================================================================================
COMPREHENSIVE STATISTICAL AND MACHINE LEARNING ANALYSIS REPORT
================================================================================
Date of analysis: 2026-05-31 00:20
Factors: Irrigation, Genotype, Silicon
Responses: hs, fs, fr, ft, ds, dr, dt, rwc, chla, chlb, chlt, car, gp, ml
Observations: 120
================================================================================

================================================================================
1. DESCRIPTIVE STATISTICS
================================================================================

--- Factor: Irrigation ---
Statistic            Value
-------------------------
  (categorical: ['Ctrl', 'Drought'])

--- Factor: Genotype ---
Statistic            Value
-------------------------
  (categorical: ['G20', 'G61', 'G62'])

--- Factor: Silicon ---
Statistic            Value
-------------------------
  (categorical: ['Ctrl', 'N-Si', 'Si'])

--- Response: hs ---
Statistic            Value
-------------------------
mean               37.8261
std                 9.4197
min                23.5000
25%                29.5000
50%                35.2500
75%                46.0000
max                57.0000

--- Response: fs ---
Statistic            Value
-------------------------
mean               10.7807
std                 4.7457
min                 2.9900
25%                 6.6600
50%                10.6350
75%                15.0750
max                21.4200

--- Response: fr ---
Statistic            Value
-------------------------
mean               11.9334
std                 5.6635
min                 3.0200
25%                 7.1450
50%                11.6300
75%                16.3600
max                24.9000

--- Response: ft ---
Statistic            Value
-------------------------
mean               22.7232
std                10.1873
min                 6.3100
25%                13.5550
50%                23.7300
75%                31.0650
max                44.4100

--- Response: ds ---
Statistic            Value
-------------------------
mean                1.2383
std                 0.3934
min                 0.5700
25%                 0.9500
50%                 1.1800
75%                 1.5475
max                 2.2100

--- Response: dr ---
Statistic            Value
-------------------------
mean                1.8442
std                 0.6635
min                 0.6400
25%                 1.3100
50%                 1.7300
75%                 2.2650
max                 3.6600

--- Response: dt ---
Statistic            Value
-------------------------
mean                3.1367
std                 1.0426
min                 1.4500
25%                 2.3700
50%                 2.9200
75%                 3.9350
max                 5.7100

--- Response: rwc ---
Statistic            Value
-------------------------
mean                0.8403
std                 0.0437
min                 0.7300
25%                 0.8100
50%                 0.8400
75%                 0.8700
max                 0.9500

--- Response: chla ---
Statistic            Value
-------------------------
mean                0.9457
std                 0.2534
min                 0.3600
25%                 0.7700
50%                 0.9000
75%                 1.1300
max                 1.5700

--- Response: chlb ---
Statistic            Value
-------------------------
mean                0.3313
std                 0.0968
min                 0.1300
25%                 0.2675
50%                 0.3300
75%                 0.3900
max                 0.5600

--- Response: chlt ---
Statistic            Value
-------------------------
mean                1.3237
std                 0.3102
min                 0.5700
25%                 1.1275
50%                 1.3050
75%                 1.5525
max                 1.9900

--- Response: car ---
Statistic            Value
-------------------------
mean                3.2852
std                 0.7345
min                 1.5000
25%                 2.7175
50%                 3.2500
75%                 3.8600
max                 4.8600

--- Response: gp ---
Statistic            Value
-------------------------
mean               26.1951
std                 9.0696
min                10.4500
25%                19.1925
50%                24.8100
75%                31.8250
max                47.8900

--- Response: ml ---
Statistic            Value
-------------------------
mean                0.5058
std                 0.1628
min                 0.1000
25%                 0.4000
50%                 0.5150
75%                 0.6225
max                 0.8900

--- Treatment Combination Means ---

hs:
  Ctrl_G62_Ctrl                     55.2000
  Ctrl_G62_N-Si                     52.0000
  Ctrl_G62_Si                       48.8000
  Ctrl_G20_Ctrl                     48.4000
  Ctrl_G20_N-Si                     46.8630
  Ctrl_G20_Si                       43.7000
  Ctrl_G61_Ctrl                     42.1000
  Ctrl_G61_N-Si                     40.8000
  Ctrl_G61_Si                       39.4000
  Drought_G20_N-Si                  31.3500
  Drought_G62_N-Si                  31.0000
  Drought_G62_Ctrl                  30.2000
  Drought_G61_Ctrl                  29.9000
  Drought_G20_Ctrl                  29.8000
  Drought_G62_Si                    28.4000
  Drought_G20_Si                    27.8500
  Drought_G61_N-Si                  27.6000
  Drought_G61_Si                    26.5000

fs:
  Ctrl_G20_Ctrl                     18.1480
  Ctrl_G62_Ctrl                     16.0800
  Ctrl_G62_N-Si                     15.4360
  Ctrl_G20_N-Si                     15.3170
  Ctrl_G62_Si                       14.9780
  Ctrl_G20_Si                       14.5180
  Ctrl_G61_Si                       13.4620
  Ctrl_G61_N-Si                     12.2420
  Ctrl_G61_Ctrl                     12.2280
  Drought_G62_Ctrl                   7.6980
  Drought_G20_N-Si                   7.5630
  Drought_G20_Ctrl                   6.9540
  Drought_G61_Ctrl                   6.3300
  Drought_G20_Si                     6.2830
  Drought_G62_Si                     6.1980
  Drought_G62_N-Si                   6.1540
  Drought_G61_N-Si                   5.4980
  Drought_G61_Si                     4.8660

fr:
  Ctrl_G61_Ctrl                     22.3700
  Ctrl_G61_Si                       19.0800
  Ctrl_G62_Si                       18.5900
  Ctrl_G61_N-Si                     16.9540
  Ctrl_G20_Si                       16.8430
  Ctrl_G20_Ctrl                     15.9650
  Ctrl_G20_N-Si                     15.5960
  Ctrl_G62_Ctrl                     14.8820
  Ctrl_G62_N-Si                     13.4880
  Drought_G62_Ctrl                   9.1140
  Drought_G20_N-Si                   8.6030
  Drought_G62_Si                     7.7520
  Drought_G20_Ctrl                   6.9120
  Drought_G62_N-Si                   6.7620
  Drought_G61_Ctrl                   6.7500
  Drought_G20_Si                     6.1330
  Drought_G61_N-Si                   5.6600
  Drought_G61_Si                     4.8960

ft:
  Ctrl_G61_Ctrl                     35.2040
  Ctrl_G61_Si                       33.5700
  Ctrl_G20_Si                       32.7580
  Ctrl_G20_Ctrl                     32.4670
  Ctrl_G62_Si                       32.2560
  Ctrl_G62_Ctrl                     31.3640
  Ctrl_G20_N-Si                     30.8560
  Ctrl_G61_N-Si                     29.9660
  Ctrl_G62_N-Si                     29.7260
  Drought_G20_N-Si                  16.1660
  Drought_G62_Ctrl                  16.1480
  Drought_G62_Si                    13.9500
  Drought_G20_Ctrl                  13.8660
  Drought_G61_Ctrl                  13.0800
  Drought_G62_N-Si                  12.9040
  Drought_G20_Si                    12.1820
  Drought_G61_N-Si                  10.8360
  Drought_G61_Si                     9.7620

ds:
  Ctrl_G20_Ctrl                      1.6430
  Ctrl_G20_N-Si                      1.6060
  Ctrl_G62_N-Si                      1.6020
  Ctrl_G20_Si                        1.5900
  Ctrl_G62_Si                        1.5740
  Ctrl_G62_Ctrl                      1.5580
  Ctrl_G61_Si                        1.4620
  Ctrl_G61_Ctrl                      1.4360
  Ctrl_G61_N-Si                      1.3620
  Drought_G61_Ctrl                   1.1020
  Drought_G62_Ctrl                   1.0540
  Drought_G20_Ctrl                   0.9970
  Drought_G20_N-Si                   0.9870
  Drought_G62_Si                     0.8900
  Drought_G20_Si                     0.8430
  Drought_G61_N-Si                   0.7960
  Drought_G61_Si                     0.7840
  Drought_G62_N-Si                   0.7660

dr:
  Ctrl_G61_N-Si                      2.9980
  Ctrl_G61_Si                        2.9940
  Ctrl_G61_Ctrl                      2.8920
  Ctrl_G62_Si                        2.4120
  Ctrl_G20_Si                        2.3020
  Ctrl_G20_N-Si                      2.1540
  Ctrl_G62_N-Si                      1.9800
  Ctrl_G20_Ctrl                      1.8800
  Ctrl_G62_Ctrl                      1.8020
  Drought_G61_Ctrl                   1.8020
  Drought_G20_N-Si                   1.6830
  Drought_G20_Si                     1.3800
  Drought_G61_N-Si                   1.3780
  Drought_G20_Ctrl                   1.2450
  Drought_G62_Ctrl                   1.2360
  Drought_G62_N-Si                   1.1760
  Drought_G61_Si                     1.1640
  Drought_G62_Si                     1.1400

dt:
  Ctrl_G61_Ctrl                      5.2100
  Ctrl_G61_Si                        4.4960
  Ctrl_G61_N-Si                      4.2460
  Ctrl_G62_Si                        4.0880
  Ctrl_G20_Si                        3.8440
  Ctrl_G20_N-Si                      3.6430
  Ctrl_G20_Ctrl                      3.6420
  Ctrl_G62_Ctrl                      3.5120
  Ctrl_G62_N-Si                      3.4680
  Drought_G61_Ctrl                   3.1040
  Drought_G20_N-Si                   2.6220
  Drought_G20_Ctrl                   2.3370
  Drought_G62_Ctrl                   2.2900
  Drought_G20_Si                     2.2230
  Drought_G61_N-Si                   2.1740
  Drought_G62_N-Si                   2.0920
  Drought_G62_Si                     2.0300
  Drought_G61_Si                     1.9480

