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Ordinary least squares — Lodestar.Stats.Regression

Two ways to fit a linear model by ordinary least squares. OrdinaryLeastSquares.Fit fits a linear model and returns what a statsmodels summary table holds — the estimates, and how sure it is of each of them. OrdinaryLeastSquares.Estimate fits the same model and stops at the coefficients, their standard errors and the residual sum of squares, for a caller fitting many.

Spans in, one summary out. A design is row-major, featureCount values per row, with no constant column of your own: WithIntercept adds it. That is the shape Lodestar.Metrics and Lodestar.Preprocessing already use, so a matrix crosses between them without being reshaped.

Why this exists

The estimate is the cheap half. Read through a MetadataLoadContext rather than through a README, MathNet.Numerics 5.0.0 exports 5 333 members and every regression entry point among them returns coefficients: MultipleRegression.QR, .Svd, .NormalEquations, .DirectMethod, SimpleRegression.Fit, WeightedRegression.Weighted. GoodnessOfFit adds five whole-model scalars. A coefficient covariance matrix does exist in that assembly — Optimization.NonlinearMinimizationResult exports Covariance, Correlation and StandardErrors — but it belongs to the non-linear minimisers and is unreachable from LinearRegression. Past it there is no t statistic, no p-value, no interval on a coefficient, no adjusted R-squared, no overall F and no VIF anywhere in the assembly.

Accord.Statistics 3.8.0 did have the whole table, and its repository is archived: last release 2017-10-19, last push 2020-11-18, LGPL-2.1. So the gap is not an unexplored one. It is a maintained, permissively licensed, framework-free OLS table. decisions/0003 has the reading and what it decided.

Types

Type	What it is
OrdinaryLeastSquares	Fits the model and builds the table.
OlsSummary	The fitted model, its errors, its p-values and its diagnostics.
OlsEstimate	The coefficients, their standard errors and t statistics, and the residual sum of squares.
OlsOptions	Whether to fit an intercept, and at what confidence.
CovarianceType	How the covariance of the estimates is estimated.

See also

• Regression inference — reading the table.
• Weighted least squares — the same table, one weight per row.
• statsmodels → .NET — what is delegated and what is not.
• Python → C# equivalence.