Table 3 Analysis of variance (ANOVA) for the quadratic polynomial mode.

From: Optimization of ultrasound-aided extraction of bioactive ingredients from Vitis vinifera seeds using RSM and ANFIS modeling with machine learning algorithm

Source

Sum of squares

dfa

Mean square

F-valueb

p-valuec

TPC (y1)d

 Model

439,900

20

21,993.66

18.49

 < 0.0001

 X1

395,800

1

3.96E+05

332.8

 < 0.0001

 X2

270.07

1

270.07

0.2271

0.6373

 X3

440.06

1

440.06

0.37

0.5477

 X4

6447.81

1

6447.81

5.42

0.0271

 X5

489.66

1

489.66

0.4118

0.5261

 X1X2

2830.15

1

2830.15

2.38

0.1337

 X1X3

222.29

1

222.29

0.1869

0.6687

 X1X4

290.77

1

290.77

0.2445

0.6247

 X1X5

2198.84

1

2198.84

1.85

0.1844

 X2X3

545

1

545

0.4583

0.5038

 X2X4

1117.46

1

1117.46

0.9397

0.3404

 X3X4

710.46

1

710.46

0.5974

0.4458

 X3X5

33.74

1

33.74

0.0284

0.8674

 X4X5

3002.74

1

3002.74

2.53

0.1229

 X12

3677.82

1

3677.82

3.09

0.0892

 X22

1430.88

1

1430.88

1.2

0.2817

 X32

6893.43

1

6893.43

5.8

0.0226

 X42

8144.72

1

8144.72

6.85

0.0139

 X52

2849.08

1

2849.08

2.4

0.1325

 Residual

11,581.3

1

11,581.28

9.74

0.0041

 Lack of fit

34,486.8

29

1189.2

  

 Pure error

34,470.1

22

1566.82

656.48

 < 0.0001

 Cor total

16.71

7

2.39

  

TFC (y2)e

 Model

129,800

20

6491.91

19.96

 < 0.0001

 X1

115,600

1

1.16E+05

355.45

 < 0.0001

 X2

679.09

1

679.09

2.09

0.1592

 X3

221.21

1

221.21

0.6801

0.4163

 X4

2763.7

1

2763.7

8.5

0.0068

 X5

737.91

1

737.91

2.27

0.1428

 X1X2

213.72

1

213.72

0.657

0.4242

 X1X3

1015

1

1015

3.12

0.0878

 X1X4

243.55

1

243.55

0.7488

0.394

 X1X5

720.84

1

720.84

2.22

0.1474

 X2X3

57.46

1

57.46

0.1767

0.6774

 X2X4

496.9

1

496.9

1.53

0.2264

 X3X4

32.37

1

32.37

0.0995

0.7547

 X3X5

0.0021

1

0.0021

6.40E-06

0.998

 X4X5

1006.91

1

1006.91

3.1

0.0891

 X12

317.76

1

317.76

0.9769

0.3311

 X22

660.42

1

660.42

2.03

0.1649

 X32

1594.97

1

1594.97

4.9

0.0348

 X42

1575.56

1

1575.56

4.84

0.0359

 X52

894.54

1

894.54

2.75

0.108

 Residual

3497.2

1

3497.2

10.75

0.0027

 Lack of fit

9432.79

29

325.27

  

 Pure error

9424.85

22

428.4

378.08

 < 0.0001

 Cor total

7.93

7

1.13

  

%DPPH*sc (y3)f

 Model

3314.9

20

165.74

13.73

 < 0.0001

 X1

2645.01

1

2645.01

219.12

 < 0.0001

 X2

33.29

1

33.29

2.76

0.1076

 X3

7.45

1

7.45

0.617

0.4385

 X4

49.66

1

49.66

4.11

0.0518

 X5

5.49

1

5.49

0.455

0.5053

 X1X2

0.1164

1

0.1164

0.0096

0.9224

 X1X3

3.06

1

3.06

0.2532

0.6186

 X1X4

67.48

1

67.48

5.59

0.025

 X1X5

5.64

1

5.64

0.4669

0.4998

 X2X3

26.44

1

26.44

2.19

0.1496

 X2X4

67.77

1

67.77

5.61

0.0247

 X3X4

0.1093

1

0.1093

0.0091

0.9249

 X3X5

23.38

1

23.38

1.94

0.1746

 X4X5

69.24

1

69.24

5.74

0.0233

 X12

90.01

1

90.01

7.46

0.0106

 X22

105.14

1

105.14

8.71

0.0062

 X32

110.2

1

110.2

9.13

0.0052

 X42

37.65

1

37.65

3.12

0.0879

 X52

42.31

1

42.31

3.51

0.0713

 Residual

20.21

1

20.21

1.67

0.2059

 Lack of fit

350.06

29

12.07

  