rwc:
  Ctrl_G62_Ctrl                      0.8980
  Ctrl_G20_Ctrl                      0.8900
  Ctrl_G20_N-Si                      0.8840
  Ctrl_G62_N-Si                      0.8760
  Ctrl_G20_Si                        0.8650
  Ctrl_G61_Ctrl                      0.8560
  Ctrl_G61_N-Si                      0.8560
  Ctrl_G62_Si                        0.8500
  Ctrl_G61_Si                        0.8460
  Drought_G20_N-Si                   0.8310
  Drought_G20_Ctrl                   0.8170
  Drought_G62_Ctrl                   0.8160
  Drought_G62_Si                     0.8160
  Drought_G20_Si                     0.8000
  Drought_G61_Ctrl                   0.7960
  Drought_G61_Si                     0.7960
  Drought_G62_N-Si                   0.7960
  Drought_G61_N-Si                   0.7900

chla:
  Drought_G20_Si                     1.2220
  Drought_G61_N-Si                   1.1780
  Drought_G61_Si                     1.1640
  Drought_G20_N-Si                   1.1280
  Drought_G62_Si                     1.1080
  Drought_G20_Ctrl                   1.0180
  Drought_G61_Ctrl                   1.0100
  Ctrl_G62_Ctrl                      1.0000
  Drought_G62_N-Si                   0.9800
  Drought_G62_Ctrl                   0.9640
  Ctrl_G20_N-Si                      0.9200
  Ctrl_G20_Ctrl                      0.8210
  Ctrl_G20_Si                        0.8200
  Ctrl_G62_Si                        0.7720
  Ctrl_G62_N-Si                      0.7700
  Ctrl_G61_Si                        0.6620
  Ctrl_G61_Ctrl                      0.6420
  Ctrl_G61_N-Si                      0.5900

chlb:
  Drought_G20_Si                     0.4280
  Drought_G62_Si                     0.4260
  Drought_G20_N-Si                   0.4070
  Drought_G61_Si                     0.3980
  Drought_G20_Ctrl                   0.3820
  Drought_G61_N-Si                   0.3720
  Drought_G61_Ctrl                   0.3640
  Drought_G62_N-Si                   0.3560
  Drought_G62_Ctrl                   0.3520
  Ctrl_G20_N-Si                      0.3080
  Ctrl_G62_Ctrl                      0.3040
  Ctrl_G20_Ctrl                      0.2940
  Ctrl_G62_N-Si                      0.2880
  Ctrl_G20_Si                        0.2760
  Ctrl_G62_Si                        0.2480
  Ctrl_G61_N-Si                      0.2280
  Ctrl_G61_Ctrl                      0.2180
  Ctrl_G61_Si                        0.2080

chlt:
  Drought_G20_Si                     1.7370
  Drought_G20_Ctrl                   1.6580
  Drought_G61_Si                     1.6460
  Drought_G20_N-Si                   1.6190
  Drought_G61_N-Si                   1.4620
  Drought_G61_Ctrl                   1.4040
  Drought_G62_Si                     1.4000
  Drought_G62_Ctrl                   1.3980
  Drought_G62_N-Si                   1.3360
  Ctrl_G62_Ctrl                      1.2760
  Ctrl_G20_N-Si                      1.2550
  Ctrl_G62_N-Si                      1.2220
  Ctrl_G20_Ctrl                      1.1390
  Ctrl_G62_Si                        1.0580
  Ctrl_G20_Si                        1.0570
  Ctrl_G61_Si                        0.9640
  Ctrl_G61_Ctrl                      0.8620
  Ctrl_G61_N-Si                      0.8120

car:
  Drought_G61_Si                     4.2480
  Drought_G20_Ctrl                   4.1630
  Drought_G20_Si                     3.9790
  Drought_G20_N-Si                   3.7690
  Drought_G62_Si                     3.7360
  Drought_G61_N-Si                   3.6640
  Drought_G61_Ctrl                   3.5000
  Ctrl_G62_Ctrl                      3.3760
  Drought_G62_N-Si                   3.1940
  Drought_G62_Ctrl                   3.1400
  Ctrl_G20_N-Si                      3.0140
  Ctrl_G62_Si                        3.0060
  Ctrl_G20_Ctrl                      2.8970
  Ctrl_G61_Si                        2.6440
  Ctrl_G62_N-Si                      2.6200
  Ctrl_G20_Si                        2.5900
  Ctrl_G61_Ctrl                      2.5560
  Ctrl_G61_N-Si                      2.3360

gp:
  Drought_G61_N-Si                  38.2460
  Drought_G61_Ctrl                  38.0440
  Drought_G20_Si                    37.3450
  Drought_G61_Si                    35.6460
  Drought_G20_Ctrl                  32.1290
  Drought_G20_N-Si                  27.8190
  Drought_G62_N-Si                  25.2140
  Ctrl_G61_Si                       24.6900
  Drought_G62_Ctrl                  22.5700
  Ctrl_G62_Ctrl                     22.1780
  Ctrl_G61_N-Si                     21.8940
  Drought_G62_Si                    21.6980
  Ctrl_G20_Si                       21.1570
  Ctrl_G20_N-Si                     20.8110
  Ctrl_G20_Ctrl                     20.3750
  Ctrl_G61_Ctrl                     20.2280
  Ctrl_G62_Si                       19.8740
  Ctrl_G62_N-Si                     19.1280

ml:
  Drought_G20_Si                     0.6700
  Drought_G61_N-Si                   0.6440
  Drought_G62_N-Si                   0.6220
  Drought_G20_N-Si                   0.6180
  Drought_G61_Si                     0.6060
  Drought_G62_Si                     0.5860
  Drought_G62_Ctrl                   0.5780
  Drought_G61_Ctrl                   0.5760
  Drought_G20_Ctrl                   0.5650
  Ctrl_G61_Si                        0.4860
  Ctrl_G20_Si                        0.4520
  Ctrl_G20_Ctrl                      0.4400
  Ctrl_G61_Ctrl                      0.4340
  Ctrl_G62_Ctrl                      0.3960
  Ctrl_G61_N-Si                      0.3940
  Ctrl_G20_N-Si                      0.3760
  Ctrl_G62_Si                        0.2940
  Ctrl_G62_N-Si                      0.2800


================================================================================
2. STATISTICAL ASSUMPTION CHECKS
================================================================================

Table 1: Normality (Shapiro-Wilk) and Homogeneity of Variances (Levene)
Response Shapiro-Wilk W Shapiro p Distribution Levene W Levene p Variances      IQR Bounds Outliers
      hs         0.9165    0.0000   Non-normal   1.7525   0.1283     Equal   [4.75, 70.75]   ✅ None
      fs         0.9384    0.0000   Non-normal   1.6104   0.1629     Equal  [-5.96, 27.70]   ✅ None
      fr         0.9542    0.0004   Non-normal   1.7231   0.1349     Equal  [-6.68, 30.18]   ✅ None
      ft         0.9329    0.0000   Non-normal   2.3191   0.0478   Unequal [-12.71, 57.33]   ✅ None
      ds         0.9661    0.0040   Non-normal   1.2687   0.2823     Equal    [0.05, 2.44]   ✅ None
      dr         0.9655    0.0036   Non-normal   1.4860   0.1998     Equal   [-0.12, 3.70]   ✅ None
      dt         0.9550    0.0005   Non-normal   3.2194   0.0093   Unequal    [0.02, 6.28]   ✅ None
     rwc         0.9913    0.6508       Normal   0.6166   0.6874     Equal    [0.72, 0.96]   ✅ None
    chla         0.9868    0.2973       Normal   2.5031   0.0344   Unequal    [0.23, 1.67]   ✅ None
    chlb         0.9762    0.0314   Non-normal   6.4100   0.0000   Unequal    [0.08, 0.57]   ✅ None
    chlt         0.9891    0.4534       Normal   0.5577   0.7322     Equal    [0.49, 2.19]   ✅ None
     car         0.9765    0.0335   Non-normal   2.7845   0.0207   Unequal    [1.00, 5.57]   ✅ None
      gp         0.9585    0.0010   Non-normal   1.7256   0.1343     Equal   [0.24, 50.77]   ✅ None
      ml         0.9895    0.4891       Normal   0.3861   0.8575     Equal    [0.07, 0.96]   ✅ None


Outlier Detection Summary:
  hs: 0 outlier(s), IQR bounds: [4.75, 70.75]
  fs: 0 outlier(s), IQR bounds: [-5.96, 27.70]
  fr: 0 outlier(s), IQR bounds: [-6.68, 30.18]
  ft: 0 outlier(s), IQR bounds: [-12.71, 57.33]
  ds: 0 outlier(s), IQR bounds: [0.05, 2.44]
  dr: 0 outlier(s), IQR bounds: [-0.12, 3.70]
  dt: 0 outlier(s), IQR bounds: [0.02, 6.28]
  rwc: 0 outlier(s), IQR bounds: [0.72, 0.96]
  chla: 0 outlier(s), IQR bounds: [0.23, 1.67]
  chlb: 0 outlier(s), IQR bounds: [0.08, 0.57]
  chlt: 0 outlier(s), IQR bounds: [0.49, 2.19]
  car: 0 outlier(s), IQR bounds: [1.00, 5.57]
  gp: 0 outlier(s), IQR bounds: [0.24, 50.77]
  ml: 0 outlier(s), IQR bounds: [0.07, 0.96]


================================================================================
3. PEARSON CORRELATION COEFFICIENTS
================================================================================

