================================================================================
FAME — FACTORIAL ANALYSIS & MACHINE LEARNING ENGINE
Comprehensive Statistical and Machine Learning Analysis Report
================================================================================
Date of analysis: 2026-05-31 01:29
Factors: WaterDeficit_pct, Chitosan_pct
Responses: FreshWeight, DryWeight, Chla_b_ratio, Chlt, CAT, POD, Protein
Observations: 36
================================================================================

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

--- Factor: WaterDeficit_pct ---
Statistic            Value
-------------------------
mean               25.0000
std                20.7020
min                 0.0000
25%                 0.0000
50%                25.0000
75%                50.0000
max                50.0000

--- Factor: Chitosan_pct ---
Statistic            Value
-------------------------
mean                1.1250
std                 0.7500
min                 0.0000
25%                 0.7500
50%                 1.2500
75%                 1.6250
max                 2.0000

--- Response: FreshWeight ---
Statistic            Value
-------------------------
mean                0.1328
std                 0.0561
min                 0.0300
25%                 0.0900
50%                 0.1150
75%                 0.1825
max                 0.2500

--- Response: DryWeight ---
Statistic            Value
-------------------------
mean                0.0467
std                 0.0207
min                 0.0100
25%                 0.0300
50%                 0.0400
75%                 0.0600
max                 0.0900

--- Response: Chla_b_ratio ---
Statistic            Value
-------------------------
mean                2.1481
std                 0.7295
min                 1.1100
25%                 1.3850
50%                 2.3300
75%                 2.7675
max                 3.2900

--- Response: Chlt ---
Statistic            Value
-------------------------
mean                1.4261
std                 1.1630
min                 0.2300
25%                 0.3775
50%                 0.9850
75%                 2.9100
max                 3.2000

--- Response: CAT ---
Statistic            Value
-------------------------
mean             1805.0411
std               683.7155
min               666.6700
25%              1333.3300
50%              1733.3350
75%              2000.0000
max              3600.0000

--- Response: POD ---
Statistic            Value
-------------------------
mean             2171.7217
std              1072.6707
min               728.7400
25%              1202.4250
50%              2040.4800
75%              2793.5200
max              4251.0100

--- Response: Protein ---
Statistic            Value
-------------------------
mean               51.1981
std                 8.3397
min                37.8000
25%                44.5425
50%                48.6750
75%                57.6975
max                68.4600

--- Treatment Combination Means ---

FreshWeight:
  25_1.5                             0.2200
  50_2.0                             0.2033
  0_2.0                              0.1833
  50_1.5                             0.1800
  0_1.5                              0.1367
  25_1.0                             0.1267
  0_1.0                              0.1200
  25_2.0                             0.1133
  0_0.0                              0.0933
  50_1.0                             0.0900
  25_0.0                             0.0767
  50_0.0                             0.0500

DryWeight:
  50_2.0                             0.0733
  0_2.0                              0.0700
  25_1.5                             0.0667
  50_1.5                             0.0633
  0_1.5                              0.0500
  25_1.0                             0.0500
  0_1.0                              0.0467
  25_2.0                             0.0333
  0_0.0                              0.0300
  50_1.0                             0.0300
  25_0.0                             0.0267
  50_0.0                             0.0200

Chla_b_ratio:
  25_1.0                             3.1500
  25_1.5                             2.9067
  25_0.0                             2.7833
  25_2.0                             2.7333
  50_0.0                             2.3100
  50_2.0                             2.2433
  50_1.0                             2.2133
  50_1.5                             2.0733
  0_0.0                              1.4267
  0_2.0                              1.3233
  0_1.0                              1.3200
  0_1.5                              1.2933

Chlt:
  0_1.5                              3.0900
  0_2.0                              2.9967
  0_1.0                              2.9500
  0_0.0                              2.8433
  25_1.5                             1.4600
  25_1.0                             1.1767
  25_2.0                             0.7633
  25_0.0                             0.5600
  50_2.0                             0.3867
  50_1.5                             0.3467
  50_1.0                             0.2967
  50_0.0                             0.2433

