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COMPREHENSIVE STATISTICAL AND MACHINE LEARNING ANALYSIS REPORT
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Date of analysis: 2026-05-31 00:27
Factors: Cu, NO3, Ca, Cd
Responses: Shikonin
Observations: 105
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1. DESCRIPTIVE STATISTICS
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--- Factor: Cu ---
Statistic            Value
-------------------------
mean               16.5000
std                 6.4852
min                 3.0000
25%                 9.7500
50%                16.5000
75%                23.2500
max                30.0000

--- Factor: NO3 ---
Statistic            Value
-------------------------
mean               80.0000
std                 9.6077
min                60.0000
25%                70.0000
50%                80.0000
75%                90.0000
max               100.0000

--- Factor: Ca ---
Statistic            Value
-------------------------
mean                1.5000
std                 0.4804
min                 0.5000
25%                 1.0000
50%                 1.5000
75%                 2.0000
max                 2.5000

--- Factor: Cd ---
Statistic            Value
-------------------------
mean               45.0000
std                16.8135
min                10.0000
25%                27.5000
50%                45.0000
75%                62.5000
max                80.0000

--- Response: Shikonin ---
Statistic            Value
-------------------------
mean               17.9996
std                 3.4165
min                10.3400
25%                15.9000
50%                18.2400
75%                20.2000
max                25.0200

--- Treatment Combination Means ---

Shikonin:
  16.5_60_1.5_45.0                  23.5850
  9.8_70_2.0_27.5                   23.3775
  23.2_70_1.0_62.5                  22.2675
  9.8_90_2.0_27.5                   21.7250
  23.2_90_1.0_62.5                  21.5350
  9.8_70_2.0_62.5                   20.7900
  16.5_80_1.5_10.0                  19.8425
  23.2_70_1.0_27.5                  19.6275
  9.8_90_1.0_62.5                   19.4075
  9.8_70_1.0_62.5                   19.1275
  9.8_70_1.0_27.5                   18.9325
  16.5_80_2.5_45.0                  18.7150
  23.2_70_2.0_27.5                  18.2350
  3.0_80_1.5_45.0                   18.0750
  30.0_80_1.5_45.0                  17.9050
  16.5_80_0.5_45.0                  17.7375
  16.5_80_1.5_45.0                  17.6656
  23.2_70_2.0_62.5                  16.8875
  16.5_80_1.5_80.0                  16.3075
  9.8_90_1.0_27.5                   14.9100
  9.8_90_2.0_62.5                   13.6550
  23.2_90_2.0_27.5                  13.4875
  16.5_100_1.5_45.0                 13.2775
  23.2_90_1.0_27.5                  11.9025
  23.2_90_2.0_62.5                  11.4300


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2. STATISTICAL ASSUMPTION CHECKS
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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
Shikonin         0.9787    0.0889       Normal   3.5703   0.0012   Unequal [9.45, 26.65]   ✅ None


Outlier Detection Summary:
  Shikonin: 0 outlier(s), IQR bounds: [9.45, 26.65]


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3. PEARSON CORRELATION COEFFICIENTS
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Table 2: Factor-Response Pearson Correlations
Response Factor  Pearson r  p-value Sig.
Shikonin     Cu    -0.1979   0.0430    *
Shikonin    NO3    -0.6070   0.0000  ***
Shikonin     Ca    -0.0723   0.4638   ns
Shikonin     Cd    -0.0488   0.6208   ns


Interpretation:
  • Cu vs Shikonin: weak negative correlation (r=-0.198, p=0.0430, *)
  • NO3 vs Shikonin: moderate negative correlation (r=-0.607, p=0.0000, ***)


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4. N-WAY ANOVA RESULTS
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--- Shikonin ---
                        sum_sq    df        F  PR(>F)      η²
C(Cu_cat)               0.0000   2.0   0.0000  1.0000  0.0000
C(NO3_cat)              0.0000   2.0   0.0000  1.0000  0.0000
C(Ca_cat)               6.5765   2.0   0.5555  0.4580  0.0122
C(Cd_cat)              48.9557   2.0   4.1353  0.0449  0.0842
C(Cu_cat):C(NO3_cat)  167.3703   4.0   7.0689  0.0003  0.2391
C(Cu_cat):C(Ca_cat)    56.5174   4.0   2.3870  0.0742  0.0959
C(Cu_cat):C(Cd_cat)   106.6430   4.0   4.5041  0.0054  0.1668
C(NO3_cat):C(Ca_cat)  171.1007   4.0   7.2264  0.0002  0.2431
C(NO3_cat):C(Cd_cat)  169.9052   4.0   7.1759  0.0002  0.2418
C(Ca_cat):C(Cd_cat)   257.1734   4.0  10.8617  0.0000  0.3256
Residual              532.7335  90.0      NaN     NaN     NaN

  Significant effects (p < 0.05):
    • C(Cd_cat): F=4.14, p=0.0449, η²=0.0842 (medium effect)
    • C(Cu_cat):C(NO3_cat): F=7.07, p=0.0003, η²=0.2391 (large effect)
    • C(Cu_cat):C(Cd_cat): F=4.50, p=0.0054, η²=0.1668 (large effect)
    • C(NO3_cat):C(Ca_cat): F=7.23, p=0.0002, η²=0.2431 (large effect)
    • C(NO3_cat):C(Cd_cat): F=7.18, p=0.0002, η²=0.2418 (large effect)
    • C(Ca_cat):C(Cd_cat): F=10.86, p=0.0000, η²=0.3256 (large effect)