Table 2: Factor-Response Pearson Correlations
Response     Factor Pearson r p-value Sig.
      hs Irrigation       N/A     N/A  N/A
      hs   Genotype       N/A     N/A  N/A
      hs    Silicon       N/A     N/A  N/A
      fs Irrigation       N/A     N/A  N/A
      fs   Genotype       N/A     N/A  N/A
      fs    Silicon       N/A     N/A  N/A
      fr Irrigation       N/A     N/A  N/A
      fr   Genotype       N/A     N/A  N/A
      fr    Silicon       N/A     N/A  N/A
      ft Irrigation       N/A     N/A  N/A
      ft   Genotype       N/A     N/A  N/A
      ft    Silicon       N/A     N/A  N/A
      ds Irrigation       N/A     N/A  N/A
      ds   Genotype       N/A     N/A  N/A
      ds    Silicon       N/A     N/A  N/A
      dr Irrigation       N/A     N/A  N/A
      dr   Genotype       N/A     N/A  N/A
      dr    Silicon       N/A     N/A  N/A
      dt Irrigation       N/A     N/A  N/A
      dt   Genotype       N/A     N/A  N/A
      dt    Silicon       N/A     N/A  N/A
     rwc Irrigation       N/A     N/A  N/A
     rwc   Genotype       N/A     N/A  N/A
     rwc    Silicon       N/A     N/A  N/A
    chla Irrigation       N/A     N/A  N/A
    chla   Genotype       N/A     N/A  N/A
    chla    Silicon       N/A     N/A  N/A
    chlb Irrigation       N/A     N/A  N/A
    chlb   Genotype       N/A     N/A  N/A
    chlb    Silicon       N/A     N/A  N/A
    chlt Irrigation       N/A     N/A  N/A
    chlt   Genotype       N/A     N/A  N/A
    chlt    Silicon       N/A     N/A  N/A
     car Irrigation       N/A     N/A  N/A
     car   Genotype       N/A     N/A  N/A
     car    Silicon       N/A     N/A  N/A
      gp Irrigation       N/A     N/A  N/A
      gp   Genotype       N/A     N/A  N/A
      gp    Silicon       N/A     N/A  N/A
      ml Irrigation       N/A     N/A  N/A
      ml   Genotype       N/A     N/A  N/A
      ml    Silicon       N/A     N/A  N/A


Interpretation:
  • Irrigation vs hs: insufficient data (N/A)
  • Genotype vs hs: insufficient data (N/A)
  • Silicon vs hs: insufficient data (N/A)
  • Irrigation vs fs: insufficient data (N/A)
  • Genotype vs fs: insufficient data (N/A)
  • Silicon vs fs: insufficient data (N/A)
  • Irrigation vs fr: insufficient data (N/A)
  • Genotype vs fr: insufficient data (N/A)
  • Silicon vs fr: insufficient data (N/A)
  • Irrigation vs ft: insufficient data (N/A)
  • Genotype vs ft: insufficient data (N/A)
  • Silicon vs ft: insufficient data (N/A)
  • Irrigation vs ds: insufficient data (N/A)
  • Genotype vs ds: insufficient data (N/A)
  • Silicon vs ds: insufficient data (N/A)
  • Irrigation vs dr: insufficient data (N/A)
  • Genotype vs dr: insufficient data (N/A)
  • Silicon vs dr: insufficient data (N/A)
  • Irrigation vs dt: insufficient data (N/A)
  • Genotype vs dt: insufficient data (N/A)
  • Silicon vs dt: insufficient data (N/A)
  • Irrigation vs rwc: insufficient data (N/A)
  • Genotype vs rwc: insufficient data (N/A)
  • Silicon vs rwc: insufficient data (N/A)
  • Irrigation vs chla: insufficient data (N/A)
  • Genotype vs chla: insufficient data (N/A)
  • Silicon vs chla: insufficient data (N/A)
  • Irrigation vs chlb: insufficient data (N/A)
  • Genotype vs chlb: insufficient data (N/A)
  • Silicon vs chlb: insufficient data (N/A)
  • Irrigation vs chlt: insufficient data (N/A)
  • Genotype vs chlt: insufficient data (N/A)
  • Silicon vs chlt: insufficient data (N/A)
  • Irrigation vs car: insufficient data (N/A)
  • Genotype vs car: insufficient data (N/A)
  • Silicon vs car: insufficient data (N/A)
  • Irrigation vs gp: insufficient data (N/A)
  • Genotype vs gp: insufficient data (N/A)
  • Silicon vs gp: insufficient data (N/A)
  • Irrigation vs ml: insufficient data (N/A)
  • Genotype vs ml: insufficient data (N/A)
  • Silicon vs ml: insufficient data (N/A)


================================================================================
4. N-WAY ANOVA RESULTS
================================================================================

--- hs ---
                                      sum_sq     df          F  PR(>F)      η²
C(Irrigation_cat)                  8723.2916    1.0  1726.8173  0.0000  0.9422
C(Genotype_cat)                     646.9143    2.0    64.0299  0.0000  0.5471
C(Silicon_cat)                      263.5693    2.0    26.0874  0.0000  0.3299
C(Irrigation_cat):C(Genotype_cat)   333.7523    2.0    33.0339  0.0000  0.3840
C(Irrigation_cat):C(Silicon_cat)     35.9528    2.0     3.5585  0.0319  0.0629
C(Genotype_cat):C(Silicon_cat)       20.0111    4.0     0.9903  0.4162  0.0360
Residual                            535.4758  106.0        NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=1726.82, p=0.0000, η²=0.9422 (large effect)
    • C(Genotype_cat): F=64.03, p=0.0000, η²=0.5471 (large effect)
    • C(Silicon_cat): F=26.09, p=0.0000, η²=0.3299 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=33.03, p=0.0000, η²=0.3840 (large effect)
    • C(Irrigation_cat):C(Silicon_cat): F=3.56, p=0.0319, η²=0.0629 (medium effect)

--- fs ---
                                      sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  2169.5405    1.0  742.9954  0.0000  0.8751
C(Genotype_cat)                     115.1888    2.0   19.7242  0.0000  0.2712
C(Silicon_cat)                       42.1065    2.0    7.2100  0.0012  0.1197
C(Irrigation_cat):C(Genotype_cat)    20.6002    2.0    3.5274  0.0329  0.0624
C(Irrigation_cat):C(Silicon_cat)      8.2640    2.0    1.4151  0.2475  0.0260
C(Genotype_cat):C(Silicon_cat)       14.8212    4.0    1.2689  0.2869  0.0457
Residual                            309.5191  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=743.00, p=0.0000, η²=0.8751 (large effect)
    • C(Genotype_cat): F=19.72, p=0.0000, η²=0.2712 (large effect)
    • C(Silicon_cat): F=7.21, p=0.0012, η²=0.1197 (medium effect)
    • C(Irrigation_cat):C(Genotype_cat): F=3.53, p=0.0329, η²=0.0624 (medium effect)

--- fr ---
                                      sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  2897.9824    1.0  541.6730  0.0000  0.8363
C(Genotype_cat)                      18.9240    2.0    1.7686  0.1756  0.0323
C(Silicon_cat)                       18.6920    2.0    1.7469  0.1793  0.0319
C(Irrigation_cat):C(Genotype_cat)   156.3467    2.0   14.6117  0.0000  0.2161
C(Irrigation_cat):C(Silicon_cat)     65.1548    2.0    6.0892  0.0031  0.1031
C(Genotype_cat):C(Silicon_cat)       92.8071    4.0    4.3367  0.0027  0.1406
Residual                            567.1063  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=541.67, p=0.0000, η²=0.8363 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=14.61, p=0.0000, η²=0.2161 (large effect)
    • C(Irrigation_cat):C(Silicon_cat): F=6.09, p=0.0031, η²=0.1031 (medium effect)
    • C(Genotype_cat):C(Silicon_cat): F=4.34, p=0.0027, η²=0.1406 (large effect)

--- ft ---
                                       sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  10373.2207    1.0  670.9472  0.0000  0.8636
C(Genotype_cat)                       19.1885    2.0    0.6206  0.5396  0.0116
C(Silicon_cat)                        42.9703    2.0    1.3897  0.2537  0.0256
C(Irrigation_cat):C(Genotype_cat)    102.5205    2.0    3.3156  0.0401  0.0589
C(Irrigation_cat):C(Silicon_cat)     100.5335    2.0    3.2513  0.0426  0.0578
C(Genotype_cat):C(Silicon_cat)        72.6386    4.0    1.1746  0.3262  0.0424
Residual                            1638.8197  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=670.95, p=0.0000, η²=0.8636 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=3.32, p=0.0401, η²=0.0589 (small effect)
    • C(Irrigation_cat):C(Silicon_cat): F=3.25, p=0.0426, η²=0.0578 (small effect)

--- ds ---
                                    sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  12.1158    1.0  241.2313  0.0000  0.6947
C(Genotype_cat)                     0.2914    2.0    2.9014  0.0593  0.0519
C(Silicon_cat)                      0.2632    2.0    2.6202  0.0775  0.0471
C(Irrigation_cat):C(Genotype_cat)   0.1200    2.0    1.1945  0.3069  0.0220
C(Irrigation_cat):C(Silicon_cat)    0.1737    2.0    1.7294  0.1824  0.0316
C(Genotype_cat):C(Silicon_cat)      0.1280    4.0    0.6369  0.6373  0.0235
Residual                            5.3238  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=241.23, p=0.0000, η²=0.6947 (large effect)

