Table 3 Analysis of variance for evaluation of the second-order model

Regression	Degrees of freedom	Type I sum of squares	r2	F-value	p-value
Covariates	5	0.42846	0.3054	7.94	0.0006
Linear	4	0.56331	0.4016	13.04	<0.0001
Quadratic	4	0.20883	0.1489	4.84	0.0095
Interactions	6	0.02942	0.0210	0.45	0.8318
Total model	19	1.23002	0.8768	6.00	0.0004
Residual	Degrees of freedom	Sum of squares	Mean square	F-value	p-value
Lack of fit	10	0.15710	0.01571	6.02	0.0197
Pure error	6	0.01567	0.00261
Total error	16	0.17276	0.01080