linreg-core

A lightweight, self-contained linear regression library written in Rust. Compiles to WebAssembly for browser use, Python bindings via PyO3, a native Windows DLL for Excel VBA, an Excel XLL add-in with 27 worksheet UDFs, or runs as a native Rust crate.

Key design principle: All linear algebra and statistical distribution functions are implemented from scratch — no external math libraries required. This keeps binary sizes small and makes the crate highly portable.

Live Demo Link

Table of Contents

Section	Description
Features	Regression methods, model statistics, feature importance, diagnostic tests
Rust Usage	Native Rust crate usage
WebAssembly Usage	Browser/JavaScript usage
Python Usage	Python bindings via PyO3
VBA / Excel Usage	Excel VBA via native Windows DLL
Excel XLL Add-in	Native Excel worksheet UDFs
Feature Flags	Build configuration options
Validation	Testing and verification
Implementation Notes	Technical details

---

Features

Regression Methods

• OLS Regression: Coefficients, standard errors, t-statistics, p-values, confidence intervals, model selection criteria (AIC, BIC, log-likelihood)
• Ridge Regression: L2-regularized regression with optional standardization, effective degrees of freedom, model selection criteria
• Lasso Regression: L1-regularized regression via coordinate descent with automatic variable selection, convergence tracking, model selection criteria
• Elastic Net: Combined L1 + L2 regularization for variable selection with multicollinearity handling, active set convergence, model selection criteria
• Polynomial Regression: Polynomial fitting of any degree with centering/standardization for numerical stability
• LOESS: Locally estimated scatterplot smoothing for non-parametric curve fitting with configurable span, polynomial degree, and robust fitting
• WLS (Weighted Least Squares): Regression with observation weights for heteroscedastic data, includes confidence intervals
• Prediction Intervals: Uncertainty bounds for individual future observations (OLS, Ridge, Lasso, Elastic Net)
• K-Fold Cross Validation: Model evaluation and hyperparameter tuning for all regression types (OLS, Ridge, Lasso, Elastic Net) with customizable folds, shuffling, and seeding
• Lambda Path Generation: Create regularization paths for cross-validation
• Model Serialization: Save/load trained models to/from JSON for all model types

Model Statistics

• Fit Metrics: R-squared, Adjusted R-squared, F-statistic, F-test p-value
• Error Metrics: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE)
• Model Selection: Log-likelihood, AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion)
• Residuals: Raw residuals, standardized residuals, fitted values, leverage (hat matrix diagonal)
• Multicollinearity: Variance Inflation Factor (VIF) for each predictor

Feature Importance

• Standardized Coefficients: Coefficients scaled by standard deviation for cross-variable comparison
• SHAP Values: Exact SHAP (Shapley Additive Explanations) for linear models — local and global importance
• Permutation Importance: Performance drop when feature values are randomly shuffled
• VIF Ranking: Automatic multicollinearity assessment with interpretation guidance

Diagnostic Tests

Category	Tests
Linearity	Rainbow Test, Harvey-Collier Test, RESET Test
Heteroscedasticity	Breusch-Pagan (Koenker variant), White Test (R & Python methods)
Normality	Jarque-Bera, Shapiro-Wilk (n ≤ 5000), Anderson-Darling
Autocorrelation	Durbin-Watson, Breusch-Godfrey (higher-order)
Multicollinearity	Variance Inflation Factor (VIF)
Influence	Cook's Distance, DFBETAS, DFFITS

---

Rust Usage

Add to your Cargo.toml:

[dependencies]
linreg-core = { version = "0.8", default-features = false }

OLS Regression (Rust)

use linreg_core::core::ols_regression;

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3];
    let x = vec![vec![1.0, 2.0, 3.0, 4.0, 5.0]];
    let names = vec!["Intercept".to_string(), "X1".to_string()];

    let result = ols_regression(&y, &x, &names)?;

    println!("Coefficients: {:?}", result.coefficients);
    println!("R-squared: {:.4}", result.r_squared);
    println!("F-statistic: {:.4}", result.f_statistic);
    println!("Log-likelihood: {:.4}", result.log_likelihood);
    println!("AIC: {:.4}", result.aic);
    println!("BIC: {:.4}", result.bic);

    Ok(())
}

Ridge Regression (Rust)

use linreg_core::regularized::{ridge_fit, RidgeFitOptions};
use linreg_core::linalg::Matrix;

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3];
    let x = Matrix::new(5, 2, vec![
        1.0, 1.0,  // row 0: intercept, x1
        1.0, 2.0,  // row 1
        1.0, 3.0,  // row 2
        1.0, 4.0,  // row 3
        1.0, 5.0,  // row 4
    ]);

    let options = RidgeFitOptions {
        lambda: 1.0,
        standardize: true,
        intercept: true,
    };

    let result = ridge_fit(&x, &y, &options)?;
    println!("Intercept: {}", result.intercept);
    println!("Coefficients: {:?}", result.coefficients);
    println!("R-squared: {:.4}", result.r_squared);
    println!("Effective degrees of freedom: {:.2}", result.effective_df);
    println!("AIC: {:.4}", result.aic);
    println!("BIC: {:.4}", result.bic);

    Ok(())
}

Lasso Regression (Rust)

use linreg_core::regularized::{lasso_fit, LassoFitOptions};
use linreg_core::linalg::Matrix;

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3];
    let x = Matrix::new(5, 3, vec![
        1.0, 1.0, 0.5,
        1.0, 2.0, 1.0,
        1.0, 3.0, 1.5,
        1.0, 4.0, 2.0,
        1.0, 5.0, 2.5,
    ]);

    let options = LassoFitOptions {
        lambda: 0.1,
        standardize: true,
        intercept: true,
        ..Default::default()
    };

    let result = lasso_fit(&x, &y, &options)?;
    println!("Intercept: {}", result.intercept);
    println!("Coefficients: {:?}", result.coefficients);
    println!("Non-zero coefficients: {}", result.n_nonzero);
    println!("AIC: {:.4}", result.aic);
    println!("BIC: {:.4}", result.bic);

    Ok(())
}

Elastic Net Regression (Rust)

use linreg_core::regularized::{elastic_net_fit, ElasticNetOptions};
use linreg_core::linalg::Matrix;

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3];
    let x = Matrix::new(5, 3, vec![
        1.0, 1.0, 0.5,
        1.0, 2.0, 1.0,
        1.0, 3.0, 1.5,
        1.0, 4.0, 2.0,
        1.0, 5.0, 2.5,
    ]);

    let options = ElasticNetOptions {
        lambda: 0.1,
        alpha: 0.5,   // 0 = Ridge, 1 = Lasso, 0.5 = balanced
        standardize: true,
        intercept: true,
        ..Default::default()
    };

    let result = elastic_net_fit(&x, &y, &options)?;
    println!("Intercept: {}", result.intercept);
    println!("Coefficients: {:?}", result.coefficients);
    println!("Non-zero coefficients: {}", result.n_nonzero);
    println!("AIC: {:.4}", result.aic);
    println!("BIC: {:.4}", result.bic);

    Ok(())
}

Polynomial Regression (Rust)

use linreg_core::polynomial::{polynomial_regression, polynomial_predict};

