Struct OlsFit 

pub struct OlsFit { /* private fields */ }

A fitted ordinary-least-squares model: the shared representation every diagnostic in this crate is computed from.

Intercept convention

The caller owns the design matrix X, including any intercept column. This crate does not silently prepend a column of ones. There are two constructors, and the choice is explicit at the call site:

• OlsFit::new fits exactly the columns you pass. If one of them is constant it is auto-detected and treated as the intercept (this drives the centered-vs-uncentered R² choice, and excludes that column from VIF); if none is constant the model is fit through the origin.
• OlsFit::with_intercept prepends a ones column for you and marks it as the intercept.

Getting this wrong silently corrupts every downstream diagnostic, so the convention is stated here rather than buried in the implementation.

What is computed and cached

Construction performs a single QR factorization of X and caches the coefficients, fitted values, residuals, leverage vector diag(H), (XᵀX)⁻¹, the design’s singular values, and the residual variance. Diagnostics read these cached quantities rather than refactorizing.

Coefficients are obtained by a QR solve of X, never by inverting XᵀX — that matters for the multicollinearity diagnostics specifically, since forming XᵀX squares the condition number they exist to measure. Leverage is read from the thin Q factor, so the full n × n hat matrix is never formed.

Example

use ndarray::{array, Array2};
use regression_diagnostics::OlsFit;

// y = 1 + 2*x exactly; supply the intercept ourselves.
let x = array![[1.0, 0.0], [1.0, 1.0], [1.0, 2.0], [1.0, 3.0]];
let y = array![1.0, 3.0, 5.0, 7.0];
let fit = OlsFit::new(x, y).unwrap();
assert!((fit.coefficients()[0] - 1.0).abs() < 1e-9);
assert!((fit.coefficients()[1] - 2.0).abs() < 1e-9);

Implementations

impl OlsFit

pub fn new(x: Array2<f64>, y: Array1<f64>) -> Result<Self>

Fit y ~ X by OLS, using the columns of X exactly as given.

A constant column, if present, is auto-detected as the intercept. See the type-level docs for the full convention.

Errors

• RegressionError::EmptyInput if X or y is empty.
• RegressionError::ShapeMismatch if X.nrows() != y.len().
• RegressionError::NoResidualDegreesOfFreedom if n <= p.
• RegressionError::RankDeficient if the columns are collinear.

pub fn with_intercept(x: Array2<f64>, y: Array1<f64>) -> Result<Self>

Fit y ~ [1 | X] by OLS, prepending a column of ones as the intercept.

Errors are the same as OlsFit::new, evaluated against the augmented design (so a design with n == p_original + 1 will fail the residual-degrees-of-freedom check).

pub fn n_observations(&self) -> usize

Number of observations n.

pub fn n_parameters(&self) -> usize

Number of model parameters p (design-matrix columns, intercept included if present).

pub fn has_intercept(&self) -> bool

Whether the model includes an intercept (constant) column.

pub fn intercept_column(&self) -> Option<usize>

Index of the intercept column within the design matrix, if any.

pub fn design_matrix(&self) -> ArrayView2<'_, f64>

The design matrix X as fitted (with the intercept column if one was added or detected).

pub fn response(&self) -> ArrayView1<'_, f64>

The response vector y.

pub fn coefficients(&self) -> ArrayView1<'_, f64>

Estimated coefficients, one per design-matrix column.

pub fn fitted_values(&self) -> ArrayView1<'_, f64>

Fitted values ŷ = X β.

pub fn residuals(&self) -> ArrayView1<'_, f64>

Raw residuals e = y − ŷ.

pub fn leverage(&self) -> ArrayView1<'_, f64>

Leverage vector diag(H). Each entry lies in [0, 1] and the vector sums to p (the number of parameters) — a standard identity worth checking as a correctness probe.

pub fn residual_sum_of_squares(&self) -> f64

Residual sum of squares Σ eᵢ².

pub fn df_residual(&self) -> f64

Residual degrees of freedom n − p.

pub fn df_model(&self) -> f64

Model degrees of freedom: p − 1 with an intercept, p without.

pub fn residual_variance(&self) -> f64

Unbiased residual variance estimate s² = RSS / (n − p).

pub fn residual_standard_error(&self) -> f64

Residual standard error s = √(RSS / (n − p)).

pub fn coefficient_standard_errors(&self) -> Array1<f64>

Standard errors of the coefficients: sⱼ = s · √((XᵀX)⁻¹ⱼⱼ).

pub fn singular_values(&self) -> &[f64]

Singular values of the design matrix, in descending order.

impl OlsFit

pub fn summary(&self) -> Summary

Compute the full Summary for this fit — every statistic in Milestones 2–6 in one call.

use ndarray::array;
use regression_diagnostics::OlsFit;

let x = array![[1.0, 0.0], [1.0, 1.0], [1.0, 2.0], [1.0, 3.0], [1.0, 4.0]];
let y = array![1.0, 3.1, 4.9, 7.0, 9.1];
let fit = OlsFit::new(x, y).unwrap();
let s = fit.summary();
println!("{s}");
assert!(s.r_squared > 0.99);

Trait Implementations

impl Clone for OlsFit

fn clone(&self) -> OlsFit

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for OlsFit

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.