 Pure error

321.82

22

14.63

3.63

0.0431

 Cor total

28.24

7

4.03

  

%ABTS*sc (y4)g

 Model

3196.49

20

159.82

9.97

 < 0.0001

 X1

2543.85

1

2543.85

158.7

 < 0.0001

 X2

58.62

1

58.62

3.66

0.0658

 X3

6.13

1

6.13

0.3825

0.5411

 X4

61.36

1

61.36

3.83

0.0601

 X5

4.51

1

4.51

0.2812

0.6

 X1X2

2.43

1

2.43

0.1513

0.7001

 X1X3

10.66

1

10.66

0.6651

0.4214

 X1X4

73.84

1

73.84

4.61

0.0403

 X1X5

0.4209

1

0.4209

0.0263

0.8724

 X2X3

19.58

1

19.58

1.22

0.2782

 X2X4

56.9

1

56.9

3.55

0.0696

 X3X4

0.5913

1

0.5913

0.0369

0.849

 X3X5

38.43

1

38.43

2.4

0.1324

 X4X5

94.57

1

94.57

5.9

0.0216

 X12

52.56

1

52.56

3.28

0.0806

 X22

98.26

1

98.26

6.13

0.0194

 X32

74.67

1

74.67

4.66

0.0393

 X42

18.14

1

18.14

1.13

0.2961

 X52

35.28

1

35.28

2.2

0.1487

 Residual

14.48

1

14.48

0.9032

0.3498

 Lack of fit

464.86

29

16.03

  

 Pure error

428.67

22

19.48

3.77

0.039

 Cor total

36.19

7

5.17

  

FRAP (y5)h

 Model

3282.89

20

164.14

10.64

 < 0.0001

 X1

2564.2

1

2564.2

166.17

 < 0.0001

 X2

76.61

1

76.61

4.96

0.0338

 X3

7.49

1

7.49

0.4854

0.4915

 X4

67.35

1

67.35

4.36

0.0456

 X5

3.5

1

3.5

0.2269

0.6374

 X1X2

2.48

1

2.48

0.1608

0.6914

 X1X3

14.62

1

14.62

0.9475

0.3384

 X1X4

67.31

1

67.31

4.36

0.0456

 X1X5

2.57

1

2.57

0.1666

0.6862

 X2X3

18.93

1

18.93

1.23

0.2772

 X2X4

59.98

1

59.98

3.89

0.0583

 X3X4

0.0109

1

0.0109

0.0007

0.979

 X3X5

26.48

1

26.48

1.72

0.2005

 X4X5

106.32

1

106.32

6.89

0.0137

 X12

59.32

1

59.32

3.84

0.0596

 X22

120.83

1

120.83

7.83

0.009

 X32

80.57

1

80.57

5.22

0.0298

 X42

25.1

1

25.1

1.63

0.2123

 X52

48.08

1

48.08

3.12

0.0881

 Residual

12.03

1

12.03

0.7794

0.3846

 Lack of fit

447.5

29

15.43

  

 Pure error

416.99

22

18.95

4.35

0.0264

 Cor total

30.51

7

4.36

  
  1. aDegrees of freedom.
  2. bTest for comparing model variance with residual (error) variance.
  3. cProbability of seeing the observed F value if the null hypothesis is true.
  4. dStd Dev: 34.48; Mean: 526.91; R2 = 0.9273; R2 predicted = 0.6930; R2 adjusted = 0.8772.
  5. eStd Dev: 18.04; Mean: 347.09; R2 = 0.9323; adjusted R2 = 0.8856; predicted R2 = 0.7567.
  6. fStd Dev: 3.47; Mean: 67.88; R2 = 0.9045; adjusted R2 = 0.8386; predicted R2 = 0.6661.
  7. gStd Dev: 4.0; Mean: 63.43; R2 = 0.8730; adjusted R2 = 0.7855; predicted R2 = 0.5611.
  8. hStd Dev: 3.93; Mean: 58.74; R2 = 0.8800; adjusted R2 = 0.7973; predicted R2 = 0.5789.
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