AnoFox Statistics Extension

In-Database Regression Analysis & Statistical Inference in SQL

Build predictive models directly in DuckDB with 5 regression types, comprehensive diagnostics, and hypothesis testing—zero Python overhead.

30-Second Example

-- Load the extension
LOAD anofox_statistics;

-- Simple linear regression
SELECT
    coefficient,
    std_error,
    t_statistic,
    p_value,
    r_squared,
    rmse
FROM anofox_statistics_ols(
    'sales_data',
    'revenue',
    ARRAY['marketing_spend', 'team_size']
);

Output: Coefficients with statistical significance tests, goodness-of-fit metrics, and standard errors.

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What's Included

Component	Coverage	Highlights
Regression Models	5 types	OLS, Ridge, WLS, RLS, Elastic Net
Inference	10+ functions	t-tests, p-values, confidence intervals, prediction intervals
Diagnostics	5 types	Residuals, VIF, normality tests, outlier detection, AIC/BIC
Aggregates	GROUP BY & OVER	Per-group models, rolling regression, expanding windows
Utilities	Basic metrics	R², RMSE, MSE, information criteria

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Function Finder

What I Want to Do → Function to Use

Goal	Function	Guide
Fit simple linear regression	anofox_statistics_ols	Basic Workflow
Test coefficient significance	anofox_statistics_ols_inference	Inference & Testing
Detect multicollinearity	anofox_statistics_vif	Handling Multicollinearity
Make predictions with uncertainty	anofox_statistics_ols_predict_interval	Prediction Intervals
Analyze per segment/group	anofox_statistics_ols_agg	Grouped Analysis
Rolling regression over time	anofox_statistics_ols_agg OVER (...)	Rolling Regression
Handle correlated predictors	anofox_statistics_ridge	Model Types
Adaptive online learning	anofox_statistics_rls	Model Types
Select best model	anofox_statistics_information_criteria	Model Selection
Check regression assumptions	Diagnostics functions	Diagnostics

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Why AnoFox Statistics?

Native In-Database Processing

• No data export/import cycles
• Direct SQL integration with your data pipeline
• Zero Python dependency overhead

Production-Ready Algorithms

• OLS: The statistical workhorse (BLUE property guaranteed)
• Ridge: Handle multicollinearity with L2 regularization
• WLS: Heteroscedastic data with weighted observations
• RLS: Online adaptive learning with forgetting factor
• Elastic Net: Combined L1+L2 for feature selection

Comprehensive Statistical Inference

• Coefficient significance testing (t-tests, p-values)
• Confidence intervals for parameters
• Prediction intervals (individual vs. mean)
• Hypothesis testing framework built-in
• Multiple comparison corrections

Enterprise Diagnostics

• Residual analysis (leverage, Cook's distance)
• Multicollinearity detection (VIF)
• Normality testing (Jarque-Bera)
• Information criteria (AIC, BIC)
• Per-group analysis via GROUP BY

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Getting Started Paths

👤 New to Statistics?

Start with Understanding Regression → Quickstart → Basic Workflow

👨‍💼 Business Analyst

Quickstart → Basic Workflow → Production Deployment

👨‍🔬 Data Scientist

Model Types → Grouped Analysis → Advanced Guides

🏭 Production Focus

Installation → Quickstart → Production Deployment

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Key Concepts at a Glance

Linear Regression Equation

y = β₀ + β₁x₁ + β₂x₂ + ... + βₚxₚ + ε

• β₀: Intercept
• βⱼ: Coefficient (marginal effect of xⱼ)
• ε: Error term (unobserved noise)

R² (Coefficient of Determination)

Proportion of variance explained: 0 (no fit) to 1 (perfect fit)

p-Value

Probability of observing this coefficient under null hypothesis (H₀: β = 0). p < 0.05 = significant.

Prediction Intervals vs. Confidence Intervals

• Confidence Interval: Uncertainty about the mean prediction
• Prediction Interval: Wider; includes individual variation

Multicollinearity

Correlated predictors inflate standard errors, weaken inference. VIF > 10 = problematic.

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Next Steps

• Installation — Get the extension running
• Quickstart — Fit your first model in 5 minutes
• Concepts — Understand regression fundamentals
• Function Reference — Complete API documentation
• GitHub Repository — Source code and discussions

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Key Takeaways

• ✅ 5 regression models for different data types
• ✅ Full statistical inference (tests, intervals, significance)
• ✅ Comprehensive diagnostics (residuals, VIF, normality)
• ✅ GROUP BY and window functions for complex analyses
• ✅ Production-grade in-database processing
• ✅ Zero Python/R integration friction