Statistics and Machine Learning Toolbox: Worked examples
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Why the workbook includes multiple examples
The Statistics and Machine Learning Toolbox includes five distinct model fixtures. Rather than demonstrating only a single algorithm, these fixtures exercise binary classification, regularized continuous regression, centroid-based unsupervised clustering, decision tree rule partitioning, and spectral dimensionality reduction within the exact same spreadsheet geometry.
The Marimo reactive engine reads the shared worksheet tables, identifies the active dataset via Start!B6, fits the appropriate scikit-learn estimator, runs stratified cross-validation, and publishes normalized results.
Example matrix
| Model ID | Domain & Problem | Task Family | Algorithm | Primary Metric | Top Feature (Rank 1) | Diagnostic Notes |
|---|---|---|---|---|---|---|
customer_churn_logistic |
Telecom subscriber churn | Classification | LogisticRegression |
Accuracy: 1.000000 | Feature3 (w=1.135471) |
7 checks PASS |
housing_regression_ridge |
Residential property appraisal | Regression | Ridge |
\(R^2\): 0.986518 | Feature1 (w=60.173745) |
7 checks PASS |
iris_clustering_kmeans |
Botanical flower segmentation | Clustering | KMeans |
Silhouette: 0.540379 | Feature2 (w=0.317303) |
7 checks PASS |
credit_default_tree |
Retail lending default underwriting | Classification | DecisionTreeClassifier |
Accuracy: 1.000000 | Feature4 (w=1.000000) |
6 PASS, 1 FAIL (Generalization gap) |
feature_pca |
Correlated signal reduction | Decomposition | PCA |
ExpVar: 1.000000 | Feature1 (w=0.500750) |
6 PASS, 1 FAIL (Condition number \(\kappa\)) |
1. Customer Churn Prediction (Logistic Regression)
Business context
A subscription telecom provider seeks to identify customers at high risk of canceling their contracts. Identifying churn drivers allows retention teams to proactively offer targeted promotional incentives before cancellation occurs.
Input dataset (Data!A5:G21)
The dataset contains 16 customer accounts:
| SampleID | Feature1 (Usage Min) | Feature2 (Tenure Mo) | Feature3 (Complaints) | Feature4 (MonthlySpend $) | Target (Churn) |
|---|---|---|---|---|---|
| 1 | 120.0 | 24.0 | 0.0 | 65.0 | 0 |
| 2 | 350.0 | 6.0 | 2.0 | 85.0 | 1 |
| 3 | 210.0 | 36.0 | 1.0 | 55.0 | 0 |
| 4 | 80.0 | 4.0 | 3.0 | 95.0 | 1 |
| 5 | 450.0 | 48.0 | 0.0 | 45.0 | 0 |
| 6 | 190.0 | 12.0 | 1.0 | 75.0 | 0 |
| 7 | 95.0 | 3.0 | 4.0 | 110.0 | 1 |
| 8 | 300.0 | 60.0 | 0.0 | 40.0 | 0 |
| 9 | 140.0 | 8.0 | 2.0 | 90.0 | 1 |
| 10 | 280.0 | 18.0 | 0.0 | 70.0 | 0 |
| 11 | 410.0 | 30.0 | 0.0 | 50.0 | 0 |
| 12 | 115.0 | 5.0 | 3.0 | 105.0 | 1 |
| 13 | 260.0 | 40.0 | 1.0 | 60.0 | 0 |
| 14 | 175.0 | 10.0 | 2.0 | 80.0 | 1 |
| 15 | 320.0 | 22.0 | 0.0 | 65.0 | 0 |
| 16 | 90.0 | 2.0 | 4.0 | 115.0 | 1 |
Mathematical formulation
\[\min_{\mathbf{w}, b} \; \frac{1}{2} \|\mathbf{w}\|_2^2 + C \sum_{i=1}^{16} \mathcal{L}_{\text{BCE}}(y_i, \sigma(\mathbf{w}^T \mathbf{x}_i + b))\]
where \(C = 1.0\), features are standardized (\(z = (x - \mu)/\sigma\)), and optimization uses L-BFGS.