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.1, 4.9, 10.8, 19.5, 32.1];  // Quadratic relationship
    let x = vec![1.0, 2.0, 3.0, 4.0, 5.0];

    // Fit degree-2 polynomial with centering for numerical stability
    let fit = polynomial_regression(&y, &x, 2, true, true)?;

    println!("R²: {:.4}", fit.ols_output.r_squared);
    println!("Coefficients: {:?}", fit.ols_output.coefficients);

    // Predict at new x values
    let new_x = vec![2.5, 5.5];
    let predictions = polynomial_predict(&fit, &new_x)?;
    println!("Predictions: {:?}", predictions);

    Ok(())
}

Feature Importance (Rust)

use linreg_core::feature_importance::{
    standardized_coefficients, shap_values_linear,
    permutation_importance_ols, PermutationImportanceOptions,
};

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3];
    let x1 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
    let x2 = vec![2.0, 4.0, 5.0, 4.0, 3.0];

    // Standardized coefficients for comparison
    let std_coef = standardized_coefficients(&[0.8, 0.5], &[x1.clone(), x2.clone()])?;
    println!("Standardized: {:?}", std_coef.standardized_coefficients);

    // SHAP values for local explanations
    let shap = shap_values_linear(&[x1, x2], &[1.5, 0.3])?;
    println!("SHAP: {:?}", shap.mean_abs_shap);

    // Permutation importance
    let perm = permutation_importance_ols(
        &y, &[x1, x2], &PermutationImportanceOptions::default()
    )?;
    println!("Importance: {:?}", perm.importance);

    Ok(())
}

Diagnostic Tests (Rust)

use linreg_core::diagnostics::{
    breusch_pagan_test, durbin_watson_test, jarque_bera_test,
    shapiro_wilk_test, rainbow_test, harvey_collier_test,
    white_test, anderson_darling_test, breusch_godfrey_test,
    cooks_distance_test, dfbetas_test, dffits_test, vif_test,
    reset_test, BGTestType, RainbowMethod, ResetType, WhiteMethod
};

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![/* your data */];
    let x = vec![vec![/* predictor 1 */], vec![/* predictor 2 */]];

    // Heteroscedasticity tests
    let bp = breusch_pagan_test(&y, &x)?;
    println!("Breusch-Pagan: LM={:.4}, p={:.4}", bp.statistic, bp.p_value);

    let white = white_test(&y, &x, WhiteMethod::R)?;
    println!("White: statistic={:.4}, p={:.4}", white.statistic, white.p_value);

    // Autocorrelation tests
    let dw = durbin_watson_test(&y, &x)?;
    println!("Durbin-Watson: {:.4}", dw.statistic);

    let bg = breusch_godfrey_test(&y, &x, 2, BGTestType::Chisq)?;
    println!("Breusch-Godfrey (order 2): statistic={:.4}, p={:.4}", bg.statistic, bg.p_value);

    // Normality tests
    let jb = jarque_bera_test(&y, &x)?;
    println!("Jarque-Bera: JB={:.4}, p={:.4}", jb.statistic, jb.p_value);

    let sw = shapiro_wilk_test(&y, &x)?;
    println!("Shapiro-Wilk: W={:.4}, p={:.4}", sw.statistic, sw.p_value);

    let ad = anderson_darling_test(&y, &x)?;
    println!("Anderson-Darling: A={:.4}, p={:.4}", ad.statistic, ad.p_value);

    // Linearity tests
    let rainbow = rainbow_test(&y, &x, 0.5, RainbowMethod::R)?;
    println!("Rainbow: F={:.4}, p={:.4}",
        rainbow.r_result.as_ref().unwrap().statistic,
        rainbow.r_result.as_ref().unwrap().p_value);

    let hc = harvey_collier_test(&y, &x)?;
    println!("Harvey-Collier: t={:.4}, p={:.4}", hc.statistic, hc.p_value);

    let reset = reset_test(&y, &x, &[2, 3], ResetType::Fitted)?;
    println!("RESET: F={:.4}, p={:.4}", reset.f_statistic, reset.p_value);

    // Influence diagnostics
    let cd = cooks_distance_test(&y, &x)?;
    println!("Cook's Distance: {} influential points", cd.influential_4_over_n.len());

    let dfbetas = dfbetas_test(&y, &x)?;
    println!("DFBETAS: {} influential observations", dfbetas.influential_observations.len());

    let dffits = dffits_test(&y, &x)?;
    println!("DFFITS: {} influential observations", dffits.influential_observations.len());

    // Multicollinearity
    let vif = vif_test(&y, &x)?;
    println!("VIF: {:?}", vif.vif_values);

    Ok(())
}

WLS Regression (Rust)

use linreg_core::weighted_regression::wls_regression;

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.0, 4.0, 6.0, 8.0, 10.0];
    let x1 = vec![1.0, 2.0, 3.0, 4.0, 5.0];

    // Equal weights = OLS
    let weights = vec![1.0, 1.0, 1.0, 1.0, 1.0];

    let fit = wls_regression(&y, &[x1], &weights)?;

    println!("Intercept: {} (SE: {}, t: {}, p: {})",
        fit.coefficients[0],
        fit.standard_errors[0],
        fit.t_statistics[0],
        fit.p_values[0]
    );
    println!("F-statistic: {} (p: {})", fit.f_statistic, fit.f_p_value);
    println!("R-squared: {:.4}", fit.r_squared);

    // Access confidence intervals
    for (i, (&coef, &lower, &upper)) in fit.coefficients.iter()
        .zip(fit.conf_int_lower.iter())
        .zip(fit.conf_int_upper.iter())
        .enumerate()
    {
        println!("Coefficient {}: [{}, {}]", i, lower, upper);
    }

    Ok(())
}

LOESS Regression (Rust)

use linreg_core::loess::{loess_fit, LoessOptions};

fn main() -> Result<(), linreg_core::Error> {
    // Single predictor only
    let x = vec![0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
    let y = vec![1.0, 3.5, 4.8, 6.2, 8.5, 11.0, 13.2, 14.8, 17.5, 19.0, 22.0];

    // Default options: span=0.75, degree=2, robust iterations=0
    let options = LoessOptions::default();

    let result = loess_fit(&y, &[x], &options)?;

    println!("Fitted values: {:?}", result.fitted_values);
    println!("Residuals: {:?}", result.residuals);

    Ok(())
}

Custom LOESS options:

use linreg_core::loess::{loess_fit, LoessOptions, LoessSurface};

let options = LoessOptions {
    span: 0.5,              // Smoothing parameter (0-1, smaller = less smooth)
    degree: 1,              // Polynomial degree (0=constant, 1=linear, 2=quadratic)
    surface: LoessSurface::Direct,  // Note: only "direct" is currently supported; "interpolate" is planned
    robust_iterations: 3,   // Number of robust fitting iterations (0 = disabled)
};

let result = loess_fit(&y, &[x], &options)?;

K-Fold Cross Validation (Rust)