--- dr ---
                                    sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  26.3110    1.0  208.7346  0.0000  0.6632
C(Genotype_cat)                     5.6440    2.0   22.3880  0.0000  0.2970
C(Silicon_cat)                      0.5642    2.0    2.2379  0.1117  0.0405
C(Irrigation_cat):C(Genotype_cat)   3.5368    2.0   14.0294  0.0000  0.2093
C(Irrigation_cat):C(Silicon_cat)    1.4105    2.0    5.5950  0.0049  0.0955
C(Genotype_cat):C(Silicon_cat)      1.5636    4.0    3.1011  0.0186  0.1048
Residual                           13.3613  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=208.73, p=0.0000, η²=0.6632 (large effect)
    • C(Genotype_cat): F=22.39, p=0.0000, η²=0.2970 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=14.03, p=0.0000, η²=0.2093 (large effect)
    • C(Irrigation_cat):C(Silicon_cat): F=5.60, p=0.0049, η²=0.0955 (medium effect)
    • C(Genotype_cat):C(Silicon_cat): F=3.10, p=0.0186, η²=0.1048 (medium effect)

--- dt ---
                                    sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  77.4092    1.0  251.7088  0.0000  0.7037
C(Genotype_cat)                     6.5616    2.0   10.6681  0.0001  0.1676
C(Silicon_cat)                      0.9124    2.0    1.4834  0.2315  0.0272
C(Irrigation_cat):C(Genotype_cat)   4.3200    2.0    7.0236  0.0014  0.1170
C(Irrigation_cat):C(Silicon_cat)    1.9602    2.0    3.1870  0.0453  0.0567
C(Genotype_cat):C(Silicon_cat)      5.5976    4.0    4.5504  0.0020  0.1465
Residual                           32.5987  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=251.71, p=0.0000, η²=0.7037 (large effect)
    • C(Genotype_cat): F=10.67, p=0.0001, η²=0.1676 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=7.02, p=0.0014, η²=0.1170 (medium effect)
    • C(Irrigation_cat):C(Silicon_cat): F=3.19, p=0.0453, η²=0.0567 (small effect)
    • C(Genotype_cat):C(Silicon_cat): F=4.55, p=0.0020, η²=0.1465 (large effect)

--- rwc ---
                                   sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  0.1184    1.0  148.9910  0.0000  0.5843
C(Genotype_cat)                    0.0121    2.0    7.6278  0.0008  0.1258
C(Silicon_cat)                     0.0069    2.0    4.3619  0.0151  0.0760
C(Irrigation_cat):C(Genotype_cat)  0.0002    2.0    0.1179  0.8889  0.0022
C(Irrigation_cat):C(Silicon_cat)   0.0017    2.0    1.0766  0.3445  0.0199
C(Genotype_cat):C(Silicon_cat)     0.0038    4.0    1.2029  0.3140  0.0434
Residual                           0.0843  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=148.99, p=0.0000, η²=0.5843 (large effect)
    • C(Genotype_cat): F=7.63, p=0.0008, η²=0.1258 (medium effect)
    • C(Silicon_cat): F=4.36, p=0.0151, η²=0.0760 (medium effect)

--- chla ---
                                   sum_sq     df        F  PR(>F)      η²
C(Irrigation_cat)                  2.6731    1.0  74.5206  0.0000  0.4128
C(Genotype_cat)                    0.2664    2.0   3.7128  0.0276  0.0655
C(Silicon_cat)                     0.0790    2.0   1.1018  0.3361  0.0204
C(Irrigation_cat):C(Genotype_cat)  0.4006    2.0   5.5836  0.0049  0.0953
C(Irrigation_cat):C(Silicon_cat)   0.2626    2.0   3.6601  0.0290  0.0646
C(Genotype_cat):C(Silicon_cat)     0.1599    4.0   1.1143  0.3537  0.0404
Residual                           3.8022  106.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=74.52, p=0.0000, η²=0.4128 (large effect)
    • C(Genotype_cat): F=3.71, p=0.0276, η²=0.0655 (medium effect)
    • C(Irrigation_cat):C(Genotype_cat): F=5.58, p=0.0049, η²=0.0953 (medium effect)
    • C(Irrigation_cat):C(Silicon_cat): F=3.66, p=0.0290, η²=0.0646 (medium effect)

--- chlb ---
                                   sum_sq     df        F  PR(>F)      η²
C(Irrigation_cat)                  0.4392    1.0  82.0202  0.0000  0.4362
C(Genotype_cat)                    0.0526    2.0   4.9091  0.0091  0.0848
C(Silicon_cat)                     0.0035    2.0   0.3279  0.7212  0.0061
C(Irrigation_cat):C(Genotype_cat)  0.0163    2.0   1.5252  0.2223  0.0280
C(Irrigation_cat):C(Silicon_cat)   0.0336    2.0   3.1404  0.0473  0.0559
C(Genotype_cat):C(Silicon_cat)     0.0025    4.0   0.1145  0.9772  0.0043
Residual                           0.5676  106.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=82.02, p=0.0000, η²=0.4362 (large effect)
    • C(Genotype_cat): F=4.91, p=0.0091, η²=0.0848 (medium effect)
    • C(Irrigation_cat):C(Silicon_cat): F=3.14, p=0.0473, η²=0.0559 (small effect)

--- chlt ---
                                   sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  6.4821    1.0  264.0142  0.0000  0.7135
C(Genotype_cat)                    1.0315    2.0   21.0068  0.0000  0.2838
C(Silicon_cat)                     0.0047    2.0    0.0966  0.9080  0.0018
C(Irrigation_cat):C(Genotype_cat)  0.7945    2.0   16.1795  0.0000  0.2339
C(Irrigation_cat):C(Silicon_cat)   0.2719    2.0    5.5362  0.0052  0.0946
C(Genotype_cat):C(Silicon_cat)     0.2670    4.0    2.7186  0.0335  0.0930
Residual                           2.6025  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=264.01, p=0.0000, η²=0.7135 (large effect)
    • C(Genotype_cat): F=21.01, p=0.0000, η²=0.2838 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=16.18, p=0.0000, η²=0.2339 (large effect)
    • C(Irrigation_cat):C(Silicon_cat): F=5.54, p=0.0052, η²=0.0946 (medium effect)
    • C(Genotype_cat):C(Silicon_cat): F=2.72, p=0.0335, η²=0.0930 (medium effect)

--- car ---
                                    sum_sq     df         F  PR(>F)      η²
C(Irrigation_cat)                  28.8316    1.0  120.5605  0.0000  0.5321
C(Genotype_cat)                     1.6444    2.0    3.4381  0.0358  0.0609
C(Silicon_cat)                      0.7636    2.0    1.5966  0.2074  0.0292
C(Irrigation_cat):C(Genotype_cat)   4.0186    2.0    8.4019  0.0004  0.1368
C(Irrigation_cat):C(Silicon_cat)    1.3383    2.0    2.7981  0.0654  0.0501
C(Genotype_cat):C(Silicon_cat)      2.2614    4.0    2.3640  0.0576  0.0819
Residual                           25.3495  106.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=120.56, p=0.0000, η²=0.5321 (large effect)
    • C(Genotype_cat): F=3.44, p=0.0358, η²=0.0609 (medium effect)
    • C(Irrigation_cat):C(Genotype_cat): F=8.40, p=0.0004, η²=0.1368 (medium effect)

--- gp ---
                                      sum_sq     df        F  PR(>F)      η²
C(Irrigation_cat)                  3168.6046    1.0  71.1271  0.0000  0.4016
C(Genotype_cat)                     983.7054    2.0  11.0408  0.0000  0.1724
C(Silicon_cat)                       94.3300    2.0   1.0587  0.3505  0.0196
C(Irrigation_cat):C(Genotype_cat)   621.4817    2.0   6.9753  0.0014  0.1163
C(Irrigation_cat):C(Silicon_cat)     24.0098    2.0   0.2695  0.7643  0.0051
C(Genotype_cat):C(Silicon_cat)      174.4976    4.0   0.9793  0.4222  0.0356
Residual                           4722.1375  106.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=71.13, p=0.0000, η²=0.4016 (large effect)
    • C(Genotype_cat): F=11.04, p=0.0000, η²=0.1724 (large effect)
    • C(Irrigation_cat):C(Genotype_cat): F=6.98, p=0.0014, η²=0.1163 (medium effect)

--- ml ---
                                   sum_sq     df        F  PR(>F)      η²
C(Irrigation_cat)                  1.3000    1.0  87.5825  0.0000  0.4524
C(Genotype_cat)                    0.0864    2.0   2.9098  0.0589  0.0520
C(Silicon_cat)                     0.0285    2.0   0.9585  0.3868  0.0178
C(Irrigation_cat):C(Genotype_cat)  0.0437    2.0   1.4723  0.2340  0.0270
C(Irrigation_cat):C(Silicon_cat)   0.0790    2.0   2.6602  0.0746  0.0478
C(Genotype_cat):C(Silicon_cat)     0.0426    4.0   0.7182  0.5813  0.0264
Residual                           1.5734  106.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Irrigation_cat): F=87.58, p=0.0000, η²=0.4524 (large effect)