Verified baseline results
- Primary metric (Accuracy):
1.000000(100.0%) - Secondary metric (F1 score):
1.000000 - Tertiary metric (ROC-AUC):
1.000000 - Cross-validation mean (3-fold):
0.944444(94.4%) - Feature importance rankings:
Feature3(Complaints): Weight =1.135471, Odds Ratio =3.1127, Rank 1Feature4(MonthlySpend): Weight =0.874974, Odds Ratio =2.3988, Rank 2Feature2(Tenure): Weight =-0.801402, Odds Ratio =0.4487, Rank 3Feature1(Usage): Weight =-0.174595, Odds Ratio =0.8398, Rank 4
- Sample predictions:
- Sample 1: Actual = 0, Predicted = 0, Probability =
0.1176, Split =Train, Correct =YES - Sample 2: Actual = 1, Predicted = 1, Probability =
0.9632, Split =Train, Correct =YES
- Sample 1: Actual = 0, Predicted = 0, Probability =
- Diagnostics: All 7 checks report
PASS.
2. Property Valuation (Ridge Regression)
Business context
A real estate appraisal desk needs a reliable, regularized model to estimate residential market prices from physical and location attributes, avoiding the erratic coefficients often produced by ordinary least squares under correlated housing features.
Input dataset (Data!A22:G33)
The dataset contains 12 residential properties:
| SampleID | Feature1 (Sqft) | Feature2 (Bedrooms) | Feature3 (Age Yrs) | Feature4 (Dist CBD Mi) | Target (Price $k) |
|---|---|---|---|---|---|
| 1 | 1400.0 | 3.0 | 15.0 | 5.0 | 320.0 |
| 2 | 1800.0 | 3.0 | 10.0 | 3.5 | 395.0 |
| 3 | 2200.0 | 4.0 | 5.0 | 2.0 | 490.0 |
| 4 | 1200.0 | 2.0 | 25.0 | 8.0 | 260.0 |
| 5 | 2600.0 | 4.0 | 2.0 | 1.5 | 580.0 |
| 6 | 1600.0 | 3.0 | 18.0 | 4.0 | 350.0 |
| 7 | 1950.0 | 3.0 | 8.0 | 3.0 | 425.0 |
| 8 | 2400.0 | 4.0 | 4.0 | 2.5 | 520.0 |
| 9 | 1100.0 | 2.0 | 30.0 | 9.0 | 240.0 |
| 10 | 1700.0 | 3.0 | 12.0 | 4.5 | 375.0 |
| 11 | 2800.0 | 5.0 | 1.0 | 1.0 | 640.0 |
| 12 | 1500.0 | 3.0 | 20.0 | 6.0 | 330.0 |
Mathematical formulation
\[\min_{\mathbf{w}} \; \frac{1}{24} \|\mathbf{y} - \mathbf{X}\mathbf{w}\|_2^2 + \frac{\alpha}{2} \|\mathbf{w}\|_2^2\]
with \(\alpha = 1.0\) configured on Model Config!C7.
Verified baseline results
- Primary metric (\(R^2\)):
0.986518(98.65% variance explained) - Secondary metric (RMSE):
14.398038($14,398 prediction error) - Tertiary metric (MAE):
10.988185($10,988 mean absolute error) - Cross-validation mean (3-fold):
0.953845 - Feature coefficients:
Feature1(Sqft): Weight =60.173745, AbsImportance =60.173745, Rank 1Feature2(Bedrooms): Weight =31.544822, AbsImportance =31.544822, Rank 2Feature3(Age): Weight =-17.500994, AbsImportance =17.500994, Rank 3Feature4(Distance): Weight =-8.434350, AbsImportance =8.434350, Rank 4
- Sample predictions (Holdout Sample 1):
- Actual Price:
$320.0k - Predicted Price:
$340.92k - Residual (
Predictions!Probability):-$20.92k - Split:
Test - Correct tag:
Residual
- Actual Price:
- Diagnostics: All 7 checks report
PASS. Residual normality via Shapiro-Wilk yields \(p = 0.5843 \ge 0.05\).
