Table 2.

Analysis of variance (ANOVA) for Box–Behnken design

Source of variation	Sum of square			Degree of freedom			Mean square			F-value			p value
	α′	α	β	α′	α	β	α′	α	β	α′	α	β	α′	α	β
Model	3157.09	2098.37	2539.5	9	9	9	350.79	233.15	282.17	81.67	30.68	57.53	< 0.0001	< 0.0001	< 0.0001
X1	938.31	31.84	0.64	1	1	1	938.31	31.84	0.64	218.47	4.19	0.13	< 0.0001	0.0799	0.7289
X2	21.03	701.81	679.15	1	1	1	21.03	701.81	679.15	4.9	92.34	138.46	0.0626	< 0.0001	< 0.0001
X3	145.27	0.15	18.88	1	1	1	145.27	0.15	18.88	33.82	0.02	3.85	0.0007	0.8928	0.0906
X1 X2	0.77	7.05	0.44	1	1	1	0.77	7.05	0.44	0.18	0.93	0.09	0.6855	0.3676	0.7727
X1 X3	0.48	1.2	1.43	1	1	1	0.48	1.2	1.43	0.11	0.16	0.29	0.7472	0.7031	0.6062
X2 X3	3.17	22.37	0.25	1	1	1	3.17	22.37	0.25	0.74	2.94	0.051	0.4188	0.1299	0.8278
X21	913.82	402.77	114.6	1	1	1	913.82	402.77	114.6	212.77	53	23.36	< 0.0001	0.0002	0.0019
X22	451.43	422.57	1412.3	1	1	1	451.43	422.57	1412.3	105.11	55.6	287.94	< 0.0001	0.0001	< 0.0001
X23	474.84	368.33	183.66	1	1	1	474.84	368.33	183.66	110.56	48.46	37.44	< 0.0001	0.0002	0.0005
Residual	30.06	53.2	34.33	7	7	7	4.29	7.60	4.90
Lack of fit	17.01	33.97	3.58	3	3	3	5.67	11.32	1.19	1.74	2.36	0.16	0.2972	0.2131	0.9211
Pure error	13.05	19.23	30.75	4	4	4	3.26	4.81	7.69
Total error	3187.15	2151.57	2573.84	16	16	16