Significant Two-Way Interactions (p < 0.05):
Response   Factor_1 Factor_2     F_int        p_int Sig.        Type
      hs Irrigation Genotype 33.033933 7.065177e-12  *** Synergistic
      hs Irrigation  Silicon  3.558513 3.193215e-02    *    Moderate
      fs Irrigation Genotype  3.527433 3.287608e-02    *    Moderate
      fr Irrigation Genotype 14.611681 2.485818e-06  *** Synergistic
      fr Irrigation  Silicon  6.089164 3.138377e-03   **    Moderate
      fr   Genotype  Silicon  4.336732 2.744443e-03   **    Moderate
      ft Irrigation Genotype  3.315550 4.011617e-02    *    Moderate
      ft Irrigation  Silicon  3.251287 4.261872e-02    *    Moderate
      dr Irrigation Genotype 14.029407 3.931479e-06  *** Synergistic
      dr Irrigation  Silicon  5.595009 4.897878e-03   **    Moderate
      dr   Genotype  Silicon  3.101121 1.858250e-02    *    Moderate
      dt Irrigation Genotype  7.023578 1.366348e-03   **    Moderate
      dt Irrigation  Silicon  3.186960 4.528327e-02    *    Moderate
      dt   Genotype  Silicon  4.550360 1.974022e-03   **    Moderate
    chla Irrigation Genotype  5.583571 4.948818e-03   **    Moderate
    chla Irrigation  Silicon  3.660142 2.903388e-02    *    Moderate
    chlb Irrigation  Silicon  3.140440 4.731546e-02    *    Moderate
    chlt Irrigation Genotype 16.179494 7.375982e-07  *** Synergistic
    chlt Irrigation  Silicon  5.536222 5.165501e-03   **    Moderate
    chlt   Genotype  Silicon  2.718625 3.351327e-02    *    Moderate
     car Irrigation Genotype  8.401890 4.101935e-04  ***    Moderate
      gp Irrigation Genotype  6.975343 1.425824e-03   **    Moderate


Kruskal-Wallis Non-Parametric Validation:
Response     Factor ANOVA p KW H-statistic KW p-value              Agreement
      hs Irrigation  0.0000          89.40     0.0000     ✅ Both significant
      hs   Genotype  0.0000           9.09     0.0106     ✅ Both significant
      hs    Silicon  0.0000           4.58     0.1013          ⚠️ ANOVA only
      fs Irrigation  0.0000          89.26     0.0000     ✅ Both significant
      fs   Genotype  0.0000           6.56     0.0376     ✅ Both significant
      fs    Silicon  0.0012           2.46     0.2926          ⚠️ ANOVA only
      fr Irrigation  0.0000          88.07     0.0000     ✅ Both significant
      fr   Genotype  0.1756           0.17     0.9206 ✅ Both non-significant
      fr    Silicon  0.1793           0.41     0.8130 ✅ Both non-significant
      ft Irrigation  0.0000          89.26     0.0000     ✅ Both significant
      ft   Genotype  0.5396           0.36     0.8357 ✅ Both non-significant
      ft    Silicon  0.2537           0.66     0.7188 ✅ Both non-significant
      ds Irrigation  0.0000          82.18     0.0000     ✅ Both significant
      ds   Genotype  0.0593           1.68     0.4325 ✅ Both non-significant
      ds    Silicon  0.0775           2.05     0.3594 ✅ Both non-significant
      dr Irrigation  0.0000          64.96     0.0000     ✅ Both significant
      dr   Genotype  0.0000           8.35     0.0154     ✅ Both significant
      dr    Silicon  0.1117           1.24     0.5393 ✅ Both non-significant
      dt Irrigation  0.0000          75.46     0.0000     ✅ Both significant
      dt   Genotype  0.0001           3.94     0.1393          ⚠️ ANOVA only
      dt    Silicon  0.2315           1.06     0.5893 ✅ Both non-significant
     rwc Irrigation  0.0000          68.94     0.0000     ✅ Both significant
     rwc   Genotype  0.0008           5.69     0.0581          ⚠️ ANOVA only
     rwc    Silicon  0.0151           3.80     0.1495          ⚠️ ANOVA only
    chla Irrigation  0.0000          41.49     0.0000     ✅ Both significant
    chla   Genotype  0.0276           3.34     0.1887          ⚠️ ANOVA only
    chla    Silicon  0.3361           0.93     0.6266 ✅ Both non-significant
    chlb Irrigation  0.0000          49.00     0.0000     ✅ Both significant
    chlb   Genotype  0.0091           3.92     0.1406          ⚠️ ANOVA only
    chlb    Silicon  0.7212           0.26     0.8803 ✅ Both non-significant
    chlt Irrigation  0.0000          72.05     0.0000     ✅ Both significant
    chlt   Genotype  0.0000           8.81     0.0122     ✅ Both significant
    chlt    Silicon  0.9080           0.02     0.9904 ✅ Both non-significant
     car Irrigation  0.0000          54.39     0.0000     ✅ Both significant
     car   Genotype  0.0358           3.28     0.1938          ⚠️ ANOVA only
     car    Silicon  0.2074           1.11     0.5730 ✅ Both non-significant
      gp Irrigation  0.0000          38.59     0.0000     ✅ Both significant
      gp   Genotype  0.0000          10.38     0.0056     ✅ Both significant
      gp    Silicon  0.3505           0.84     0.6570 ✅ Both non-significant
      ml Irrigation  0.0000          52.88     0.0000     ✅ Both significant
      ml   Genotype  0.0589           2.29     0.3177 ✅ Both non-significant
      ml    Silicon  0.3868           0.63     0.7306 ✅ Both non-significant


================================================================================
5. POST-HOC MEAN COMPARISONS
================================================================================

--- hs (Fisher's LSD, CD = 2.4297) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G62_Ctrl                          55.2000     2.1679        a
Ctrl_G62_N-Si                          52.0000     2.3452        b
Ctrl_G62_Si                            48.8000     3.6332        c
Ctrl_G20_Ctrl                          48.4000     2.1318        c
Ctrl_G20_N-Si                          46.8630     2.3290        c
Ctrl_G20_Si                            43.7000     2.5949        d
Ctrl_G61_Ctrl                          42.1000     1.5969       de
Ctrl_G61_N-Si                          40.8000     1.2042        e
Ctrl_G61_Si                            39.4000     2.9026        e
Drought_G20_N-Si                       31.3500     1.6675        f
Drought_G62_N-Si                       31.0000     1.0000       fg
Drought_G62_Ctrl                       30.2000     1.6432      fgh
Drought_G61_Ctrl                       29.9000     0.9618      fgh
Drought_G20_Ctrl                       29.8000     1.5670      fgh
Drought_G62_Si                         28.4000     2.0736      ghi
Drought_G20_Si                         27.8500     3.5750       hi
Drought_G61_N-Si                       27.6000     1.6733       hi
Drought_G61_Si                         26.5000     1.3693        i

--- fs (Fisher's LSD, CD = 1.7759) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G20_Ctrl                          18.1480     1.7279        a
Ctrl_G62_Ctrl                          16.0800     2.2398        b
Ctrl_G62_N-Si                          15.4360     2.3326       bc
Ctrl_G20_N-Si                          15.3170     2.0363       bc
Ctrl_G62_Si                            14.9780     1.1570       bc
Ctrl_G20_Si                            14.5180     1.2336       bc
Ctrl_G61_Si                            13.4620     1.2416       cd
Ctrl_G61_N-Si                          12.2420     1.1111        d
Ctrl_G61_Ctrl                          12.2280     1.4836        d
Drought_G62_Ctrl                        7.6980     0.9592        e
Drought_G20_N-Si                        7.5630     1.9186        e
Drought_G20_Ctrl                        6.9540     2.4754       ef
Drought_G61_Ctrl                        6.3300     1.8048      efg
Drought_G20_Si                          6.2830     0.7023      efg
Drought_G62_Si                          6.1980     1.0046      efg
Drought_G62_N-Si                        6.1540     0.7016      efg
Drought_G61_N-Si                        5.4980     0.9797       fg
Drought_G61_Si                          4.8660     1.4398        g

--- fr (Fisher's LSD, CD = 2.4928) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G61_Ctrl                          22.3700     2.4277        a
Ctrl_G61_Si                            19.0800     3.0254        b
Ctrl_G62_Si                            18.5900     2.2445        b
Ctrl_G61_N-Si                          16.9540     2.0626       bc
Ctrl_G20_Si                            16.8430     2.8529       bc
Ctrl_G20_Ctrl                          15.9650     2.2563       cd
Ctrl_G20_N-Si                          15.5960     2.2653       cd
Ctrl_G62_Ctrl                          14.8820     1.6226       cd
Ctrl_G62_N-Si                          13.4880     3.3238        d
Drought_G62_Ctrl                        9.1140     0.8746        e
Drought_G20_N-Si                        8.6030     2.2526        e
Drought_G62_Si                          7.7520     2.0224       ef
Drought_G20_Ctrl                        6.9120     2.5868       ef
Drought_G62_N-Si                        6.7620     0.7787       ef
Drought_G61_Ctrl                        6.7500     1.9223       ef
Drought_G20_Si                          6.1330     2.3827        f
Drought_G61_N-Si                        5.6600     2.1611        f
Drought_G61_Si                          4.8960     1.3607        f

--- ft (Fisher's LSD, CD = 4.3157) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G61_Ctrl                          35.2040     5.2507        a
Ctrl_G61_Si                            33.5700     5.5629       ab
Ctrl_G20_Si                            32.7580     4.9792       ab
Ctrl_G20_Ctrl                          32.4670     5.5539       ab
Ctrl_G62_Si                            32.2560     1.5554       ab
Ctrl_G62_Ctrl                          31.3640     2.7802       ab
Ctrl_G20_N-Si                          30.8560     3.8703        b
Ctrl_G61_N-Si                          29.9660     3.4730        b
Ctrl_G62_N-Si                          29.7260     3.1836        b
Drought_G20_N-Si                       16.1660     3.8830        c
Drought_G62_Ctrl                       16.1480     1.4469       cd
Drought_G62_Si                         13.9500     2.9107      cde
Drought_G20_Ctrl                       13.8660     4.8917      cde
Drought_G61_Ctrl                       13.0800     3.6397      cde
Drought_G62_N-Si                       12.9040     0.9664      cde
Drought_G20_Si                         12.1820     3.0974       de
Drought_G61_N-Si                       10.8360     3.4561        e
Drought_G61_Si                          9.7620     2.5710        e

