linreg-core

A lightweight, self-contained linear regression library written in Rust. Compiles to WebAssembly for browser use, Python bindings via PyO3, 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.

Section	Description
Features	Regression methods, model statistics, diagnostic tests
Rust Usage	Native Rust crate usage
WebAssembly Usage	Browser/JavaScript usage
Python Usage	Python bindings via PyO3
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
LOESS: Locally estimated scatterplot smoothing for non-parametric curve fitting with configurable span, polynomial degree, and robust fitting
Lambda Path Generation: Create regularization paths for cross-validation

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

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 = "0.5", 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(())
}

Diagnostic Tests (Rust)

use linreg_core::diagnostics::{
    breusch_pagan_test, durbin_watson_test, jarque_bera_test,
    shapiro_wilk_test, RainbowMethod, rainbow_test
};

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

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

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

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

    // Linearity
    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);

    Ok(())
}

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
}

WebAssembly Usage

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);

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" or "interpolate")
    0         // robust iterations (0=disabled, >0=number of iterations)
));

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

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!"

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}")

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}")

Feature Flags

Feature	Default	Description
`wasm`	Yes	Enables WASM bindings and browser support
`python`	No	Enables Python bindings via PyO3
`validation`	No	Includes test data for validation tests

For native Rust without WASM overhead:

linreg-core = { version = "0.5", 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


# 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.

License

Dual-licensed under MIT or Apache-2.0.

linreg-core 0.5.0