CAT:
  50_2.0                          3400.0000
  25_1.5                          2222.2233
  25_2.0                          2166.6667
  25_1.0                          2111.1100
  50_1.5                          1933.3333
  50_1.0                          1800.0000
  25_0.0                          1685.1867
  0_1.5                           1666.6667
  0_1.0                           1361.1100
  0_2.0                           1280.8633
  50_0.0                          1200.0000
  0_0.0                            833.3333

POD:
  50_2.0                          4032.3833
  50_1.5                          3902.8267
  50_1.0                          2931.1667
  50_0.0                          2720.6433
  25_1.5                          2623.4767
  25_1.0                          2331.9767
  25_2.0                          1894.7333
  25_0.0                          1408.9000
  0_1.5                           1214.5700
  0_1.0                           1153.8400
  0_2.0                           1068.8200
  0_0.0                            777.3233

Protein:
  50_2.0                            67.2267
  50_1.5                            60.3400
  25_2.0                            59.0367
  50_1.0                            56.8633
  50_0.0                            56.0667
  0_1.0                             49.2533
  25_1.5                            48.0233
  0_2.0                             45.7033
  25_1.0                            45.0500
  0_1.5                             43.0200
  0_0.0                             42.2967
  25_0.0                            41.4967


================================================================================
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
 FreshWeight         0.9578    0.1844       Normal   0.1989   0.9961     Equal       [-0.05, 0.32]   ✅ None
   DryWeight         0.9530    0.1301       Normal   0.4895   0.8915     Equal       [-0.01, 0.10]   ✅ None
Chla_b_ratio         0.8724    0.0007   Non-normal   0.9333   0.5267     Equal       [-0.69, 4.84]   ✅ None
        Chlt         0.7961    0.0000   Non-normal   0.6431   0.7749     Equal       [-3.42, 6.71]   ✅ None
         CAT         0.9183    0.0112   Non-normal   0.6744   0.7484     Equal   [333.32, 3000.01]     ⚠️ 3
         POD         0.9138    0.0083   Non-normal   1.1083   0.3966     Equal [-1184.22, 5180.16]   ✅ None
     Protein         0.9435    0.0655       Normal   0.2571   0.9886     Equal      [24.81, 77.43]   ✅ None


Outlier Detection Summary:
  FreshWeight: 0 outlier(s), IQR bounds: [-0.05, 0.32]
  DryWeight: 0 outlier(s), IQR bounds: [-0.01, 0.10]
  Chla_b_ratio: 0 outlier(s), IQR bounds: [-0.69, 4.84]
  Chlt: 0 outlier(s), IQR bounds: [-3.42, 6.71]
  CAT: 3 outlier(s), IQR bounds: [333.32, 3000.01]
    Row 33: value=3400.0, IQR [333.32, 3000.01]; Z-score=3.75
    Row 34: value=3600.0, IQR [333.32, 3000.01]; Z-score=4.20
    Row 35: value=3200.0, IQR [333.32, 3000.01]
  POD: 0 outlier(s), IQR bounds: [-1184.22, 5180.16]
  Protein: 0 outlier(s), IQR bounds: [24.81, 77.43]


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

Table 2: Factor-Response Pearson Correlations
    Response           Factor  Pearson r  p-value Sig.
 FreshWeight WaterDeficit_pct    -0.0185   0.9149   ns
 FreshWeight     Chitosan_pct     0.7114   0.0000  ***
   DryWeight WaterDeficit_pct    -0.0500   0.7721   ns
   DryWeight     Chitosan_pct     0.6625   0.0000  ***
Chla_b_ratio WaterDeficit_pct     0.4933   0.0022   **
Chla_b_ratio     Chitosan_pct    -0.0478   0.7817   ns
        Chlt WaterDeficit_pct    -0.9440   0.0000  ***
        Chlt     Chitosan_pct     0.0795   0.6448   ns
         CAT WaterDeficit_pct     0.4831   0.0028   **
         CAT     Chitosan_pct     0.5571   0.0004  ***
         POD WaterDeficit_pct     0.9044   0.0000  ***
         POD     Chitosan_pct     0.2879   0.0887   ns
     Protein WaterDeficit_pct     0.7475   0.0000  ***
     Protein     Chitosan_pct     0.4248   0.0098   **


