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Fits a linear model with one weight per row and reports what a summary table holds.

public static OlsSummary Fit(ReadOnlySpan<double> design, ReadOnlySpan<double> response, ReadOnlySpan<double> weights, int featureCount, OlsOptions options = null)

public static OlsSummary Fit(ReadOnlySpan<double> design, ReadOnlySpan<double> response, ReadOnlySpan<double> weights, ReadOnlySpan<int> clusters, int featureCount, OlsOptions options)

The second overload is the cluster-robust weighted fit, whose options must ask for CovarianceType.Cluster.

Parameters — design is the regressors, row-major: featureCount values per row, with no constant column of your own. response is one observed value per row of design. weights is one non-negative, finite weight per row, proportional to the inverse of that row's variance. clusters is one label per row, any integers in any order, naming at least two clusters. featureCount is how many regressors each row carries. options chooses whether to fit an intercept, which covariance to estimate, and at what confidence; null fits an intercept at 0.95.

Returns — OlsSummary: the fitted model, with its standard errors, t statistics, p-values, confidence intervals and variance inflation factors.

Exceptions — ArgumentOutOfRangeException when featureCount is not positive, or when a weight is negative, NaN or infinite. ArgumentException when design is not a whole number of rows, when response, weights or clusters has a different length, when no residual degrees of freedom are left, when fewer rows carry a positive weight than the model has parameters, when a column of the weighted design is collinear with the columns before it, or when options and the overload disagree, as on OrdinaryLeastSquares.Fit.

Example — the robust covariances apply to a weighted fit as they do to an ordinary one.

using Lodestar.Stats.Regression;

double[] dose = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0];
double[] meanResponse = [2.3, 3.8, 6.4, 7.7, 11.6, 10.9];
double[] groupSize = [40.0, 35.0, 30.0, 12.0, 5.0, 3.0];

OlsSummary robust = WeightedLeastSquares.Fit(
    dose, meanResponse, groupSize, featureCount: 1,
    new OlsOptions { CovarianceType = CovarianceType.Hc1 });

double explained = Math.Round(robust.RSquared, 4);          // => 0.9694
double error = Math.Round(robust.StandardErrors[1], 4);     // => 0.1688
int freedom = robust.ResidualDegreesOfFreedom;              // => 4

Remarks — each row and its response is scaled by the square root of its weight and fitted as OrdinaryLeastSquares.Fit would, the robust covariances on the scaled rows included. Three numbers follow the reference rather than the scaled rows:

• RSquared is weighted — centred on the weighted mean of the response with an intercept, against zero without one — and AdjustedRSquared and the overall F test read it.
• A zero weight keeps its row. It adds nothing to the estimate and still counts in ResidualDegreesOfFreedom and in HC1's correction, as statsmodels counts it.
• VarianceInflationFactors are those of the design as given, which is what variance_inflation_factor returns for the same exog; the reference's WLS reports none.
• Hac and Cluster read the scores of the scaled rows — each scaled row times its scaled residual — which is what the reference sums.

Equal weights reproduce OrdinaryLeastSquares.Fit exactly, and a constant weight moves only ResidualStandardError. Weights the reference would crash on or answer through a pseudo-inverse are refused instead — the equivalence table lists each.

Applies to — net10.0, netstandard2.0.

See also — OlsSummary, OlsOptions, CovarianceType, the weighted least squares index.