Cross-validation is used for model evaluation and hyperparameter tuning. The library supports K-Fold CV for all regression types:

use linreg_core::cross_validation::{kfold_cv_ols, kfold_cv_ridge, kfold_cv_lasso, kfold_cv_elastic_net, KFoldOptions};

fn main() -> Result<(), linreg_core::Error> {
    let y = vec![2.5, 3.7, 4.2, 5.1, 6.3, 7.0, 7.5, 8.1];
    let x1 = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0];
    let x2 = vec![2.0, 4.0, 5.0, 4.0, 3.0, 4.5, 5.5, 6.0];
    let names = vec!["Intercept".to_string(), "X1".to_string(), "X2".to_string()];

    // Configure CV options
    let options = KFoldOptions {
        n_folds: 5,
        shuffle: true,
        seed: Some(42),  // For reproducibility
    };

    // OLS cross-validation
    let ols_cv = kfold_cv_ols(&y, &[x1.clone(), x2.clone()], &names, &options)?;
    println!("OLS CV RMSE: {:.4} (±{:.4})", ols_cv.mean_rmse, ols_cv.std_rmse);
    println!("OLS CV R²: {:.4} (±{:.4})", ols_cv.mean_r_squared, ols_cv.std_r_squared);

    // Ridge cross-validation (for lambda selection)
    let lambda = 1.0;
    let ridge_cv = kfold_cv_ridge(&[x1.clone(), x2.clone()], &y, lambda, true, &options)?;
    println!("Ridge CV RMSE: {:.4}", ridge_cv.mean_rmse);

    // Lasso cross-validation
    let lasso_cv = kfold_cv_lasso(&[x1.clone(), x2.clone()], &y, 0.1, true, &options)?;
    println!("Lasso CV RMSE: {:.4}", lasso_cv.mean_rmse);

    // Elastic Net cross-validation
    let enet_cv = kfold_cv_elastic_net(&[x1, x2], &y, 0.1, 0.5, true, &options)?;
    println!("Elastic Net CV RMSE: {:.4}", enet_cv.mean_rmse);

    // Access per-fold results
    for fold in &ols_cv.fold_results {
        println!("Fold {}: train={}, test={}, R²={:.4}",
            fold.fold_index, fold.train_size, fold.test_size, fold.r_squared);
    }

    Ok(())
}

CV Result fields:

• mean_rmse, std_rmse - Mean and std of RMSE across folds
• mean_mae, std_mae - Mean and std of MAE across folds
• mean_r_squared, std_r_squared - Mean and std of R² across folds
• mean_train_r_squared - Mean training R² (for overfitting detection)
• fold_results - Per-fold metrics (train/test sizes, MSE, RMSE, MAE, R²)
• fold_coefficients - Coefficients from each fold (for stability analysis)

Lambda Path Generation (Rust)

use linreg_core::regularized::{make_lambda_path, LambdaPathOptions};
use linreg_core::linalg::Matrix;

let x = Matrix::new(100, 5, vec![0.0; 500]);
let y = vec![0.0; 100];

let options = LambdaPathOptions {
    nlambda: 100,
    lambda_min_ratio: Some(0.01),
    alpha: 1.0,  // Lasso
    ..Default::default()
};

let lambdas = make_lambda_path(&x, &y, &options, None, Some(0));

for &lambda in lambdas.iter() {
    // Fit model with this lambda
}

Model Save/Load (Rust)

All trained models can be saved to disk and loaded back later:

use linreg_core::{ModelSave, ModelLoad};

// Train a model
let result = ols_regression(&y, &[x1], &names)?;

// Save to file
result.save("my_model.json")?;

// Or with a custom name
result.save_with_name("my_model.json", Some("My Housing Model".to_string()))?;

// Load back
let loaded = linreg_core::core::RegressionOutput::load("my_model.json")?;

The same save() and load() methods work for all model types: RegressionOutput, RidgeFit, LassoFit, ElasticNetFit, WlsFit, and LoessFit.

---

WebAssembly Usage

Live Demo →

Build with wasm-pack:

wasm-pack build --release --target web

OLS Regression (WASM)

import init, { ols_regression } from './pkg/linreg_core.js';

async function run() {
    await init();

    const y = [1, 2, 3, 4, 5];
    const x = [[1, 2, 3, 4, 5]];
    const names = ["Intercept", "X1"];

    const resultJson = ols_regression(
        JSON.stringify(y),
        JSON.stringify(x),
        JSON.stringify(names)
    );

    const result = JSON.parse(resultJson);
    console.log("Coefficients:", result.coefficients);
    console.log("R-squared:", result.r_squared);
    console.log("Log-likelihood:", result.log_likelihood);
    console.log("AIC:", result.aic);
    console.log("BIC:", result.bic);
}

run();

Ridge Regression (WASM)

const result = JSON.parse(ridge_regression(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify(["Intercept", "X1", "X2"]),
    1.0,      // lambda
    true      // standardize
));

console.log("Coefficients:", result.coefficients);
console.log("R-squared:", result.r_squared);
console.log("Effective degrees of freedom:", result.effective_df);
console.log("AIC:", result.aic);
console.log("BIC:", result.bic);

Lasso Regression (WASM)

const result = JSON.parse(lasso_regression(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify(["Intercept", "X1", "X2"]),
    0.1,      // lambda
    true,     // standardize
    100000,   // max_iter
    1e-7      // tol
));

console.log("Coefficients:", result.coefficients);
console.log("Non-zero coefficients:", result.n_nonzero);
console.log("AIC:", result.aic);
console.log("BIC:", result.bic);

Elastic Net Regression (WASM)

const result = JSON.parse(elastic_net_regression(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify(["Intercept", "X1", "X2"]),
    0.1,      // lambda
    0.5,      // alpha (0 = Ridge, 1 = Lasso, 0.5 = balanced)
    true,     // standardize
    100000,   // max_iter
    1e-7      // tol
));

console.log("Coefficients:", result.coefficients);
console.log("Non-zero coefficients:", result.n_nonzero);
console.log("AIC:", result.aic);
console.log("BIC:", result.bic);

Lambda Path Generation (WASM)

const path = JSON.parse(make_lambda_path(
    JSON.stringify(y),
    JSON.stringify(x),
    100,              // n_lambda
    0.01              // lambda_min_ratio (as fraction of lambda_max)
));

console.log("Lambda sequence:", path.lambda_path);
console.log("Lambda max:", path.lambda_max);

WLS Regression (WASM)

const result = JSON.parse(wls_regression(
    JSON.stringify([2, 4, 6, 8, 10]),
    JSON.stringify([[1, 2, 3, 4, 5]]),
    JSON.stringify([1, 1, 1, 1, 1])  // weights (equal weights = OLS)
));

console.log("Coefficients:", result.coefficients);
console.log("Standard errors:", result.standard_errors);
console.log("P-values:", result.p_values);
console.log("R-squared:", result.r_squared);
console.log("F-statistic:", result.f_statistic);
console.log("Confidence intervals (lower):", result.conf_int_lower);
console.log("Confidence intervals (upper):", result.conf_int_upper);

LOESS Regression (WASM)

const result = JSON.parse(loess_fit(
    JSON.stringify(y),
    JSON.stringify(x[0]),    // Single predictor only (flattened array)
    0.5,      // span (smoothing parameter: 0-1)
    1,        // degree (0=constant, 1=linear, 2=quadratic)
    "direct", // surface method ("direct" only; "interpolate" is planned)
    0         // robust iterations (0=disabled, >0=number of iterations)
));

console.log("Fitted values:", result.fitted_values);
console.log("Residuals:", result.residuals);

