Table 4 Analysis of variance for evaluation of the third-order model

Regression	Degrees of freedom	Type I sum of squares	r2	F-value	p-value
Covariates	5	0.42846	0.3054	13.20	0.0002
Linear	4	0.56331	0.4016	21.69	<0.0001
Quadratic	4	0.20883	0.1489	8.04	0.0022
Cubic	4	0.09484	0.0676	3.65	0.0362
Interactions	6	0.02942	0.0210	0.75	0.6179
Total model	23	1.32486	0.9444	8.87	0.0002
Residual	Degrees of freedom	Sum of squares	Mean square	F-value	p-value
Lack of fit	6	0.06226	0.01038	3.97	0.0587
Pure error	6	0.01567	0.00261
Total error	12	0.07793	0.00649