	-1	1	7
1	-1	1	55
-1	1	1	15
1	1	1	41
0	0	0	29
0	0	0	28.5
0	0	0	30
0	0	0	27
0	0	0	28

a. Perform a thorough analysis of the results including residual plots.

b. Perform the appropriate test for lack of fit.