K-Fold Cross Validation (WASM)

// OLS cross-validation
const ols_cv = JSON.parse(kfold_cv_ols(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify(["Intercept", "X1", "X2"]),
    5,         // n_folds
    "true",    // shuffle (JSON boolean)
    "42"       // seed (JSON string number, or "null" for no seed)
));

console.log("OLS CV RMSE:", ols_cv.mean_rmse, "±", ols_cv.std_rmse);
console.log("OLS CV R²:", ols_cv.mean_r_squared, "±", ols_cv.std_r_squared);

// Ridge cross-validation
const ridge_cv = JSON.parse(kfold_cv_ridge(
    JSON.stringify(y),
    JSON.stringify(x),
    1.0,       // lambda
    true,      // standardize
    5,         // n_folds
    "true",    // shuffle
    "42"       // seed
));

// Lasso cross-validation
const lasso_cv = JSON.parse(kfold_cv_lasso(
    JSON.stringify(y),
    JSON.stringify(x),
    0.1,       // lambda
    true,      // standardize
    5,         // n_folds
    "true",    // shuffle
    "42"       // seed
));

// Elastic Net cross-validation
const enet_cv = JSON.parse(kfold_cv_elastic_net(
    JSON.stringify(y),
    JSON.stringify(x),
    0.1,       // lambda
    0.5,       // alpha (0 = Ridge, 1 = Lasso)
    true,      // standardize
    5,         // n_folds
    "true",    // shuffle
    "42"       // seed
));

// Access per-fold results
ols_cv.fold_results.forEach(fold => {
    console.log(`Fold ${fold.fold_index}: R²=${fold.r_squared.toFixed(4)}`);
});

Note: In WASM, boolean and seed parameters are passed as JSON strings. Use "true"/"false" for shuffle and "42" or "null" for seed.

Diagnostic Tests (WASM)

// Rainbow test
const rainbow = JSON.parse(rainbow_test(
    JSON.stringify(y),
    JSON.stringify(x),
    0.5,      // fraction
    "r"       // method: "r", "python", or "both"
));

// Harvey-Collier test
const hc = JSON.parse(harvey_collier_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Breusch-Pagan test
const bp = JSON.parse(breusch_pagan_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// White test (method selection: "r", "python", or "both")
const white = JSON.parse(white_test(
    JSON.stringify(y),
    JSON.stringify(x),
    "r"
));

// White test - R-specific method
const whiteR = JSON.parse(r_white_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// White test - Python-specific method
const whitePy = JSON.parse(python_white_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Jarque-Bera test
const jb = JSON.parse(jarque_bera_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Durbin-Watson test
const dw = JSON.parse(durbin_watson_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Shapiro-Wilk test
const sw = JSON.parse(shapiro_wilk_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Anderson-Darling test
const ad = JSON.parse(anderson_darling_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// Cook's Distance
const cd = JSON.parse(cooks_distance_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// DFBETAS (influence on coefficients)
const dfbetas = JSON.parse(dfbetas_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// DFFITS (influence on fitted values)
const dffits = JSON.parse(dffits_test(
    JSON.stringify(y),
    JSON.stringify(x)
));

// VIF test (multicollinearity)
const vif = JSON.parse(vif_test(
    JSON.stringify(y),
    JSON.stringify(x)
));
console.log("VIF values:", vif.vif_values);

// RESET test (functional form)
const reset = JSON.parse(reset_test(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify([2, 3]),  // powers
    "fitted"                  // type: "fitted", "regressor", or "princomp"
));

// Breusch-Godfrey test (higher-order autocorrelation)
const bg = JSON.parse(breusch_godfrey_test(
    JSON.stringify(y),
    JSON.stringify(x),
    1,        // order
    "chisq"   // test_type: "chisq" or "f"
));

Statistical Utilities (WASM)

// Student's t CDF: P(T <= t)
const tCDF = get_t_cdf(1.96, 20);

// Critical t-value for two-tailed test
const tCrit = get_t_critical(0.05, 20);

// Normal inverse CDF (probit)
const zScore = get_normal_inverse(0.975);

// Descriptive statistics (all return JSON strings)
const mean = JSON.parse(stats_mean(JSON.stringify([1, 2, 3, 4, 5])));
const variance = JSON.parse(stats_variance(JSON.stringify([1, 2, 3, 4, 5])));
const stddev = JSON.parse(stats_stddev(JSON.stringify([1, 2, 3, 4, 5])));
const median = JSON.parse(stats_median(JSON.stringify([1, 2, 3, 4, 5])));
const quantile = JSON.parse(stats_quantile(JSON.stringify([1, 2, 3, 4, 5]), 0.5));
const correlation = JSON.parse(stats_correlation(
    JSON.stringify([1, 2, 3, 4, 5]),
    JSON.stringify([2, 4, 6, 8, 10])
));

CSV Parsing (WASM)

const csv = parse_csv(csvContent);
const parsed = JSON.parse(csv);
console.log("Headers:", parsed.headers);
console.log("Numeric columns:", parsed.numeric_columns);

Helper Functions (WASM)

const version = get_version();  // e.g., "0.5.0"
const msg = test();             // "Rust WASM is working!"

Model Serialization (WASM)

// Train a model
const resultJson = ols_regression(
    JSON.stringify(y),
    JSON.stringify(x),
    JSON.stringify(names)
);
const result = JSON.parse(resultJson);

// Serialize with metadata
const serialized = serialize_model(
    resultJson,        // model JSON
    "OLS",             // model type: "OLS", "Ridge", "Lasso", "ElasticNet", "WLS", "LOESS"
    "My Model"         // optional name (null to omit)
);

// Get metadata without loading full model
const metadataJson = get_model_metadata(serialized);
const metadata = JSON.parse(metadataJson);
console.log("Model type:", metadata.model_type);
console.log("Created:", metadata.created_at);

// Deserialize to get model data back
const modelJson = deserialize_model(serialized);
const model = JSON.parse(modelJson);

// Download in browser
const blob = new Blob([serialized], { type: 'application/json' });
const url = URL.createObjectURL(blob);
const a = document.createElement('a');
a.href = url;
a.download = 'model.json';
a.click();

Domain Security (WASM)

Optional domain restriction via build-time environment variable:

LINREG_DOMAIN_RESTRICT=example.com,mysite.com wasm-pack build --release --target web

When NOT set (default), all domains are allowed.

