Analysis Reports

Diagnostics & Reports

Detailed breakdown of the analysis: data sources, descriptive statistics, pairwise correlations, OLS model, diagnostics, and validation checks. All results reflect v1.0.0.

Summary

✅

Phase IV Published: R² = 0.812 (n = 16) · 5 indicators · 7 figures · 6 findings · κ(X) ≈ 78,500.

Model R²

0.812

adjusted R² = 0.744

Sample

n = 16

complete-case 2004–2019

κ(X)

78,500

condition number (severe)

Findings

associational results

Data Sources

Five World Bank WDI indicators, plus national indicators from Morocco's 2025 State of the Environment Report.

Indicator	Code	Coverage	Status
Annual freshwater withdrawals	ER.H2O.FWTL.K3	2000–2022	PASS
Agricultural land irrigated (%)	AG.LND.IRIG.AG.ZS	2004–2019	PASS
Population growth (annual %)	SP.POP.GROW	2000–2025	PASS
Cereal yield (kg/ha)	AG.YLD.CREL.KG	2000–2024	PASS
Arable land (% of land area)	AG.LND.ARBL.ZS	2000–2024	PASS

Descriptive Statistics

National water balance, sectoral allocation, and rainfall recovery from the 2025 State of the Environment Report.

Metric	Value	Year / Note
Renewable water per capita	≈ 600 m³/person/year	2025
Potential natural resources	≈ 22 billion m³/year	—
Technically mobilizable	≈ 8 billion m³/year	—
Groundwater abstraction	≈ 5 billion m³/year	—
Water-stress index	50.75%	2022
Agriculture share	≈ 88%	Sectoral allocation
Drinking water share	≈ 11%	Sectoral allocation
Industry & tourism share	≈ 1%	Sectoral allocation

Pairwise Correlations

Pearson correlations on pairwise-complete observations. n varies by pair.

Pair	r	n
Withdrawals ↔ Irrigated land	−0.70	16
Withdrawals ↔ Cereal yield	−0.36	23
Withdrawals ↔ Population growth	0.49	23
Withdrawals ↔ Arable land	0.67	23
Irrigated land ↔ Population growth	−0.89	16
Population growth ↔ Arable land	0.78	25
Irrigated land ↔ Arable land	−0.44	16

OLS Model (2004–2019, n = 16)

Model fit and predictor coefficients.

Statistic	Value
R²	0.812
Adjusted R²	0.744
Condition number κ(X)	≈ 78,500

Predictor	Approx. coefficient	Reading
Irrigated land	≈ −3	Negative, CI excludes zero
Population growth	≈ −14	Largest magnitude, wide CI
Cereal yield	≈ 0	Close to zero, narrow CI
Arable land	small positive	CI near zero

Diagnostics

Multicollinearity, sample size, and model stability checks.

Check	Result	Status
R² / adjusted R²	0.812 / 0.744	PASS
Condition number κ(X)	≈ 78,500	WARN
Sample size	n = 16	PASS
Missing values	None imputed	PASS
Causal claims	None	PASS

Validation Scenarios

End-to-end checks executed. All pass at v1.0.0.

Scenario	Expected	Status
Model fit	R² ≥ 0.8	PASS
Diagnostics	κ(X) reported (no rejection)	PASS
Data integrity	No imputation	PASS
Reproducibility	Script + data available	PASS
External review	Recorded 2026-11-02	PASS

Methodological Principles

Each principle is documented and tested.

Associational

No causal claims.

No Imputation

Missing values kept missing.

Pairwise-Complete

n varies by pair.

Diagnostics

VIF, condition number, CIs.

Reproducibility

Script + data available.

Open Data

World Bank (CC-BY-4.0).

Model Specification

# Regression
FW_t = β0 + β1·IRRIG_t + β2·POPGR_t + β3·YIELD_t + β4·ARABLE_t + ε_t

β̂ = (XᵀX)⁻¹ Xᵀy

# Fit
R² = 0.812 (n = 16, adjusted 0.744)

# Diagnostics
κ(X) ≈ 78,500  →  severe multicollinearity
r(IRRIG, POPGR) = −0.89  →  inseparable

# Golden rule
All relationships are associational. No causal claims.
    

Limitations Coverage

6 limitations documented; each is stated in the manuscript.

ID	Limitation	Coverage
L1	Small sample (n = 16)	Stated
L2	Multicollinearity (κ ≈ 78,500)	Stated
L3	Missing climate variables	Stated
L4	National aggregation	Stated
L5	Associational inference only	Stated
L6	Indicator coverage (through 2022)	Stated

Scope & Limits

Explicit scope of v1.0.0.

Concern	Mitigation
Sample size (n = 16)	Stated; future work to extend
Multicollinearity	Reported as finding, not corrected
Climate variables	Discussed qualitatively
National aggregation	Stated; basin-level is future work
Causal identification	Deferred (associational only)