Interpretation:
  • Chitosan_pct vs FreshWeight: strong positive correlation (r=0.711, p=0.0000, ***)
  • Chitosan_pct vs DryWeight: moderate positive correlation (r=0.662, p=0.0000, ***)
  • WaterDeficit_pct vs Chla_b_ratio: moderate positive correlation (r=0.493, p=0.0022, **)
  • WaterDeficit_pct vs Chlt: strong negative correlation (r=-0.944, p=0.0000, ***)
  • WaterDeficit_pct vs CAT: moderate positive correlation (r=0.483, p=0.0028, **)
  • Chitosan_pct vs CAT: moderate positive correlation (r=0.557, p=0.0004, ***)
  • WaterDeficit_pct vs POD: strong positive correlation (r=0.904, p=0.0000, ***)
  • WaterDeficit_pct vs Protein: strong positive correlation (r=0.748, p=0.0000, ***)
  • Chitosan_pct vs Protein: moderate positive correlation (r=0.425, p=0.0098, **)


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

--- FreshWeight ---
                                             sum_sq    df        F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      0.0001   2.0   0.0419  0.9591  0.0031
C(Chitosan_pct_cat)                          0.0583   2.0  33.7870  0.0000  0.7145
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)  0.0285   4.0   8.2607  0.0002  0.5503
Residual                                     0.0233  27.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Chitosan_pct_cat): F=33.79, p=0.0000, η²=0.7145 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=8.26, p=0.0002, η²=0.5503 (large effect)

--- DryWeight ---
                                             sum_sq    df        F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      0.0002   2.0   0.4064  0.6701  0.0292
C(Chitosan_pct_cat)                          0.0059   2.0  15.9381  0.0000  0.5414
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)  0.0040   4.0   5.3955  0.0025  0.4442
Residual                                     0.0050  27.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Chitosan_pct_cat): F=15.94, p=0.0000, η²=0.5414 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=5.40, p=0.0025, η²=0.4442 (large effect)

--- Chla_b_ratio ---
                                              sum_sq    df        F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      14.5306   2.0  50.3661  0.0000  0.7886
C(Chitosan_pct_cat)                           0.0996   2.0   0.3452  0.7112  0.0249
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)   0.0994   4.0   0.1723  0.9507  0.0249
Residual                                      3.8948  27.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(WaterDeficit_pct_cat): F=50.37, p=0.0000, η²=0.7886 (large effect)

--- Chlt ---
                                              sum_sq    df         F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      45.6115   2.0  857.4981  0.0000  0.9845
C(Chitosan_pct_cat)                           0.5181   2.0    9.7402  0.0007  0.4191
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)   0.4956   4.0    4.6585  0.0055  0.4083
Residual                                      0.7181  27.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(WaterDeficit_pct_cat): F=857.50, p=0.0000, η²=0.9845 (large effect)
    • C(Chitosan_pct_cat): F=9.74, p=0.0007, η²=0.4191 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=4.66, p=0.0055, η²=0.4083 (large effect)

--- CAT ---
                                                   sum_sq    df        F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      4.866968e+06   2.0  20.1068  0.0000  0.5983
C(Chitosan_pct_cat)                          3.909412e+06   2.0  16.1509  0.0000  0.5447
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)  4.317214e+06   4.0   8.9178  0.0001  0.5692
Residual                                     3.267748e+06  27.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(WaterDeficit_pct_cat): F=20.11, p=0.0000, η²=0.5983 (large effect)
    • C(Chitosan_pct_cat): F=16.15, p=0.0000, η²=0.5447 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=8.92, p=0.0001, η²=0.5692 (large effect)