--- ds (Fisher's LSD, CD = 0.2444) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G20_Ctrl                           1.6430     0.3621        a
Ctrl_G20_N-Si                           1.6060     0.1702       ab
Ctrl_G62_N-Si                           1.6020     0.2749       ab
Ctrl_G20_Si                             1.5900     0.2157       ab
Ctrl_G62_Si                             1.5740     0.4145       ab
Ctrl_G62_Ctrl                           1.5580     0.2119       ab
Ctrl_G61_Si                             1.4620     0.1695       ab
Ctrl_G61_Ctrl                           1.4360     0.2762       ab
Ctrl_G61_N-Si                           1.3620     0.1766       bc
Drought_G61_Ctrl                        1.1020     0.3679       cd
Drought_G62_Ctrl                        1.0540     0.1122       de
Drought_G20_Ctrl                        0.9970     0.1481      def
Drought_G20_N-Si                        0.9870     0.1815      def
Drought_G62_Si                          0.8900     0.1007      def
Drought_G20_Si                          0.8430     0.1553       ef
Drought_G61_N-Si                        0.7960     0.1201       ef
Drought_G61_Si                          0.7840     0.1899       ef
Drought_G62_N-Si                        0.7660     0.1021        f

--- dr (Fisher's LSD, CD = 0.3860) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G61_N-Si                           2.9980     0.3836        a
Ctrl_G61_Si                             2.9940     0.4232        a
Ctrl_G61_Ctrl                           2.8920     0.3966        a
Ctrl_G62_Si                             2.4120     0.1844        b
Ctrl_G20_Si                             2.3020     0.5073        b
Ctrl_G20_N-Si                           2.1540     0.3233       bc
Ctrl_G62_N-Si                           1.9800     0.1933      bcd
Ctrl_G20_Ctrl                           1.8800     0.3621       cd
Ctrl_G62_Ctrl                           1.8020     0.2770       cd
Drought_G61_Ctrl                        1.8020     0.4408       cd
Drought_G20_N-Si                        1.6830     0.4175       de
Drought_G20_Si                          1.3800     0.4842       ef
Drought_G61_N-Si                        1.3780     0.3179       ef
Drought_G20_Ctrl                        1.2450     0.1465        f
Drought_G62_Ctrl                        1.2360     0.3239        f
Drought_G62_N-Si                        1.1760     0.1552        f
Drought_G61_Si                          1.1640     0.2414        f
Drought_G62_Si                          1.1400     0.1682        f

--- dt (Fisher's LSD, CD = 0.6115) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G61_Ctrl                           5.2100     0.4214        a
Ctrl_G61_Si                             4.4960     0.4349        b
Ctrl_G61_N-Si                           4.2460     0.6044       bc
Ctrl_G62_Si                             4.0880     0.6769      bcd
Ctrl_G20_Si                             3.8440     0.8604       cd
Ctrl_G20_N-Si                           3.6430     1.0254      cde
Ctrl_G20_Ctrl                           3.6420     0.4076      cde
Ctrl_G62_Ctrl                           3.5120     0.4993       de
Ctrl_G62_N-Si                           3.4680     0.5302       de
Drought_G61_Ctrl                        3.1040     0.2522       ef
Drought_G20_N-Si                        2.6220     0.3201       fg
Drought_G20_Ctrl                        2.3370     0.3499       gh
Drought_G62_Ctrl                        2.2900     0.4027       gh
Drought_G20_Si                          2.2230     0.5273       gh
Drought_G61_N-Si                        2.1740     0.4008       gh
Drought_G62_N-Si                        2.0920     0.4976       gh
Drought_G62_Si                          2.0300     0.2040       gh
Drought_G61_Si                          1.9480     0.3825        h

--- rwc (Fisher's LSD, CD = 0.0306) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Ctrl_G62_Ctrl                           0.8980     0.0370        a
Ctrl_G20_Ctrl                           0.8900     0.0271        a
Ctrl_G20_N-Si                           0.8840     0.0310       ab
Ctrl_G62_N-Si                           0.8760     0.0241      abc
Ctrl_G20_Si                             0.8650     0.0232       bc
Ctrl_G61_Ctrl                           0.8560     0.0305      bcd
Ctrl_G61_N-Si                           0.8560     0.0167      bcd
Ctrl_G62_Si                             0.8500     0.0274       cd
Ctrl_G61_Si                             0.8460     0.0251      cde
Drought_G20_N-Si                        0.8310     0.0185       de
Drought_G20_Ctrl                        0.8170     0.0403       ef
Drought_G62_Ctrl                        0.8160     0.0195       ef
Drought_G62_Si                          0.8160     0.0261       ef
Drought_G20_Si                          0.8000     0.0249        f
Drought_G61_Ctrl                        0.7960     0.0230        f
Drought_G61_Si                          0.7960     0.0230        f
Drought_G62_N-Si                        0.7960     0.0270        f
Drought_G61_N-Si                        0.7900     0.0447        f

--- chla (Fisher's LSD, CD = 0.2067) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G20_Si                          1.2220     0.2009        a
Drought_G61_N-Si                        1.1780     0.1684       ab
Drought_G61_Si                          1.1640     0.1484       ab
Drought_G20_N-Si                        1.1280     0.2641       ab
Drought_G62_Si                          1.1080     0.2817      abc
Drought_G20_Ctrl                        1.0180     0.2569       bc
Drought_G61_Ctrl                        1.0100     0.2364      bcd
Ctrl_G62_Ctrl                           1.0000     0.2027     bcde
Drought_G62_N-Si                        0.9800     0.1185     bcde
Drought_G62_Ctrl                        0.9640     0.1685     bcde
Ctrl_G20_N-Si                           0.9200     0.1246      cde
Ctrl_G20_Ctrl                           0.8210     0.1627      def
Ctrl_G20_Si                             0.8200     0.1457      def
Ctrl_G62_Si                             0.7720     0.0958     defg
Ctrl_G62_N-Si                           0.7700     0.1821      efg
Ctrl_G61_Si                             0.6620     0.2064       fg
Ctrl_G61_Ctrl                           0.6420     0.1487       fg
Ctrl_G61_N-Si                           0.5900     0.0894        g

--- chlb (Fisher's LSD, CD = 0.0806) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G20_Si                          0.4280     0.0801        a
Drought_G62_Si                          0.4260     0.1088        a
Drought_G20_N-Si                        0.4070     0.1272        a
Drought_G61_Si                          0.3980     0.0554        a
Drought_G20_Ctrl                        0.3820     0.1128        a
Drought_G61_N-Si                        0.3720     0.0377       ab
Drought_G61_Ctrl                        0.3640     0.0241       ab
Drought_G62_N-Si                        0.3560     0.0456      abc
Drought_G62_Ctrl                        0.3520     0.0691      abc
Ctrl_G20_N-Si                           0.3080     0.0607      bcd
Ctrl_G62_Ctrl                           0.3040     0.0451     bcde
Ctrl_G20_Ctrl                           0.2940     0.0660     bcde
Ctrl_G62_N-Si                           0.2880     0.0740    bcdef
Ctrl_G20_Si                             0.2760     0.0389     cdef
Ctrl_G62_Si                             0.2480     0.0228      def
Ctrl_G61_N-Si                           0.2280     0.0311      def
Ctrl_G61_Ctrl                           0.2180     0.0526       ef
Ctrl_G61_Si                             0.2080     0.0626        f

--- chlt (Fisher's LSD, CD = 0.1706) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G20_Si                          1.7370     0.1591        a
Drought_G20_Ctrl                        1.6580     0.2063        a
Drought_G61_Si                          1.6460     0.1041       ab
Drought_G20_N-Si                        1.6190     0.1156       ab
Drought_G61_N-Si                        1.4620     0.0968       bc
Drought_G61_Ctrl                        1.4040     0.2001       cd
Drought_G62_Si                          1.4000     0.1697       cd
Drought_G62_Ctrl                        1.3980     0.1580       cd
Drought_G62_N-Si                        1.3360     0.1662       cd
Ctrl_G62_Ctrl                           1.2760     0.1199      cde
Ctrl_G20_N-Si                           1.2550     0.1702       de
Ctrl_G62_N-Si                           1.2220     0.0890      def
Ctrl_G20_Ctrl                           1.1390     0.1772       ef
Ctrl_G62_Si                             1.0580     0.1264       fg
Ctrl_G20_Si                             1.0570     0.1770       fg
Ctrl_G61_Si                             0.9640     0.1270       gh
Ctrl_G61_Ctrl                           0.8620     0.2022       gh
Ctrl_G61_N-Si                           0.8120     0.0502        h

--- car (Fisher's LSD, CD = 0.5233) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G61_Si                          4.2480     0.4606        a
Drought_G20_Ctrl                        4.1630     0.4269        a
Drought_G20_Si                          3.9790     0.2997       ab
Drought_G20_N-Si                        3.7690     0.2522      abc
Drought_G62_Si                          3.7360     0.7463     abcd
Drought_G61_N-Si                        3.6640     0.4354     abcd
Drought_G61_Ctrl                        3.5000     0.8920     bcde
Ctrl_G62_Ctrl                           3.3760     0.7647     cdef
Drought_G62_N-Si                        3.1940     0.4085     defg
Drought_G62_Ctrl                        3.1400     0.5428     defg
Ctrl_G20_N-Si                           3.0140     0.3998     efgh
Ctrl_G62_Si                             3.0060     0.7744     efgh
Ctrl_G20_Ctrl                           2.8970     0.3399      fgh
Ctrl_G61_Si                             2.6440     0.7936      ghi
Ctrl_G62_N-Si                           2.6200     0.5526      ghi
Ctrl_G20_Si                             2.5900     0.2240       hi
Ctrl_G61_Ctrl                           2.5560     0.2685       hi
Ctrl_G61_N-Si                           2.3360     0.1428        i

