The natural and coded levels of independent variables based on the central composite design are shown in Table 2. The experimental values for each independent variables were chosen according to the results obtained from preliminary analysis. Table 3 indicates the four-factor, five-level CCD and the obtained and predicted values for the TC degradation rate (%) using the developed quadratic model. In RSM analysis, the approximation of y was proposed using the fitted second-order polynomial regression model which is called the quadratic model. A quadratic regression is the process of finding the equation of the parabola that fits best for a set of data [58].
Table 2 Natural and coded levels of independent variables based on the central composite design
Independent variable Symbol Coded levels
−2  −1  0  +1 +2
Natural level
pH A 2.5 5 7.5 10 12.5
Tetracycline (mg/L) B 10 30 50 70 90
Persulfate (Mm) C 1 2 3 4 5
Reaction time (min) D 30 60 90 120 150
Table 3 Four-factor five-level central composite design for RSM
Run Experimental conditions TC degradation rate (%)
pH (A) Tetracycline (mg/L) (B) Persulfate (mM) (C) Time (min) (D) Observed (%) Predicted (%)
1 7.5 (0) 50 (0) 3 (0) 90 (0) 51.06 49.82
2 2.5 (−2) 50 (0) 3 (0) 90 (0) 55.64 55.74
3 7.5 (0) 50 (0) 3 (0) 90 (0) 48.45 49.82
4 5 (−1) 70 (+1) 4 (+1) 60 (−1) 45.16 44.64
5 5 (−1) 30 (−1) 4 (+1) 120 (+1) 86.62 86.33
6 10 (+1) 70 (+1) 2 (−1) 120 (+1) 61.02 61.32
7 7.5 (0) 50 (0) 3 (0) 150 (+2) 81.85 81.17
8 5 (−1) 30 (−1) 2 (−1) 60 (−1) 34.55 35.25
9 10 (+1) 30 (−1) 2 (−1) 60 (−1) 47.25 46.91
10 10 (+1) 30 (−1) 4 (+1) 60 (−1) 70.44 69.95
11 5 (−1) 30 (−1) 2 (−1) 120 (+1) 61.85 61.79
12 7.5 (0) 50 (0) 1 (−2) 90 (0) 28.72 28.18
13 10 (+1) 70 (+1) 4 (+1) 120 (+1) 85.05 84.34
14 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82
15 10 (+1) 30 (−1) 2 (−1) 120 (+1) 75.56 76.07
16 10 (+1) 30 (−1) 4 (+1) 120 (+1) 94.25 95.04
17 5 (−1) 70 (+1) 2 (−1) 60 (−1) 12.65 11.98
18 5 (−1) 30 (−1) 4 (+1) 60 (−1) 64.04 63.86
19 7.5 (0) 90 (+2) 3 (0) 90 (0) 41.15 41.31
20 10 (+1) 70 (+1) 4 (+1) 60 (−1) 54.88 55.05
21 7.5 (0) 50 (0) 3 (0) 90 (0) 50.55 49.82
22 7.5 (0) 50 (0) 3 (0) 90 (0) 49.75 49.82
23 7.5 (0) 50 (0) 5 (+2) 90 (0) 79.38 79.82
24 12.5 (+2) 50 (0) 3 (0) 90 (0) 80.62 80.42
25 7.5 (0) 10 (−2) 3 (0) 90 (0) 75.55 75.28
26 7.5 (0) 50 (0) 3 (0) 90 (0) 49.35 49.82
27 7.5 (0) 50 (0) 3 (0) 30 (−2) 24.75 25.33
28 5 (−1) 70 (+1) 2 (−1) 120 (+1) 42.25 42.72
29 10 (+1) 70 (+1) 2 (−1) 60 (−1) 27.68 27.96
30 5 (−1) 70 (+1) 4 (+1) 120 (+1) 70.85 71.31