Statistical Summary

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🎯 Purpose

This reference provides statistical evaluation tools and interpretation guidelines for logistic regression models. It supports binary and multiclass classification workflows with model fit diagnostics, threshold-aware metrics, and probability-based summaries.

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📐 1. Core Classification Metrics

✅ Accuracy

Proportion of correct predictions.

from sklearn.metrics import accuracy_score
accuracy_score(y_true, y_pred)

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✅ Precision, Recall, and F1 Score

Evaluate class-specific predictive performance.

from sklearn.metrics import precision_score, recall_score, f1_score

• average='binary', 'macro', 'weighted' as needed

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✅ Confusion Matrix

Compare predicted vs actual labels.

from sklearn.metrics import confusion_matrix
confusion_matrix(y_true, y_pred)

• Ideal for visual + text reporting

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✅ ROC AUC (Area Under Curve)

Evaluates probability-based ranking ability.

from sklearn.metrics import roc_auc_score
roc_auc_score(y_true, y_proba)

• Best for binary or OvR for multiclass

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✅ Log Loss (Cross-Entropy)

Measures penalty for incorrect/confident predictions.

from sklearn.metrics import log_loss
log_loss(y_true, y_proba)

• Lower is better

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✅ Brier Score

Mean squared error of predicted probabilities.

from sklearn.metrics import brier_score_loss
brier_score_loss(y_true, y_proba)

• Lower = better-calibrated model

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📊 2. Logistic Regression Fit & Diagnostics

✅ McFadden’s Pseudo R²

Compares log-likelihoods against null model.

1 - (model.llf / model.llnull)  # statsmodels

• Values closer to 1 are better (but lower than OLS R²)

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✅ AIC / BIC (Model Selection Criteria)

Used to compare fit with complexity penalty.

model.aic, model.bic  # statsmodels

• Lower = better fit

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✅ Classification Report

One-line summary of precision, recall, F1, and support per class.

from sklearn.metrics import classification_report
print(classification_report(y_true, y_pred))

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📈 3. Threshold + Probability Analysis

✅ Threshold Evaluation (beyond 0.5)

from sklearn.metrics import precision_recall_curve
precision, recall, thresholds = precision_recall_curve(y_true, y_proba)

✅ Calibration Curve

Compare predicted proba vs true class probability.

from sklearn.calibration import calibration_curve
prob_true, prob_pred = calibration_curve(y_true, y_proba, n_bins=10)

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🧾 4. Suggested Report Summary Table

Field	Description
Model Type	Logistic / Multinomial / Regularized
Accuracy / F1	Basic classifier summary
ROC AUC / Log Loss	Probability performance
Pseudo R² (McFadden)	Model fit (statsmodels only)
AIC / BIC	Fit vs complexity
Confusion Matrix	Class-level correctness
Calibration Status	Raw vs Platt/Isotonic
Threshold Logic Used	0.5 default or custom cutoff

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🧠 Final Tip

“Logistic regression is interpretable, but not assumption-free. Combine statistical fit, threshold diagnostics, and class-level metrics to verify performance.”

Use with: ROC/PR Visual Guide, Evaluation Checklist, and Model Diagnostics Runner.