--- POD ---
                                                   sum_sq    df         F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      3.314706e+07   2.0  246.6283  0.0000  0.9481
C(Chitosan_pct_cat)                          3.189539e+06   2.0   23.7315  0.0000  0.6374
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)  2.120773e+06   4.0    7.8897  0.0002  0.5389
Residual                                     1.814412e+06  27.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(WaterDeficit_pct_cat): F=246.63, p=0.0000, η²=0.9481 (large effect)
    • C(Chitosan_pct_cat): F=23.73, p=0.0000, η²=0.6374 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=7.89, p=0.0002, η²=0.5389 (large effect)

--- Protein ---
                                                sum_sq    df         F  PR(>F)      η²
C(WaterDeficit_pct_cat)                      1500.8249   2.0  108.1892     0.0  0.8891
C(Chitosan_pct_cat)                           473.0363   2.0   34.0995     0.0  0.7164
C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)   273.1079   4.0    9.8437     0.0  0.5932
Residual                                      187.2751  27.0       NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(WaterDeficit_pct_cat): F=108.19, p=0.0000, η²=0.8891 (large effect)
    • C(Chitosan_pct_cat): F=34.10, p=0.0000, η²=0.7164 (large effect)
    • C(WaterDeficit_pct_cat):C(Chitosan_pct_cat): F=9.84, p=0.0000, η²=0.5932 (large effect)

Significant Two-Way Interactions (p < 0.05):
   Response         Factor_1     Factor_2    F_int    p_int Sig.     Type
FreshWeight WaterDeficit_pct Chitosan_pct 8.260737 0.000174  *** Moderate
  DryWeight WaterDeficit_pct Chitosan_pct 5.395485 0.002517   ** Moderate
       Chlt WaterDeficit_pct Chitosan_pct 4.658547 0.005454   ** Moderate
        CAT WaterDeficit_pct Chitosan_pct 8.917823 0.000100  *** Moderate
        POD WaterDeficit_pct Chitosan_pct 7.889727 0.000239  *** Moderate
    Protein WaterDeficit_pct Chitosan_pct 9.843690 0.000048  *** Moderate


Kruskal-Wallis Non-Parametric Validation:
    Response           Factor ANOVA p KW H-statistic KW p-value              Agreement
 FreshWeight WaterDeficit_pct  0.9591           0.08     0.9584 ✅ Both non-significant
 FreshWeight     Chitosan_pct  0.0000          18.30     0.0001     ✅ Both significant
   DryWeight WaterDeficit_pct  0.6701           0.46     0.7938 ✅ Both non-significant
   DryWeight     Chitosan_pct  0.0000          14.28     0.0008     ✅ Both significant
Chla_b_ratio WaterDeficit_pct  0.0000          26.44     0.0000     ✅ Both significant
Chla_b_ratio     Chitosan_pct  0.7112           0.17     0.9201 ✅ Both non-significant
        Chlt WaterDeficit_pct  0.0000          31.15     0.0000     ✅ Both significant
        Chlt     Chitosan_pct  0.0007           1.51     0.4710          ⚠️ ANOVA only
         CAT WaterDeficit_pct  0.0000          13.71     0.0011     ✅ Both significant
         CAT     Chitosan_pct  0.0000           6.43     0.0401     ✅ Both significant
         POD WaterDeficit_pct  0.0000          31.04     0.0000     ✅ Both significant
         POD     Chitosan_pct  0.0000           1.75     0.4171          ⚠️ ANOVA only
     Protein WaterDeficit_pct  0.0000          18.91     0.0001     ✅ Both significant
     Protein     Chitosan_pct  0.0000           5.79     0.0554          ⚠️ ANOVA only


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

--- FreshWeight (Tukey's HSD, CD = 0.0762) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
25_1.5                                  0.2200     0.0265        a
50_2.0                                  0.2033     0.0153       ab
0_2.0                                   0.1833     0.0252      abc
50_1.5                                  0.1800     0.0265      abc
0_1.5                                   0.1367     0.0379      bcd
25_1.0                                  0.1267     0.0208       cd
0_1.0                                   0.1200     0.0265      cde
25_2.0                                  0.1133     0.0416      cde
0_0.0                                   0.0933     0.0208       de
50_1.0                                  0.0900     0.0200       de
25_0.0                                  0.0767     0.0153       de
50_0.0                                  0.0500     0.0200        e