---

Python Usage

Install from PyPI:

pip install linreg-core

Quick Start (Python)

The recommended way to use linreg-core in Python is with native types (lists or numpy arrays):

import linreg_core

# Works with Python lists
y = [1, 2, 3, 4, 5]
x = [[1, 2, 3, 4, 5]]
names = ["Intercept", "X1"]

result = linreg_core.ols_regression(y, x, names)

# Access attributes directly
print(f"R²: {result.r_squared}")
print(f"Coefficients: {result.coefficients}")
print(f"F-statistic: {result.f_statistic}")

# Get a formatted summary
print(result.summary())

With NumPy arrays:

import numpy as np
import linreg_core

y = np.array([1, 2, 3, 4, 5])
x = np.array([[1, 2, 3, 4, 5]])

result = linreg_core.ols_regression(y, x, ["Intercept", "X1"])
print(result.summary())

Result objects provide:

• Direct attribute access (result.r_squared, result.coefficients, result.aic, result.bic, result.log_likelihood)
• summary() method for formatted output
• to_dict() method for JSON serialization

OLS Regression (Python)

import linreg_core

y = [1, 2, 3, 4, 5]
x = [[1, 2, 3, 4, 5]]
names = ["Intercept", "X1"]

result = linreg_core.ols_regression(y, x, names)
print(f"Coefficients: {result.coefficients}")
print(f"R-squared: {result.r_squared}")
print(f"F-statistic: {result.f_statistic}")
print(f"Log-likelihood: {result.log_likelihood}")
print(f"AIC: {result.aic}")
print(f"BIC: {result.bic}")

Ridge Regression (Python)

result = linreg_core.ridge_regression(
    y, x, ["Intercept", "X1"],
    1.0,      # lambda
    True      # standardize
)
print(f"Intercept: {result.intercept}")
print(f"Coefficients: {result.coefficients}")
print(f"Effective degrees of freedom: {result.effective_df:.2f}")
print(f"AIC: {result.aic}")
print(f"BIC: {result.bic}")

Lasso Regression (Python)

result = linreg_core.lasso_regression(
    y, x, ["Intercept", "X1"],
    0.1,      # lambda
    True,     # standardize
    100000,   # max_iter
    1e-7      # tol
)
print(f"Intercept: {result.intercept}")
print(f"Coefficients: {result.coefficients}")
print(f"Non-zero: {result.n_nonzero}")
print(f"Converged: {result.converged}")
print(f"AIC: {result.aic}")
print(f"BIC: {result.bic}")

Elastic Net Regression (Python)

result = linreg_core.elastic_net_regression(
    y, x, ["Intercept", "X1"],
    0.1,      # lambda
    0.5,      # alpha (0 = Ridge, 1 = Lasso, 0.5 = balanced)
    True,     # standardize
    100000,   # max_iter
    1e-7      # tol
)
print(f"Intercept: {result.intercept}")
print(f"Coefficients: {result.coefficients}")
print(f"Non-zero: {result.n_nonzero}")
print(f"AIC: {result.aic}")
print(f"BIC: {result.bic}")

LOESS Regression (Python)

result = linreg_core.loess_fit(
    y,           # Single predictor only
    [0.5],       # span (smoothing parameter: 0-1)
    2,           # degree (0=constant, 1=linear, 2=quadratic)
    "direct",    # surface ("direct" only; "interpolate" is planned)
    0            # robust iterations (0=disabled, >0=number of iterations)
)
print(f"Fitted values: {result.fitted_values}")
print(f"Residuals: {result.residuals}")

Lambda Path Generation (Python)

path = linreg_core.make_lambda_path(
    y, x,
    100,              # n_lambda
    0.01              # lambda_min_ratio
)
print(f"Lambda max: {path.lambda_max}")
print(f"Lambda min: {path.lambda_min}")
print(f"Number: {path.n_lambda}")

Diagnostic Tests (Python)

# Breusch-Pagan test (heteroscedasticity)
bp = linreg_core.breusch_pagan_test(y, x)
print(f"Statistic: {bp.statistic}, p-value: {bp.p_value}")

# Harvey-Collier test (linearity)
hc = linreg_core.harvey_collier_test(y, x)

# Rainbow test (linearity) - supports "r", "python", or "both" methods
rainbow = linreg_core.rainbow_test(y, x, 0.5, "r")

# White test - choose method: "r", "python", or "both"
white = linreg_core.white_test(y, x, "r")
# Or use specific method functions
white_r = linreg_core.r_white_test(y, x)
white_py = linreg_core.python_white_test(y, x)

# Jarque-Bera test (normality)
jb = linreg_core.jarque_bera_test(y, x)

# Durbin-Watson test (autocorrelation)
dw = linreg_core.durbin_watson_test(y, x)
print(f"DW statistic: {dw.statistic}")

# Shapiro-Wilk test (normality)
sw = linreg_core.shapiro_wilk_test(y, x)

# Anderson-Darling test (normality)
ad = linreg_core.anderson_darling_test(y, x)

# Cook's Distance (influential observations)
cd = linreg_core.cooks_distance_test(y, x)
print(f"Influential points: {cd.influential_4_over_n}")

# DFBETAS (influence on each coefficient)
dfbetas = linreg_core.dfbetas_test(y, x)
print(f"Threshold: {dfbetas.threshold}")
print(f"Influential obs: {dfbetas.influential_observations}")

# DFFITS (influence on fitted values)
dffits = linreg_core.dffits_test(y, x)
print(f"Threshold: {dffits.threshold}")
print(f"Influential obs: {dffits.influential_observations}")

# RESET test (model specification)
reset = linreg_core.reset_test(y, x, [2, 3], "fitted")

# Breusch-Godfrey test (higher-order autocorrelation)
bg = linreg_core.breusch_godfrey_test(y, x, 1, "chisq")

Statistical Utilities (Python)

# Student's t CDF
t_cdf = linreg_core.get_t_cdf(1.96, 20)

# Critical t-value (two-tailed)
t_crit = linreg_core.get_t_critical(0.05, 20)

# Normal inverse CDF (probit)
z_score = linreg_core.get_normal_inverse(0.975)

# Library version
version = linreg_core.get_version()

Descriptive Statistics (Python)

import numpy as np

# All return float directly (no parsing needed)
mean = linreg_core.stats_mean([1, 2, 3, 4, 5])
variance = linreg_core.stats_variance([1, 2, 3, 4, 5])
stddev = linreg_core.stats_stddev([1, 2, 3, 4, 5])
median = linreg_core.stats_median([1, 2, 3, 4, 5])
quantile = linreg_core.stats_quantile([1, 2, 3, 4, 5], 0.5)
correlation = linreg_core.stats_correlation([1, 2, 3, 4, 5], [2, 4, 6, 8, 10])

# Works with numpy arrays too
mean = linreg_core.stats_mean(np.array([1, 2, 3, 4, 5]))

CSV Parsing (Python)

csv_content = '''name,value,category
Alice,42.5,A
Bob,17.3,B
Charlie,99.9,A'''

result = linreg_core.parse_csv(csv_content)
print(f"Headers: {result.headers}")
print(f"Numeric columns: {result.numeric_columns}")
print(f"Data rows: {result.n_rows}")

Model Save/Load (Python)

# Train a model
result = linreg_core.ols_regression(y, x, names)

# Save to file
linreg_core.save_model(result, "my_model.json", name="My Housing Model")

# Load back
loaded = linreg_core.load_model("my_model.json")
print(f"R²: {loaded.r_squared}")
print(f"Coefficients: {loaded.coefficients}")

The save_model() and load_model() functions work with all result types: OLSResult, RidgeResult, LassoResult, ElasticNetResult, LoessResult, and WlsResult.

