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. 2024 Jan 12;14:1219. doi: 10.1038/s41598-023-49839-y

Table 3.

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

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

aDegrees of freedom.

bTest for comparing model variance with residual (error) variance.

cProbability of seeing the observed F value if the null hypothesis is true.

dStd Dev: 34.48; Mean: 526.91; R2 = 0.9273; R2 predicted = 0.6930; R2 adjusted = 0.8772.

eStd Dev: 18.04; Mean: 347.09; R2 = 0.9323; adjusted R2 = 0.8856; predicted R2 = 0.7567.

fStd Dev: 3.47; Mean: 67.88; R2 = 0.9045; adjusted R2 = 0.8386; predicted R2 = 0.6661.

gStd Dev: 4.0; Mean: 63.43; R2 = 0.8730; adjusted R2 = 0.7855; predicted R2 = 0.5611.

hStd Dev: 3.93; Mean: 58.74; R2 = 0.8800; adjusted R2 = 0.7973; predicted R2 = 0.5789.