--- DryWeight (Tukey's HSD, CD = 0.0361) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
50_2.0                                  0.0733     0.0208        a
0_2.0                                   0.0700     0.0200        a
25_1.5                                  0.0667     0.0153       ab
50_1.5                                  0.0633     0.0058      abc
0_1.5                                   0.0500     0.0100     abcd
25_1.0                                  0.0500     0.0100     abcd
0_1.0                                   0.0467     0.0115     abcd
25_2.0                                  0.0333     0.0058      bcd
0_0.0                                   0.0300     0.0100       cd
50_1.0                                  0.0300     0.0100       cd
25_0.0                                  0.0267     0.0058        d
50_0.0                                  0.0200     0.0100        d

--- Chla_b_ratio (Tukey's HSD, CD = 1.1500) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
25_1.0                                  3.1500     0.1778        a
25_1.5                                  2.9067     0.1501        a
25_0.0                                  2.7833     0.3443        a
25_2.0                                  2.7333     0.2442        a
50_0.0                                  2.3100     0.4571       ab
50_2.0                                  2.2433     0.5811       ab
50_1.0                                  2.2133     0.7353       ab
50_1.5                                  2.0733     0.6801       ab
0_0.0                                   1.4267     0.0757        b
0_2.0                                   1.3233     0.0833        b
0_1.0                                   1.3200     0.0458        b
0_1.5                                   1.2933     0.1850        b

--- Chlt (Tukey's HSD, CD = 0.2136) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
0_1.5                                   3.0900     0.1493        a
0_2.0                                   2.9967     0.1026       ab
0_1.0                                   2.9500     0.0400       ab
0_0.0                                   2.8433     0.0666        b
25_1.5                                  1.4600     0.1217        c
25_1.0                                  1.1767     0.0321        d
25_2.0                                  0.7633     0.0651        e
25_0.0                                  0.5600     0.0361       ef
50_2.0                                  0.3867     0.0208       fg
50_1.5                                  0.3467     0.0379       fg
50_1.0                                  0.2967     0.0306        g
50_0.0                                  0.2433     0.0115        g

--- CAT (Tukey's HSD, CD = 857.8505) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
50_2.0                               3400.0000   200.0000        a
25_1.5                               2222.2233   693.8873        b
25_2.0                               2166.6667   288.6751       bc
25_1.0                               2111.1100   192.4482      bcd
50_1.5                               1933.3333   115.4701     bcde
50_1.0                               1800.0000   200.0000     bcde
25_0.0                               1685.1867   305.9755    bcdef
0_1.5                                1666.6667   333.3350    bcdef
0_1.0                                1361.1100   127.2941     cdef
0_2.0                                1280.8633   187.1040      def
50_0.0                               1200.0000   200.0000       ef
0_0.0                                 833.3333   166.6650        f

--- POD (Tukey's HSD, CD = 304.7527) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
50_2.0                               4032.3833   207.5491        a
50_1.5                               3902.8267    74.2126        a
50_1.0                               2931.1667    74.2126        b
50_0.0                               2720.6433    48.5850       bc
25_1.5                               2623.4767    48.5850       cd
25_1.0                               2331.9767   222.6368        d
25_2.0                               1894.7333    84.1488        e
25_0.0                               1408.9000    48.5800        f
0_1.5                                1214.5700    48.5800       fg
0_1.0                                1153.8400    60.7300       fg
0_2.0                                1068.8200    48.5800       gh
0_0.0                                 777.3233    48.5850        h