Significant Two-Way Interactions (p < 0.05):
Response Factor_1 Factor_2     F_int    p_int Sig.        Type
Shikonin       Cu      NO3  7.068883 0.000255  ***    Moderate
Shikonin       Cu       Cd  4.504068 0.005438   **    Moderate
Shikonin      NO3       Ca  7.226437 0.000212  ***    Moderate
Shikonin      NO3       Cd  7.175948 0.000225  ***    Moderate
Shikonin       Ca       Cd 10.861717 0.000004  *** Synergistic


Kruskal-Wallis Non-Parametric Validation:
Response Factor ANOVA p KW H-statistic KW p-value              Agreement
Shikonin     Cu  1.0000           4.20     0.1225 ✅ Both non-significant
Shikonin    NO3  1.0000          28.33     0.0000             ⚠️ KW only
Shikonin     Ca  0.4580           1.77     0.4128 ✅ Both non-significant
Shikonin     Cd  0.0449           2.35     0.3087          ⚠️ ANOVA only


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5. POST-HOC MEAN COMPARISONS
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--- Shikonin (Tukey's HSD, CD = 2.8882) ---
Treatment                                 Mean         SD    Group
-----------------------------------------------------------------
16.5_60_1.5_45.0                       23.5850     0.9777        a
9.8_70_2.0_27.5                        23.3775     1.1950        a
23.2_70_1.0_62.5                       22.2675     1.3749       ab
9.8_90_2.0_27.5                        21.7250     0.7799      abc
23.2_90_1.0_62.5                       21.5350     1.6560     abcd
9.8_70_2.0_62.5                        20.7900     0.7566    abcde
16.5_80_1.5_10.0                       19.8425     0.9225    bcdef
23.2_70_1.0_27.5                       19.6275     1.5785    bcdef
9.8_90_1.0_62.5                        19.4075     1.5162    bcdef
9.8_70_1.0_62.5                        19.1275     1.3689    cdefg
9.8_70_1.0_27.5                        18.9325     1.1723    cdefg
16.5_80_2.5_45.0                       18.7150     0.5994     defg
23.2_70_2.0_27.5                       18.2350     1.1545      efg
3.0_80_1.5_45.0                        18.0750     0.8655      efg
30.0_80_1.5_45.0                       17.9050     0.9167      efg
16.5_80_0.5_45.0                       17.7375     1.3708      fgh
16.5_80_1.5_45.0                       17.6656     0.9293      fgh
23.2_70_2.0_62.5                       16.8875     1.1686      fgh
16.5_80_1.5_80.0                       16.3075     1.0556      ghi
9.8_90_1.0_27.5                        14.9100     1.1646      hij
9.8_90_2.0_62.5                        13.6550     0.7251      ijk
23.2_90_2.0_27.5                       13.4875     0.6171      ijk
16.5_100_1.5_45.0                      13.2775     0.6886       jk
23.2_90_1.0_27.5                       11.9025     1.2845        k
23.2_90_2.0_62.5                       11.4300     1.0538        k


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6. SHAP FEATURE IMPORTANCE ANALYSIS
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Table: SHAP Relative Importance (%)
Response                       Cu          NO3           Ca           Cd
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Shikonin                     19.9         47.4         16.9         15.7

Interpretation:
  • Shikonin: Dominant factor is NO3 (47.4%)


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7. PERMUTATION FEATURE IMPORTANCE (Validation)
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Table: Permutation Relative Importance (%)
Response                       Cu          NO3           Ca           Cd
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Shikonin                     15.1         40.4         23.8         20.7


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8. MODEL PERFORMANCE COMPARISON (5-Fold CV R²)
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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
Shikonin       0.696      0.042       0.265      0.221       -12.58       6.022   RF

Interpretation:
  • Shikonin: Best model = RF (RF=0.696, LR=0.265, GPR=-12.580)


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9. STANDARDIZED REGRESSION COEFFICIENTS (β) with 95% Bootstrap CI
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--- Shikonin ---
Factor                        β   95% CI Lower   95% CI Upper Significant?
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Cu                      -0.1979        -0.3513        -0.0375          Yes
NO3                     -0.6070        -0.7527        -0.4447          Yes
Ca                      -0.0723        -0.2416         0.0828           No
Cd                      -0.0488        -0.2015         0.1114           No


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10. PRINCIPAL COMPONENT ANALYSIS (PCA)
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Table: Variance Explained
Component Eigenvalue Variance (%) Cumulative (%)
      PC1      1.010        100.0          100.0


Table: PC Loadings
Response  PC1
Shikonin  1.0

Interpretation:
  • Shikonin: PC1 loading = 1.000, PC2 loading = 0.000


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11. MORF RESIDUAL CORRELATION MATRIX
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Residual correlations indicate relationships between responses after accounting for factor effects.

                  Shikonin
--------------------------
Shikonin             1.000


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SUMMARY OF KEY FINDINGS
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Best predictive models:
  • Shikonin: RF (R² = 0.696)

Most influential factors (SHAP):
  • Shikonin: NO3 (47.4%)

Significant ANOVA effects:
  • Shikonin: C(Cd_cat), C(Cu_cat):C(NO3_cat), C(Cu_cat):C(Cd_cat), C(NO3_cat):C(Ca_cat), C(NO3_cat):C(Cd_cat), C(Ca_cat):C(Cd_cat)

Significant interactions:
  • Shikonin: Cu × NO3 (Moderate, p=0.0003)
  • Shikonin: Cu × Cd (Moderate, p=0.0054)
  • Shikonin: NO3 × Ca (Moderate, p=0.0002)
  • Shikonin: NO3 × Cd (Moderate, p=0.0002)
  • Shikonin: Ca × Cd (Synergistic, p=0.0000)

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END OF REPORT
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