3. Botanical Morphological Clustering (Iris K-Means)
Business context
A botanical institute wishes to segment unlabeled flower specimens into natural morphological taxonomic groups based solely on petal and sepal dimensions, evaluating cluster coherence without relying on species tags.
Input dataset (Data!A34:G45)
The dataset contains 12 flower observations across 4 physical measurements:
| SampleID | Feature1 (SepalLen) | Feature2 (SepalWid) | Feature3 (PetalLen) | Feature4 (PetalWid) | Target (ClusterLabel) |
|---|---|---|---|---|---|
| 1 | 5.1 | 3.5 | 1.4 | 0.2 | 0 |
| 2 | 4.9 | 3.0 | 1.4 | 0.2 | 0 |
| 3 | 4.7 | 3.2 | 1.3 | 0.2 | 0 |
| 4 | 4.6 | 3.1 | 1.5 | 0.2 | 0 |
| 5 | 7.0 | 3.2 | 4.7 | 1.4 | 1 |
| 6 | 6.4 | 3.2 | 4.5 | 1.5 | 1 |
| 7 | 6.9 | 3.1 | 4.9 | 1.5 | 1 |
| 8 | 5.5 | 2.3 | 4.0 | 1.3 | 1 |
| 9 | 6.3 | 3.3 | 6.0 | 2.5 | 2 |
| 10 | 5.8 | 2.7 | 5.1 | 1.9 | 2 |
| 11 | 7.1 | 3.0 | 5.9 | 2.1 | 2 |
| 12 | 6.3 | 2.9 | 5.6 | 1.8 | 2 |
Mathematical formulation
\[\min_{\mathcal{S}, \{\boldsymbol{\mu}_k\}_{k=1}^3} \; \sum_{k=1}^3 \sum_{\mathbf{x}_i \in S_k} \|\mathbf{x}_i - \boldsymbol{\mu}_k\|_2^2\]
with \(k = 3\) centroids initialized via k-means++.
Verified baseline results
- Primary metric (Silhouette Score):
0.540379(strong cluster separation) - Secondary metric (Inertia):
11.238210 - Tertiary metric (Calinski-Harabasz):
14.868735 - CV score mean:
0.540379 - Feature variance shares:
Feature2(SepalWid): Weight =0.317303, Rank 1Feature3(PetalLen): Weight =0.242379, Rank 2Feature4(PetalWid): Weight =0.228701, Rank 3Feature1(SepalLen): Weight =0.211617, Rank 4
- Sample predictions:
- Sample 1: Actual = 0, Predicted Cluster = 1 (or assigned cluster index), Centroid Distance =
1.0623, Split =Test, Correct =ClusterAssigned
- Sample 1: Actual = 0, Predicted Cluster = 1 (or assigned cluster index), Centroid Distance =
- Diagnostics: All 7 checks report
PASS. Minimum cluster size is 4 samples (\(\ge 2\)).
4. Credit Risk Classification (Decision Tree)
Business context
A credit committee requires an interpretable rule-based underwriting model to classify consumer loan default risk. Decision trees offer clear boolean split criteria that can be directly audited by compliance regulators.