--- Protein (Tukey's HSD, CD = 5.8508) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
50_2.0                                 67.2267     1.4496        a
50_1.5                                 60.3400     1.3289        b
25_2.0                                 59.0367     1.6312        b
50_1.0                                 56.8633     1.6451        b
50_0.0                                 56.0667     1.1490        b
0_1.0                                  49.2533     1.0245        c
25_1.5                                 48.0233     1.8973       cd
0_2.0                                  45.7033     1.8511      cde
25_1.0                                 45.0500     1.8761      cde
0_1.5                                  43.0200     1.6411       de
0_0.0                                  42.2967     3.4649       de
25_0.0                                 41.4967     3.2475        e


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

Table: SHAP Relative Importance (%)
Response             WaterDeficit_pct Chitosan_pct
----------------------------------------------
FreshWeight                  16.5         83.5
DryWeight                    19.6         80.4
Chla_b_ratio                 92.2          7.8
Chlt                         91.3          8.7
CAT                          50.9         49.1
POD                          74.5         25.5
Protein                      67.3         32.7

Interpretation:
  • FreshWeight: Dominant factor is Chitosan_pct (83.5%)
  • DryWeight: Dominant factor is Chitosan_pct (80.4%)
  • Chla_b_ratio: Dominant factor is WaterDeficit_pct (92.2%)
  • Chlt: Dominant factor is WaterDeficit_pct (91.3%)
  • CAT: Dominant factor is WaterDeficit_pct (50.9%)
  • POD: Dominant factor is WaterDeficit_pct (74.5%)
  • Protein: Dominant factor is WaterDeficit_pct (67.3%)


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

Table: Permutation Relative Importance (%)
Response             WaterDeficit_pct Chitosan_pct
----------------------------------------------
FreshWeight                  18.4         81.6
DryWeight                    24.0         76.0
Chla_b_ratio                 98.2          1.8
Chlt                         97.8          2.2
CAT                          48.0         52.0
POD                          86.7         13.3
Protein                      71.0         29.0


================================================================================
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
 FreshWeight       0.446      0.177       0.400      0.154        0.115       0.133   RF
   DryWeight       0.285      0.274       0.292      0.319        0.063       0.212   LR
Chla_b_ratio       0.571      0.313      -0.025      0.482        0.671       0.220  GPR
        Chlt       0.782      0.377       0.184      1.420        0.991       0.004  GPR
         CAT       0.534      0.230       0.367      0.308       -9.281       3.164   RF
         POD       0.898      0.063       0.855      0.040       -5.471       2.217   RF
     Protein       0.635      0.240       0.382      0.464      -56.759      21.872   RF

Interpretation:
  • FreshWeight: Best model = RF (RF=0.446, LR=0.400, GPR=0.115)
  • DryWeight: Best model = LR (RF=0.285, LR=0.292, GPR=0.063)
  • Chla_b_ratio: Best model = GPR (RF=0.571, LR=-0.025, GPR=0.671)
  • Chlt: Best model = GPR (RF=0.782, LR=0.184, GPR=0.991)
  • CAT: Best model = RF (RF=0.534, LR=0.367, GPR=-9.281)
  • POD: Best model = RF (RF=0.898, LR=0.855, GPR=-5.471)
  • Protein: Best model = RF (RF=0.635, LR=0.382, GPR=-56.759)


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

--- FreshWeight ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct        -0.0185        -0.2127         0.1627           No
Chitosan_pct             0.7114         0.5059         0.9392          Yes

--- DryWeight ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct        -0.0500        -0.2883         0.1737           No
Chitosan_pct             0.6625         0.4136         0.8998          Yes

--- Chla_b_ratio ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct         0.4933         0.2145         0.7631          Yes
Chitosan_pct            -0.0478        -0.3160         0.1843           No

--- Chlt ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct        -0.9440        -1.0243        -0.8610          Yes
Chitosan_pct             0.0795        -0.0439         0.2111           No

--- CAT ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct         0.4831         0.2356         0.7309          Yes
Chitosan_pct             0.5571         0.3091         0.7802          Yes

--- POD ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct         0.9044         0.8142         0.9963          Yes
Chitosan_pct             0.2879         0.1812         0.3946          Yes