---

VBA / Excel Usage

The library ships as a native Windows DLL, letting you call it directly from Excel VBA via Declare statements. Prebuilt binaries are included in the VBA_Example/ directory:

File	Architecture
linreg_core_x64.dll	64-bit Excel (Office 2010+)
linreg_core_x86.dll	32-bit Excel (legacy)

Installation

1. Copy linreg_core_x64.dll (and/or linreg_core_x86.dll) to the same folder as your .xlsm workbook.
2. Import LinregCore.bas into your VBA project (ALT+F11 → File → Import File).
3. Optionally import ExampleMacros.bas for ready-to-run demo macros. Once both files are imported, run SetupWorkbook() from the Immediate Window or a button to automatically create example sheets and load sample data.

Building from Source

# 64-bit (modern Excel)
cargo build --release --target x86_64-pc-windows-msvc --features ffi

# 32-bit (legacy Excel)
cargo build --release --target i686-pc-windows-msvc --features ffi

The 32-bit build automatically uses linreg_core.def to strip stdcall decoration, so VBA Declare statements work without modification.

High-Level Wrappers

LinregCore.bas exposes friendly wrapper functions that return 2D Excel arrays you can drop straight into cells with Application.Transpose:

' OLS regression - returns (k+6)×5 summary array
Dim result As Variant
result = LinReg_OLS(y, X)

' Regularized regression
result = LinReg_Ridge(y, X, lambda:=1.0, standardize:=True)
result = LinReg_Lasso(y, X, lambda:=0.1)
result = LinReg_ElasticNet(y, X, lambda:=0.1, alpha:=0.5)

' Weighted OLS
result = LinReg_WLS(y, X, weights)

' Prediction intervals (n_new × 4: predicted, lower, upper, SE)
result = LinReg_PredictionIntervals(y, X, newX, alpha:=0.05)

' Diagnostic tests - each returns 1×3: {statistic, p-value, df}
result = LinReg_BreuschPagan(y, X)
result = LinReg_White(y, X)
result = LinReg_JarqueBera(y, X)
result = LinReg_ShapiroWilk(y, X)
result = LinReg_AndersonDarling(y, X)
result = LinReg_HarveyCollier(y, X)
result = LinReg_Rainbow(y, X, fraction:=0.5)
result = LinReg_Reset(y, X)
result = LinReg_DurbinWatson(y, X)   ' {DW statistic, ρ, ""}
result = LinReg_BreuschGodfrey(y, X, lagOrder:=1)

' Influence diagnostics
result = LinReg_VIF(y, X)            ' p×1
result = LinReg_CooksDistance(y, X)  ' n×1
result = LinReg_DFFITS(y, X)         ' n×1
result = LinReg_DFBETAS(y, X)        ' (n+1)×(p+1) with header row/col

' Regularization path and cross-validation
result = LinReg_LambdaPath(y, X, nLambda:=100, lmr:=0.01, alpha:=1.0)
result = LinReg_KFoldOLS(y, X, nFolds:=5)        ' 1×6 CV metrics
result = LinReg_KFoldRidge(y, X, lambda:=1.0)
result = LinReg_KFoldLasso(y, X, lambda:=0.1)
result = LinReg_KFoldElasticNet(y, X, lambda:=0.1, alpha:=0.5)

All wrappers return a 1-element array containing an error string on failure:

If IsArray(result) And UBound(result, 1) = 0 Then
    MsgBox "Error: " & result(0)
    Exit Sub
End If

Low-Level Handle API

The DLL uses an opaque handle pattern. All LR_* functions return a usize handle (0 = error); call LR_Free when done:

' --- declarations already in LinregCore.bas ---
' Private Declare PtrSafe Function LR_OLS Lib "linreg_core_x64.dll" ...
' Private Declare PtrSafe Sub LR_Free Lib "linreg_core_x64.dll" ...

Sub LowLevelExample()
    Dim n As Long, p As Long
    n = 5 : p = 1

    Dim y(4) As Double
    y(0) = 2.5 : y(1) = 3.7 : y(2) = 4.2 : y(3) = 5.1 : y(4) = 6.3

    ' X is row-major, no intercept column (added automatically)
    Dim X(4) As Double
    X(0) = 1 : X(1) = 2 : X(2) = 3 : X(3) = 4 : X(4) = 5

    Dim h As LongPtr
    h = LR_OLS(VarPtr(y(0)), n, VarPtr(X(0)), n, p)

    If h = 0 Then
        MsgBox "Regression failed"
        Exit Sub
    End If

    Dim r2 As Double, mse As Double
    r2  = LR_GetRSquared(h)
    mse = LR_GetMSE(h)

    ' Retrieve coefficient vector (intercept + slopes = p+1 values)
    Dim coefs(1) As Double
    LR_GetCoefficients h, VarPtr(coefs(0)), p + 1

    Debug.Print "R²=" & r2 & "  MSE=" & mse
    Debug.Print "Intercept=" & coefs(0) & "  Slope=" & coefs(1)

    LR_Free h
End Sub

Key FFI Functions

Category	Functions
Lifecycle	LR_Init, LR_Free, LR_GetLastError, LR_Version
Regression	LR_OLS, LR_Ridge, LR_Lasso, LR_ElasticNet, LR_WLS
Predictions	LR_PredictionIntervals
Diagnostics	LR_BreuschPagan, LR_White, LR_JarqueBera, LR_ShapiroWilk, LR_AndersonDarling, LR_HarveyCollier, LR_Rainbow, LR_Reset, LR_DurbinWatson, LR_BreuschGodfrey
Influence	LR_CooksDistance, LR_DFFITS, LR_DFBETAS, LR_VIF
Path / CV	LR_LambdaPath, LR_KFoldOLS, LR_KFoldRidge, LR_KFoldLasso, LR_KFoldElasticNet
Scalar getters	LR_GetRSquared, LR_GetAdjRSquared, LR_GetFStatistic, LR_GetFPValue, LR_GetMSE, LR_GetIntercept, LR_GetDF, LR_GetNNonzero, LR_GetStatistic, LR_GetPValue, LR_GetTestDF, LR_GetAutocorrelation
Vector getters	LR_GetCoefficients, LR_GetStdErrors, LR_GetTStats, LR_GetPValues, LR_GetResiduals, LR_GetFittedValues, LR_GetVector, LR_GetMatrix, LR_GetPredicted, LR_GetLowerBound, LR_GetUpperBound, LR_GetSEPred

Running FFI Tests

cargo test --features ffi --test ffi_tests
cargo test --features ffi --test ffi_vba_tests

---

Excel XLL Add-in

The library also compiles as a native Excel XLL add-in, exposing 27 worksheet UDFs directly in Excel. No VBA, no macros — just type =LINREG.OLS(A1:A20, B1:E20) in a cell.

The XLL is built entirely in pure Rust with zero external dependencies. No Excel SDK linkage required.