Input dataset (Data!A46:G53)
The dataset contains 8 applicant loan profiles:
| SampleID | Feature1 (Income $k) | Feature2 (DebtRatio) | Feature3 (LatePayments) | Feature4 (CreditScore) | Target (Default) |
|---|---|---|---|---|---|
| 1 | 45.0 | 0.35 | 0.0 | 720.0 | 0 |
| 2 | 85.0 | 0.22 | 0.0 | 780.0 | 0 |
| 3 | 28.0 | 0.55 | 2.0 | 610.0 | 1 |
| 4 | 35.0 | 0.42 | 1.0 | 660.0 | 0 |
| 5 | 18.0 | 0.70 | 3.0 | 580.0 | 1 |
| 6 | 95.0 | 0.18 | 0.0 | 810.0 | 0 |
| 7 | 52.0 | 0.48 | 1.0 | 640.0 | 1 |
| 8 | 65.0 | 0.30 | 0.0 | 750.0 | 0 |
Mathematical formulation
Recursive binary partitioning minimizing Gini impurity:
\[I_G(t) = 1 - \sum_{c \in \{0, 1\}} p(c \mid t)^2\]
with max_depth = 3.
Verified baseline results
- Primary metric (Accuracy):
1.000000(100.0%) - Secondary metric (F1 score):
1.000000 - Tertiary metric (ROC-AUC):
1.000000 - Cross-validation mean:
0.722222(72.2%) - Feature Gini importances:
Feature4(CreditScore): Importance =1.000000, Rank 1Feature1,Feature2,Feature3: Importance =0.000000, Rank 2–4
- Diagnostics:
- 6 checks report
PASS. - Check 4 (Generalization & stability): Reports
FAIL.- Diagnostic Evidence: Generalization gap \(|1.0000 - 0.7222| = 0.2778 > 0.25\).
- Interpretation: With only 8 samples, a tree of depth 3 isolates individual records, creating a substantial gap between training fit and out-of-fold generalization.
- Remediation: Setting
max_depth = 1on Model Config!C9 restricts the tree to a single decision stump on CreditScore, preserving high predictive power while stabilizing the generalization gap.
- 6 checks report
5. Multi-Feature Dimensionality Reduction (PCA)
Business context
An industrial engineering group collects multichannel sensor readings (Dim1 through Dim4) from manufacturing telemetry. The signals exhibit severe collinearity. The team uses PCA to extract orthogonal principal components that summarize process variance without redundancy.
Input dataset (Data!A54:G59)
The dataset contains 6 sensor measurements:
| SampleID | Feature1 (Dim1) | Feature2 (Dim2) | Feature3 (Dim3) | Feature4 (Dim4) | Target |
|---|---|---|---|---|---|
| 1 | 10.0 | 20.0 | 30.0 | 40.0 | 0 |
| 2 | 12.0 | 22.0 | 28.0 | 38.0 | 0 |
| 3 | 9.0 | 19.0 | 31.0 | 42.0 | 0 |
| 4 | 15.0 | 25.0 | 25.0 | 35.0 | 0 |
| 5 | 8.0 | 18.0 | 32.0 | 44.0 | 0 |
| 6 | 14.0 | 24.0 | 26.0 | 36.0 | 0 |
Mathematical formulation
\[\mathbf{X}_c = \mathbf{U} \mathbf{S} \mathbf{V}^T, \quad \mathbf{Z} = \mathbf{X}_c \mathbf{V}_2\]
with n_components = 2 on Model Config!C10.
Verified baseline results
- Primary metric (Total Explained Variance):
1.000000(100.0% of all sample variance captured) - Secondary metric (PC1 Explained Variance Ratio):
0.999607(99.96%) - Tertiary metric (PC2 Explained Variance Ratio):
0.000393(0.04%) - Cross-validation mean:
1.000000 - Feature loadings (PC1):
Feature1: Loading =0.500750, Rank 1Feature2: Loading =0.500750, Rank 2Feature3: Loading =-0.500750, Rank 3Feature4: Loading =-0.497745, Rank 4
- Diagnostics:
- 6 checks report
PASS. - Check 5 (Multicollinearity & conditioning): Reports
FAIL.- Diagnostic Evidence: Condition number \(\kappa = 431.13 \ge 100\).
- Interpretation: The sensor features are almost perfectly collinear. This diagnostic failure directly verifies the necessity of applying PCA to compress the collinear inputs into orthogonal latent factors.
- 6 checks report