--- gp (Fisher's LSD, CD = 7.1567) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G61_N-Si                       38.2460     7.4842        a
Drought_G61_Ctrl                       38.0440     8.6763        a
Drought_G20_Si                         37.3450     9.1043        a
Drought_G61_Si                         35.6460     4.3281        a
Drought_G20_Ctrl                       32.1290     7.1120       ab
Drought_G20_N-Si                       27.8190     7.2761       bc
Drought_G62_N-Si                       25.2140     4.5287      bcd
Ctrl_G61_Si                            24.6900     3.6538       cd
Drought_G62_Ctrl                       22.5700     4.7433       cd
Ctrl_G62_Ctrl                          22.1780     7.9584       cd
Ctrl_G61_N-Si                          21.8940     4.7010       cd
Drought_G62_Si                         21.6980     4.9956       cd
Ctrl_G20_Si                            21.1570     6.5620        d
Ctrl_G20_N-Si                          20.8110     6.8759        d
Ctrl_G20_Ctrl                          20.3750     4.8058        d
Ctrl_G61_Ctrl                          20.2280     7.6150        d
Ctrl_G62_Si                            19.8740     5.2785        d
Ctrl_G62_N-Si                          19.1280     5.4121        d

--- ml (Fisher's LSD, CD = 0.1342) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
Drought_G20_Si                          0.6700     0.1060        a
Drought_G61_N-Si                        0.6440     0.1150        a
Drought_G62_N-Si                        0.6220     0.1071       ab
Drought_G20_N-Si                        0.6180     0.1065       ab
Drought_G61_Si                          0.6060     0.2210       ab
Drought_G62_Si                          0.5860     0.0871      abc
Drought_G62_Ctrl                        0.5780     0.1023      abc
Drought_G61_Ctrl                        0.5760     0.0926      abc
Drought_G20_Ctrl                        0.5650     0.1151      abc
Ctrl_G61_Si                             0.4860     0.1210      bcd
Ctrl_G20_Si                             0.4520     0.1273       cd
Ctrl_G20_Ctrl                           0.4400     0.0811        d
Ctrl_G61_Ctrl                           0.4340     0.1106       de
Ctrl_G62_Ctrl                           0.3960     0.0868       de
Ctrl_G61_N-Si                           0.3940     0.1491       de
Ctrl_G20_N-Si                           0.3760     0.1712       de
Ctrl_G62_Si                             0.2940     0.1244        e
Ctrl_G62_N-Si                           0.2800     0.1378        e


================================================================================
6. SHAP FEATURE IMPORTANCE ANALYSIS
================================================================================

Table: SHAP Relative Importance (%)
Response               Irrigation     Genotype      Silicon
-----------------------------------------------------------
hs                           73.6         14.8         11.6
fs                           75.2         14.6         10.2
fr                           81.1         10.1          8.8
ft                           87.7          5.1          7.2
ds                           78.0         10.8         11.2
dr                           62.2         25.8         12.0
dt                           71.6         18.8          9.6
rwc                          66.5         18.3         15.2
chla                         64.3         20.8         14.9
chlb                         68.6         20.9         10.4
chlt                         65.4         26.2          8.4
car                          66.9         19.0         14.1
gp                           62.1         27.8         10.1
ml                           71.3         15.5         13.2

Interpretation:
  • hs: Dominant factor is Irrigation (73.6%)
  • fs: Dominant factor is Irrigation (75.2%)
  • fr: Dominant factor is Irrigation (81.1%)
  • ft: Dominant factor is Irrigation (87.7%)
  • ds: Dominant factor is Irrigation (78.0%)
  • dr: Dominant factor is Irrigation (62.2%)
  • dt: Dominant factor is Irrigation (71.6%)
  • rwc: Dominant factor is Irrigation (66.5%)
  • chla: Dominant factor is Irrigation (64.3%)
  • chlb: Dominant factor is Irrigation (68.6%)
  • chlt: Dominant factor is Irrigation (65.4%)
  • car: Dominant factor is Irrigation (66.9%)
  • gp: Dominant factor is Irrigation (62.1%)
  • ml: Dominant factor is Irrigation (71.3%)


================================================================================
7. PERMUTATION FEATURE IMPORTANCE (Validation)
================================================================================

Table: Permutation Relative Importance (%)
Response               Irrigation     Genotype      Silicon
-----------------------------------------------------------
hs                           87.9          9.2          2.9
fs                           89.3          7.0          3.7
fr                           87.0          7.5          5.6
ft                           95.9          1.9          2.3
ds                           90.3          4.7          5.0
dr                           68.5         22.8          8.7
dt                           77.4         15.0          7.6
rwc                          79.7         11.2          9.1
chla                         71.1         18.2         10.7
chlb                         82.7         11.1          6.3
chlt                         74.8         19.6          5.5
car                          70.8         18.1         11.0
gp                           61.6         30.7          7.7
ml                           81.5         10.7          7.7


================================================================================
8. MODEL PERFORMANCE COMPARISON (5-Fold CV R²)
================================================================================

Table: Cross-validated R² (mean ± std)
Response  RF_R2_mean  RF_R2_std  LR_R2_mean  LR_R2_std  GPR_R2_mean  GPR_R2_std Best
      hs       0.937      0.012       0.835      0.043      -15.008       1.938   RF
      fs       0.854      0.026       0.804      0.039       -0.381       0.227   RF
      fr       0.755      0.081       0.689      0.053       -0.624       0.332   RF
      ft       0.799      0.043       0.804      0.046       -3.867       1.121   LR
      ds       0.615      0.072       0.639      0.088        0.627       0.085   LR
      dr       0.636      0.148       0.390      0.275        0.637       0.167  GPR
      dt       0.643      0.144       0.514      0.160        0.588       0.111   RF
     rwc       0.448      0.174       0.506      0.071        0.508       0.066  GPR
    chla       0.304      0.085       0.284      0.128        0.294       0.108   RF
    chlb       0.269      0.075       0.323      0.104        0.321       0.097   LR
    chlt       0.652      0.113       0.478      0.187        0.628       0.094   RF
     car       0.475      0.167       0.394      0.176        0.394       0.159   RF
      gp       0.380      0.144       0.273      0.189       -6.418       0.829   RF
      ml       0.201      0.333       0.328      0.158        0.330       0.167  GPR

Interpretation:
  • hs: Best model = RF (RF=0.937, LR=0.835, GPR=-15.008)
  • fs: Best model = RF (RF=0.854, LR=0.804, GPR=-0.381)
  • fr: Best model = RF (RF=0.755, LR=0.689, GPR=-0.624)
  • ft: Best model = LR (RF=0.799, LR=0.804, GPR=-3.867)
  • ds: Best model = LR (RF=0.615, LR=0.639, GPR=0.627)
  • dr: Best model = GPR (RF=0.636, LR=0.390, GPR=0.637)
  • dt: Best model = RF (RF=0.643, LR=0.514, GPR=0.588)
  • rwc: Best model = GPR (RF=0.448, LR=0.506, GPR=0.508)
  • chla: Best model = RF (RF=0.304, LR=0.284, GPR=0.294)
  • chlb: Best model = LR (RF=0.269, LR=0.323, GPR=0.321)
  • chlt: Best model = RF (RF=0.652, LR=0.478, GPR=0.628)
  • car: Best model = RF (RF=0.475, LR=0.394, GPR=0.394)
  • gp: Best model = RF (RF=0.380, LR=0.273, GPR=-6.418)
  • ml: Best model = GPR (RF=0.201, LR=0.328, GPR=0.330)


================================================================================
9. STANDARDIZED REGRESSION COEFFICIENTS (β) with 95% Bootstrap CI
================================================================================

--- hs ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.9089        -0.9792        -0.8403          Yes
Genotype                 0.0891         0.0188         0.1555          Yes
Silicon                 -0.1501        -0.2221        -0.0810          Yes

--- fs ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.8997        -0.9734        -0.8271          Yes
Genotype                -0.0674        -0.1404        -0.0039          Yes
Silicon                 -0.1235        -0.2018        -0.0451          Yes

--- fr ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.8713        -0.9572        -0.7818          Yes
Genotype                 0.0186        -0.0639         0.1047           No
Silicon                 -0.0235        -0.1179         0.0652           No

--- ft ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.9165        -0.9865        -0.8431          Yes
Genotype                -0.0193        -0.0792         0.0431           No
Silicon                 -0.0455        -0.1169         0.0258           No

--- ds ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.8111        -0.9205        -0.7047          Yes
Genotype                -0.0588        -0.1683         0.0347           No
Silicon                 -0.1112        -0.2285        -0.0015          Yes

--- dr ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.7087        -0.8310        -0.5800          Yes
Genotype                -0.0362        -0.1306         0.0740           No
Silicon                  0.0843        -0.0460         0.2156           No

--- dt ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.7736        -0.8878        -0.6582          Yes
Genotype                -0.0156        -0.1143         0.0915           No
Silicon                 -0.0677        -0.1798         0.0397           No

--- rwc ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation              -0.7216        -0.8384        -0.6019          Yes
Genotype                -0.0929        -0.2149         0.0321           No
Silicon                 -0.1664        -0.2887        -0.0512          Yes

--- chla ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.5914         0.4542         0.7301          Yes
Genotype                -0.1174        -0.2568         0.0318           No
Silicon                  0.1003        -0.0437         0.2576           No

--- chlb ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.6275         0.4745         0.7650          Yes
Genotype                -0.1188        -0.2540         0.0291           No
Silicon                  0.0519        -0.0806         0.2011           No

--- chlt ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.7523         0.6370         0.8672          Yes
Genotype                -0.2110        -0.3239        -0.0884          Yes
Silicon                  0.0202        -0.0983         0.1403           No

--- car ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.6701         0.5374         0.7982          Yes
Genotype                -0.1402        -0.2803         0.0087           No
Silicon                  0.0056        -0.1328         0.1525           No

