# linreg-core
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[](LICENSE-MIT)
[](https://crates.io/crates/linreg-core)
[](https://docs.rs/linreg-core)
[](https://pypi.org/project/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.
---
## Table of Contents
| [Features](#features) | Regression methods, model statistics, diagnostic tests |
| [Rust Usage](#rust-usage) | Native Rust crate usage |
| [WebAssembly Usage](#webassembly-usage) | Browser/JavaScript usage |
| [Python Usage](#python-usage) | Python bindings via PyO3 |
| [Feature Flags](#feature-flags) | Build configuration options |
| [Validation](#validation) | Testing and verification |
| [Implementation Notes](#implementation-notes) | Technical details |
---
## Features
### Regression Methods
- **OLS Regression:** Coefficients, standard errors, t-statistics, p-values, confidence intervals
- **Ridge Regression:** L2-regularized regression with optional standardization
- **Lasso Regression:** L1-regularized regression via coordinate descent
- **Elastic Net:** Combined L1 + L2 regularization for variable selection with multicollinearity handling
- **Lambda Path Generation:** Create regularization paths for cross-validation
### Model Statistics
- R-squared, Adjusted R-squared, F-statistic, F-test p-value
- Residuals, fitted values, leverage (hat matrix diagonal)
- Mean Squared Error (MSE)
- Variance Inflation Factor (VIF) for multicollinearity detection
### Diagnostic 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) |
| **Influence** | Cook's Distance |
---
## Rust Usage
Add to your `Cargo.toml`:
```toml
[dependencies]
linreg-core = { version = "0.4", default-features = false }
```
### OLS Regression (Rust)
```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);
Ok(())
}
```
### Ridge Regression (Rust)
```rust,no_run
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);
Ok(())
}
```
### Lasso Regression (Rust)
```rust,no_run
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);
Ok(())
}
```
### Elastic Net Regression (Rust)
```rust,no_run
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);
Ok(())
}
```
### Diagnostic Tests (Rust)
```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)
```rust,no_run
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:
```bash
wasm-pack build --release --target web
```
### OLS Regression (WASM)
```javascript
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);
}
run();
```
### Ridge Regression (WASM)
```javascript
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);
```
### Lasso Regression (WASM)
```javascript
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);
```
### Elastic Net Regression (WASM)
```javascript
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);
```
### Lambda Path Generation (WASM)
```javascript
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);
```
### Diagnostic Tests (WASM)
```javascript
// 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)
));
// 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)
```javascript
// 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)
```javascript
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)
```javascript
const version = get_version(); // e.g., "0.4.0"
const msg = test(); // "Rust WASM is working!"
```
### Domain Security (WASM)
Optional domain restriction via build-time environment variable:
```bash
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:
```bash
pip install linreg-core
```
### Quick Start (Python)
The recommended way to use `linreg-core` in Python is with native types (lists or numpy arrays):
```python
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:**
```python
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`)
- `summary()` method for formatted output
- `to_dict()` method for JSON serialization
### OLS Regression (Python)
```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}")
```
### Ridge Regression (Python)
```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}")
```
### Lasso Regression (Python)
```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}")
```
### Elastic Net Regression (Python)
```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}")
```
### Lambda Path Generation (Python)
```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)
```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}")
# 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)
```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)
```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)
```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
| `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:
```toml
linreg-core = { version = "0.4", default-features = false }
```
For Python bindings (built with maturin):
```bash
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
```bash
# 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](LICENSE-MIT) for full terms. The software is provided "as is" without warranty of any kind.
---
## License
Dual-licensed under [MIT](LICENSE-MIT) or [Apache-2.0](LICENSE-APACHE).