Installation

1. Build (or obtain) linreg_core_xll_x64.xll
2. In Excel: File > Options > Add-ins > Manage: Excel Add-ins > Go
3. Browse to the .xll file and check the box
4. Type =LINREG.VERSION() in any cell to verify

Building from Source

cargo build --release --features xll --no-default-features
cp target/release/linreg_core.dll XLL_Example/linreg_core_xll_x64.xll

Available UDFs

Formula	Description
=LINREG.VERSION()	Library version string
=LINREG.OLS(y, X)	OLS regression — coefficient table + fit stats
=LINREG.WLS(y, X, weights)	Weighted Least Squares
=LINREG.RIDGE(y, X, lambda, [standardize])	Ridge regression
=LINREG.LASSO(y, X, lambda, [standardize])	Lasso regression
=LINREG.ELASTICNET(y, X, lambda, alpha, [standardize])	Elastic Net
=LINREG.POLYNOMIAL(y, x, [degree], [center])	Polynomial regression
=LINREG.LAMBDAPATH(y, X, [n_lambda], [alpha])	Lambda path generation
=LINREG.KFOLDOLS(y, X, [n_folds])	K-Fold CV (OLS)
=LINREG.KFOLDRIDGE(y, X, lambda, [n_folds], [standardize])	K-Fold CV (Ridge)
=LINREG.KFOLDLASSO(y, X, lambda, [n_folds], [standardize])	K-Fold CV (Lasso)
=LINREG.KFOLDELASTICNET(y, X, lambda, alpha, [n_folds], [standardize])	K-Fold CV (Elastic Net)
=LINREG.PREDICTIONINTERVALS(y, X, newX, [alpha])	Prediction intervals
=LINREG.BREUSCHPAGAN(y, X)	Breusch-Pagan heteroscedasticity test
=LINREG.WHITE(y, X)	White heteroscedasticity test
=LINREG.JARQUEBERA(y, X)	Jarque-Bera normality test
=LINREG.SHAPIROWILK(y, X)	Shapiro-Wilk normality test
=LINREG.ANDERSONDARLING(y, X)	Anderson-Darling normality test
=LINREG.HARVEYCOLLIER(y, X)	Harvey-Collier linearity test
=LINREG.RAINBOW(y, X, [fraction])	Rainbow linearity test
=LINREG.RESET(y, X)	RESET specification test
=LINREG.DURBINWATSON(y, X)	Durbin-Watson autocorrelation test
=LINREG.BREUSCHGODFREY(y, X, [lag_order])	Breusch-Godfrey autocorrelation test
=LINREG.VIF(y, X)	Variance Inflation Factors
=LINREG.COOKSDISTANCE(y, X)	Cook's Distance
=LINREG.DFFITS(y, X)	DFFITS influence measure
=LINREG.DFBETAS(y, X)	DFBETAS influence measure

All UDFs return dynamic arrays that spill automatically in Excel 365. In older versions, use Ctrl+Shift+Enter (CSE). Each function includes per-argument help visible in the Function Wizard (fx button).

Running XLL Tests

cargo test --features xll --no-default-features --test xll_tests

---

Feature Flags

Feature	Default	Description
wasm	Yes	Enables WASM bindings and browser support
python	No	Enables Python bindings via PyO3
ffi	No	Enables Windows DLL bindings for VBA/Excel use
xll	No	Enables Excel XLL add-in (27 worksheet UDFs)
validation	No	Includes test data for validation tests

For native Rust without WASM overhead:

linreg-core = { version = "0.8", default-features = false }

For Python bindings (built with maturin):

pip install linreg-core

---

Validation

Results are validated against R (lmtest, car, skedastic, nortest, glmnet) and Python (statsmodels, scipy, sklearn). See the verification/ directory for test scripts and reference outputs.

Running Tests

# Unit tests
cargo test

# WASM tests
wasm-pack test --node

# FFI tests (VBA/C bindings)
cargo test --features ffi

# Python tests (requires maturin build)
pytest tests/python/

# All tests including doctests
cargo test --all-features

---

Implementation Notes

Regularization

The Ridge and Lasso implementations follow the glmnet formulation:

minimize (1/(2n)) * Σ(yᵢ - β₀ - xᵢᵀβ)² + λ * [(1 - α) * ||β||₂² / 2 + α * ||β||₁]

• Ridge (α = 0): Closed-form solution with (X'X + λI)⁻¹X'y
• Lasso (α = 1): Coordinate descent algorithm

Numerical Precision

• QR decomposition used throughout for numerical stability
• Anderson-Darling uses Abramowitz & Stegun 7.1.26 for normal CDF (differs from R's Cephes by ~1e-6)
• Shapiro-Wilk implements Royston's 1995 algorithm matching R's implementation

Known Limitations

• Harvey-Collier test may fail on high-VIF datasets (VIF > 5) due to numerical instability in recursive residuals
• Shapiro-Wilk limited to n <= 5000 (matching R's limitation)
• White test may differ from R on collinear datasets due to numerical precision in near-singular matrices

---

Disclaimer

This library is under active development and has not reached 1.0 stability. While outputs are validated against R and Python implementations, do not use this library for critical applications (medical, financial, safety-critical systems) without independent verification. See the LICENSE for full terms. The software is provided "as is" without warranty of any kind.

---

Benchmarks

Click to expand v0.6.0 benchmark results

Benchmark results run on Windows with cargo bench --no-default-features. Times are median values.

Core Regression Benchmarks

Benchmark	Size (n × p)	Time	Throughput
OLS Regression	10 × 2	12.46 µs	802.71 Kelem/s
OLS Regression	50 × 3	53.72 µs	930.69 Kelem/s
OLS Regression	100 × 5	211.09 µs	473.73 Kelem/s
OLS Regression	500 × 10	7.46 ms	67.04 Kelem/s
OLS Regression	1000 × 20	47.81 ms	20.91 Kelem/s
OLS Regression	5000 × 50	2.86 s	1.75 Kelem/s
Ridge Regression	50 × 3	9.61 µs	5.20 Melem/s
Ridge Regression	100 × 5	70.41 µs	1.42 Melem/s
Ridge Regression	500 × 10	842.37 µs	593.56 Kelem/s
Ridge Regression	1000 × 20	1.38 ms	724.71 Kelem/s
Ridge Regression	5000 × 50	10.25 ms	487.78 Kelem/s
Lasso Regression	50 × 3	258.82 µs	193.18 Kelem/s
Lasso Regression	100 × 5	247.89 µs	403.41 Kelem/s
Lasso Regression	500 × 10	3.58 ms	139.86 Kelem/s
Lasso Regression	1000 × 20	1.54 ms	651.28 Kelem/s
Lasso Regression	5000 × 50	12.52 ms	399.50 Kelem/s
Elastic Net Regression	50 × 3	46.15 µs	1.08 Melem/s
Elastic Net Regression	100 × 5	358.07 µs	279.27 Kelem/s
Elastic Net Regression	500 × 10	1.61 ms	310.18 Kelem/s
Elastic Net Regression	1000 × 20	1.60 ms	623.66 Kelem/s
Elastic Net Regression	5000 × 50	12.57 ms	397.77 Kelem/s
WLS Regression	50 × 3	32.92 µs	1.52 Melem/s
WLS Regression	100 × 5	155.30 µs	643.93 Kelem/s
WLS Regression	500 × 10	6.63 ms	75.37 Kelem/s
WLS Regression	1000 × 20	42.68 ms	23.43 Kelem/s
WLS Regression	5000 × 50	2.64 s	1.89 Kelem/s
LOESS Fit	50 × 1	132.83 µs	376.42 Kelem/s
LOESS Fit	100 × 1	1.16 ms	86.00 Kelem/s
LOESS Fit	500 × 1	28.42 ms	17.59 Kelem/s
LOESS Fit	1000 × 1	113.00 ms	8.85 Kelem/s
LOESS Fit	100 × 2	7.10 ms	14.09 Kelem/s
LOESS Fit	500 × 2	1.05 s	476.19 elem/s