--- Protein ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
----------------------------------------------------------------------
WaterDeficit_pct         0.7475         0.5808         0.8968          Yes
Chitosan_pct             0.4248         0.2549         0.6164          Yes


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

Table: Variance Explained
Component Eigenvalue Variance (%) Cumulative (%)
      PC1      3.541         49.2           49.2
      PC2      2.127         29.5           78.7
      PC3      0.844         11.7           90.4
      PC4      0.335          4.6           95.1
      PC5      0.178          2.5           97.6


Table: PC Loadings
    Response    PC1    PC2    PC3
 FreshWeight  0.256  0.584  0.120
   DryWeight  0.218  0.593  0.122
Chla_b_ratio  0.288 -0.314  0.753
        Chlt -0.407  0.413 -0.020
         CAT  0.454  0.142  0.164
         POD  0.500 -0.076 -0.227
     Protein  0.427 -0.109 -0.570

Interpretation:
  • First 2 PCs explain 78.7% of total variance
  • FreshWeight: PC1 loading = 0.256, PC2 loading = 0.584
  • DryWeight: PC1 loading = 0.218, PC2 loading = 0.593
  • Chla_b_ratio: PC1 loading = 0.288, PC2 loading = -0.314
  • Chlt: PC1 loading = -0.407, PC2 loading = 0.413
  • CAT: PC1 loading = 0.454, PC2 loading = 0.142
  • POD: PC1 loading = 0.500, PC2 loading = -0.076
  • Protein: PC1 loading = 0.427, PC2 loading = -0.109


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

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

                FreshWeight  DryWeight Chla_b_ratio       Chlt        CAT        POD    Protein
--------------------------------------------------------------------------------------------
FreshWeight          1.000      0.635     -0.146      0.167      0.467      0.237     -0.311
DryWeight            0.635      1.000      0.093     -0.008      0.118      0.126     -0.446
Chla_b_ratio        -0.146      0.093      1.000     -0.049     -0.041      0.138      0.236
Chlt                 0.167     -0.008     -0.049      1.000      0.211      0.537     -0.061
CAT                  0.467      0.118     -0.041      0.211      1.000      0.181     -0.207
POD                  0.237      0.126      0.138      0.537      0.181      1.000      0.005
Protein             -0.311     -0.446      0.236     -0.061     -0.207      0.005      1.000

Strong residual correlations (|r| > 0.5):
  • FreshWeight ↔ DryWeight: r = 0.635
  • Chlt ↔ POD: r = 0.537


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

Best predictive models:
  • FreshWeight: RF (R² = 0.446)
  • DryWeight: LR (R² = 0.292)
  • Chla_b_ratio: GPR (R² = 0.671)
  • Chlt: GPR (R² = 0.991)
  • CAT: RF (R² = 0.534)
  • POD: RF (R² = 0.898)
  • Protein: RF (R² = 0.635)

Most influential factors (SHAP):
  • FreshWeight: Chitosan_pct (83.5%)
  • DryWeight: Chitosan_pct (80.4%)
  • Chla_b_ratio: WaterDeficit_pct (92.2%)
  • Chlt: WaterDeficit_pct (91.3%)
  • CAT: WaterDeficit_pct (50.9%)
  • POD: WaterDeficit_pct (74.5%)
  • Protein: WaterDeficit_pct (67.3%)

Significant ANOVA effects:
  • FreshWeight: C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)
  • DryWeight: C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)
  • Chla_b_ratio: C(WaterDeficit_pct_cat)
  • Chlt: C(WaterDeficit_pct_cat), C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)
  • CAT: C(WaterDeficit_pct_cat), C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)
  • POD: C(WaterDeficit_pct_cat), C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)
  • Protein: C(WaterDeficit_pct_cat), C(Chitosan_pct_cat), C(WaterDeficit_pct_cat):C(Chitosan_pct_cat)

Significant interactions:
  • FreshWeight: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0002)
  • DryWeight: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0025)
  • Chlt: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0055)
  • CAT: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0001)
  • POD: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0002)
  • Protein: WaterDeficit_pct × Chitosan_pct (Moderate, p=0.0000)

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