--- gp ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.5689         0.4347         0.7268          Yes
Genotype                -0.1749        -0.3159        -0.0228          Yes
Silicon                  0.0615        -0.0917         0.2034           No

--- ml ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
Irrigation               0.6421         0.5081         0.7787          Yes
Genotype                -0.1400        -0.2642        -0.0082          Yes
Silicon                  0.0699        -0.0580         0.1937           No


================================================================================
10. PRINCIPAL COMPONENT ANALYSIS (PCA)
================================================================================

Table: Variance Explained
Component Eigenvalue Variance (%) Cumulative (%)
      PC1      9.324         66.0           66.0
      PC2      1.437         10.2           76.2
      PC3      0.829          5.9           82.1
      PC4      0.610          4.3           86.4
      PC5      0.569          4.0           90.4


Table: PC Loadings
Response    PC1    PC2    PC3
      hs  0.280  0.339  0.006
      fs  0.292  0.267  0.046
      fr  0.309 -0.046  0.160
      ft  0.317  0.074  0.161
      ds  0.280  0.140  0.255
      dr  0.261 -0.221  0.431
      dt  0.280 -0.171  0.454
     rwc  0.229  0.426 -0.211
    chla -0.257  0.359  0.370
    chlb -0.257  0.303  0.329
    chlt -0.280  0.277  0.131
     car -0.259  0.294  0.235
      gp -0.205 -0.264  0.309
      ml -0.210 -0.270  0.179

Interpretation:
  • First 2 PCs explain 76.2% of total variance
  • hs: PC1 loading = 0.280, PC2 loading = 0.339
  • fs: PC1 loading = 0.292, PC2 loading = 0.267
  • fr: PC1 loading = 0.309, PC2 loading = -0.046
  • ft: PC1 loading = 0.317, PC2 loading = 0.074
  • ds: PC1 loading = 0.280, PC2 loading = 0.140
  • dr: PC1 loading = 0.261, PC2 loading = -0.221
  • dt: PC1 loading = 0.280, PC2 loading = -0.171
  • rwc: PC1 loading = 0.229, PC2 loading = 0.426
  • chla: PC1 loading = -0.257, PC2 loading = 0.359
  • chlb: PC1 loading = -0.257, PC2 loading = 0.303
  • chlt: PC1 loading = -0.280, PC2 loading = 0.277
  • car: PC1 loading = -0.259, PC2 loading = 0.294
  • gp: PC1 loading = -0.205, PC2 loading = -0.264
  • ml: PC1 loading = -0.210, PC2 loading = -0.270


================================================================================
11. MORF RESIDUAL CORRELATION MATRIX
================================================================================

Residual correlations indicate relationships between responses after accounting for factor effects.

                        hs         fs         fr         ft         ds         dr         dt        rwc       chla       chlb       chlt        car         gp         ml
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
hs                   1.000      0.260      0.034      0.097      0.235     -0.070     -0.033      0.238     -0.062     -0.102     -0.086      0.098      0.002     -0.016
fs                   0.260      1.000      0.380      0.650      0.399      0.228      0.217      0.155     -0.323     -0.328     -0.107     -0.158     -0.039      0.028
fr                   0.034      0.380      1.000      0.763      0.319      0.526      0.518     -0.012     -0.410     -0.414     -0.315     -0.272     -0.133     -0.036
ft                   0.097      0.650      0.763      1.000      0.521      0.581      0.562      0.088     -0.419     -0.402     -0.256     -0.232     -0.096      0.028
ds                   0.235      0.399      0.319      0.521      1.000      0.345      0.490     -0.166     -0.191     -0.176     -0.209     -0.238      0.130      0.031
dr                  -0.070      0.228      0.526      0.581      0.345      1.000      0.686     -0.128     -0.207     -0.081     -0.206     -0.119     -0.145     -0.015
dt                  -0.033      0.217      0.518      0.562      0.490      0.686      1.000     -0.319     -0.192     -0.118     -0.256     -0.194      0.021      0.129
rwc                  0.238      0.155     -0.012      0.088     -0.166     -0.128     -0.319      1.000     -0.089     -0.090     -0.029      0.067     -0.200     -0.065
chla                -0.062     -0.323     -0.410     -0.419     -0.191     -0.207     -0.192     -0.089      1.000      0.773      0.633      0.657      0.037      0.045
chlb                -0.102     -0.328     -0.414     -0.402     -0.176     -0.081     -0.118     -0.090      0.773      1.000      0.510      0.457      0.009      0.084
chlt                -0.086     -0.107     -0.315     -0.256     -0.209     -0.206     -0.256     -0.029      0.633      0.510      1.000      0.536     -0.090     -0.085
car                  0.098     -0.158     -0.272     -0.232     -0.238     -0.119     -0.194      0.067      0.657      0.457      0.536      1.000     -0.068     -0.098
gp                   0.002     -0.039     -0.133     -0.096      0.130     -0.145      0.021     -0.200      0.037      0.009     -0.090     -0.068      1.000      0.088
ml                  -0.016      0.028     -0.036      0.028      0.031     -0.015      0.129     -0.065      0.045      0.084     -0.085     -0.098      0.088      1.000

Strong residual correlations (|r| > 0.5):
  • fs ↔ ft: r = 0.650
  • fr ↔ ft: r = 0.763
  • fr ↔ dr: r = 0.526
  • fr ↔ dt: r = 0.518
  • ft ↔ ds: r = 0.521
  • ft ↔ dr: r = 0.581
  • ft ↔ dt: r = 0.562
  • dr ↔ dt: r = 0.686
  • chla ↔ chlb: r = 0.773
  • chla ↔ chlt: r = 0.633
  • chla ↔ car: r = 0.657
  • chlb ↔ chlt: r = 0.510
  • chlt ↔ car: r = 0.536


================================================================================
SUMMARY OF KEY FINDINGS
================================================================================

Best predictive models:
  • hs: RF (R² = 0.937)
  • fs: RF (R² = 0.854)
  • fr: RF (R² = 0.755)
  • ft: LR (R² = 0.804)
  • ds: LR (R² = 0.639)
  • dr: GPR (R² = 0.637)
  • dt: RF (R² = 0.643)
  • rwc: GPR (R² = 0.508)
  • chla: RF (R² = 0.304)
  • chlb: LR (R² = 0.323)
  • chlt: RF (R² = 0.652)
  • car: RF (R² = 0.475)
  • gp: RF (R² = 0.380)
  • ml: GPR (R² = 0.330)

Most influential factors (SHAP):
  • hs: Irrigation (73.6%)
  • fs: Irrigation (75.2%)
  • fr: Irrigation (81.1%)
  • ft: Irrigation (87.7%)
  • ds: Irrigation (78.0%)
  • dr: Irrigation (62.2%)
  • dt: Irrigation (71.6%)
  • rwc: Irrigation (66.5%)
  • chla: Irrigation (64.3%)
  • chlb: Irrigation (68.6%)
  • chlt: Irrigation (65.4%)
  • car: Irrigation (66.9%)
  • gp: Irrigation (62.1%)
  • ml: Irrigation (71.3%)

Significant ANOVA effects:
  • hs: C(Irrigation_cat), C(Genotype_cat), C(Silicon_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat)
  • fs: C(Irrigation_cat), C(Genotype_cat), C(Silicon_cat), C(Irrigation_cat):C(Genotype_cat)
  • fr: C(Irrigation_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat), C(Genotype_cat):C(Silicon_cat)
  • ft: C(Irrigation_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat)
  • ds: C(Irrigation_cat)
  • dr: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat), C(Genotype_cat):C(Silicon_cat)
  • dt: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat), C(Genotype_cat):C(Silicon_cat)
  • rwc: C(Irrigation_cat), C(Genotype_cat), C(Silicon_cat)
  • chla: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat)
  • chlb: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat)
  • chlt: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat), C(Irrigation_cat):C(Silicon_cat), C(Genotype_cat):C(Silicon_cat)
  • car: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat)
  • gp: C(Irrigation_cat), C(Genotype_cat), C(Irrigation_cat):C(Genotype_cat)
  • ml: C(Irrigation_cat)

Significant interactions:
  • hs: Irrigation × Genotype (Synergistic, p=0.0000)
  • hs: Irrigation × Silicon (Moderate, p=0.0319)
  • fs: Irrigation × Genotype (Moderate, p=0.0329)
  • fr: Irrigation × Genotype (Synergistic, p=0.0000)
  • fr: Irrigation × Silicon (Moderate, p=0.0031)
  • fr: Genotype × Silicon (Moderate, p=0.0027)
  • ft: Irrigation × Genotype (Moderate, p=0.0401)
  • ft: Irrigation × Silicon (Moderate, p=0.0426)
  • dr: Irrigation × Genotype (Synergistic, p=0.0000)
  • dr: Irrigation × Silicon (Moderate, p=0.0049)
  • dr: Genotype × Silicon (Moderate, p=0.0186)
  • dt: Irrigation × Genotype (Moderate, p=0.0014)
  • dt: Irrigation × Silicon (Moderate, p=0.0453)
  • dt: Genotype × Silicon (Moderate, p=0.0020)
  • chla: Irrigation × Genotype (Moderate, p=0.0049)
  • chla: Irrigation × Silicon (Moderate, p=0.0290)
  • chlb: Irrigation × Silicon (Moderate, p=0.0473)
  • chlt: Irrigation × Genotype (Synergistic, p=0.0000)
  • chlt: Irrigation × Silicon (Moderate, p=0.0052)
  • chlt: Genotype × Silicon (Moderate, p=0.0335)
  • car: Irrigation × Genotype (Moderate, p=0.0004)
  • gp: Irrigation × Genotype (Moderate, p=0.0014)

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END OF REPORT
================================================================================