Lambda Path & Elastic Net Path Benchmarks

Benchmark	Size (n × p)	Time	Throughput
Elastic Net Path	100 × 5	198.60 ms	503.52 elem/s
Elastic Net Path	500 × 10	69.46 ms	7.20 Kelem/s
Elastic Net Path	1000 × 20	39.08 ms	25.59 Kelem/s
Make Lambda Path	100 × 5	1.09 µs	91.58 Melem/s
Make Lambda Path	500 × 10	8.10 µs	61.70 Melem/s
Make Lambda Path	1000 × 20	29.96 µs	33.37 Melem/s
Make Lambda Path	5000 × 50	424.18 µs	11.79 Melem/s

Diagnostic Test Benchmarks

Benchmark	Size (n × p)	Time
Rainbow Test	50 × 3	40.34 µs
Rainbow Test	100 × 5	187.94 µs
Rainbow Test	500 × 10	8.63 ms
Rainbow Test	1000 × 20	60.09 ms
Rainbow Test	5000 × 50	3.45 s
Harvey-Collier Test	50 × 1	15.26 µs
Harvey-Collier Test	100 × 1	30.32 µs
Harvey-Collier Test	500 × 1	138.44 µs
Harvey-Collier Test	1000 × 1	298.33 µs
Breusch-Pagan Test	50 × 3	58.07 µs
Breusch-Pagan Test	100 × 5	296.74 µs
Breusch-Pagan Test	500 × 10	13.79 ms
Breusch-Pagan Test	1000 × 20	96.49 ms
Breusch-Pagan Test	5000 × 50	5.56 s
White Test	50 × 3	14.31 µs
White Test	100 × 5	44.25 µs
White Test	500 × 10	669.40 µs
White Test	1000 × 20	4.89 ms
Jarque-Bera Test	50 × 3	30.13 µs
Jarque-Bera Test	100 × 5	149.29 µs
Jarque-Bera Test	500 × 10	6.64 ms
Jarque-Bera Test	1000 × 20	47.89 ms
Jarque-Bera Test	5000 × 50	2.75 s
Durbin-Watson Test	50 × 3	31.80 µs
Durbin-Watson Test	100 × 5	152.56 µs
Durbin-Watson Test	500 × 10	6.87 ms
Durbin-Watson Test	1000 × 20	48.65 ms
Durbin-Watson Test	5000 × 50	2.76 s
Breusch-Godfrey Test	50 × 3	71.73 µs
Breusch-Godfrey Test	100 × 5	348.94 µs
Breusch-Godfrey Test	500 × 10	14.77 ms
Breusch-Godfrey Test	1000 × 20	100.08 ms
Breusch-Godfrey Test	5000 × 50	5.64 s
Shapiro-Wilk Test	10 × 2	2.04 µs
Shapiro-Wilk Test	50 × 3	4.87 µs
Shapiro-Wilk Test	100 × 5	10.67 µs
Shapiro-Wilk Test	500 × 10	110.02 µs
Shapiro-Wilk Test	1000 × 20	635.13 µs
Shapiro-Wilk Test	5000 × 50	17.53 ms
Anderson-Darling Test	50 × 3	34.02 µs
Anderson-Darling Test	100 × 5	162.28 µs
Anderson-Darling Test	500 × 10	6.95 ms
Anderson-Darling Test	1000 × 20	48.15 ms
Anderson-Darling Test	5000 × 50	2.78 s
Cook's Distance Test	50 × 3	64.52 µs
Cook's Distance Test	100 × 5	297.69 µs
Cook's Distance Test	500 × 10	12.73 ms
Cook's Distance Test	1000 × 20	94.02 ms
Cook's Distance Test	5000 × 50	5.31 s
DFBETAS Test	50 × 3	46.34 µs
DFBETAS Test	100 × 5	185.52 µs
DFBETAS Test	500 × 10	7.04 ms
DFBETAS Test	1000 × 20	49.68 ms
DFFITS Test	50 × 3	33.56 µs
DFFITS Test	100 × 5	157.62 µs
DFFITS Test	500 × 10	6.82 ms
DFFITS Test	1000 × 20	48.35 ms
VIF Test	50 × 3	5.36 µs
VIF Test	100 × 5	12.68 µs
VIF Test	500 × 10	128.04 µs
VIF Test	1000 × 20	807.30 µs
VIF Test	5000 × 50	26.33 ms
RESET Test	50 × 3	77.85 µs
RESET Test	100 × 5	359.12 µs
RESET Test	500 × 10	14.40 ms
RESET Test	1000 × 20	100.52 ms
RESET Test	5000 × 50	5.67 s
Full Diagnostics	100 × 5	2.75 ms
Full Diagnostics	500 × 10	104.01 ms
Full Diagnostics	1000 × 20	740.52 ms

Linear Algebra Benchmarks

Benchmark	Size	Time
Matrix Transpose	10 × 10	209.50 ns
Matrix Transpose	50 × 50	3.67 µs
Matrix Transpose	100 × 100	14.92 µs
Matrix Transpose	500 × 500	924.23 µs
Matrix Transpose	1000 × 1000	5.56 ms
Matrix Multiply (matmul)	10 × 10 × 10	1.54 µs
Matrix Multiply (matmul)	50 × 50 × 50	144.15 µs
Matrix Multiply (matmul)	100 × 100 × 100	1.39 ms
Matrix Multiply (matmul)	200 × 200 × 200	11.90 ms
Matrix Multiply (matmul)	1000 × 100 × 100	13.94 ms
QR Decomposition	10 × 5	1.41 µs
QR Decomposition	50 × 10	14.81 µs
QR Decomposition	100 × 20	57.61 µs
QR Decomposition	500 × 50	2.19 ms
QR Decomposition	1000 × 100	19.20 ms
QR Decomposition	5000 × 100	1.48 s
QR Decomposition	10000 × 100	8.09 s
QR Decomposition	1000 × 500	84.48 ms
SVD	10 × 5	150.36 µs
SVD	50 × 10	505.41 µs
SVD	100 × 20	2.80 ms
SVD	500 × 50	60.00 ms
SVD	1000 × 100	513.35 ms
Matrix Invert	5 × 5	877.32 ns
Matrix Invert	10 × 10	2.48 µs
Matrix Invert	20 × 20	5.46 µs
Matrix Invert	50 × 50	31.94 µs
Matrix Invert	100 × 100	141.38 µs
Matrix Invert	200 × 200	647.03 µs

Pressure Benchmarks (Large Datasets)

Benchmark	Size (n)	Time
Pressure (OLS + all diagnostics)	10000	11.28 s

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License

Dual-licensed under MIT or Apache-2.0.