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OlsOptions

What an ordinary least-squares fit should estimate, and at what confidence.

public sealed record OlsOptions

Properties — WithIntercept fits a constant term, as statsmodels.api.add_constant would; true by default. ConfidenceLevel is the level of the reported intervals; 0.95 by default, and it must lie strictly inside (0, 1). CovarianceType chooses how the covariance of the estimates is estimated; Nonrobust by default, and anything else also moves the coefficient tests from Student's t to the normal. HacLags is the lag count CovarianceType.Hac reads, statsmodels' maxlags: required with it, refused with any other type, zero or more, and accepted past the row count as the reference accepts it. SmallSampleCorrection switches the correction of Hac (n / (n - k), off when null) or Cluster (G / (G - 1) · (n - 1) / (n - k), on when null), statsmodels' use_correction; refused with any other type.

Exceptions — ArgumentOutOfRangeException when ConfidenceLevel does not lie strictly inside (0, 1), when HacLags is negative, or when CovarianceType is not a declared CovarianceType. Each is thrown where the setting is set, not where the fit reads it: an undeclared covariance type would otherwise be computed as Hc0 and echoed back as the undeclared value.

Example — a wider level widens both ends without moving the estimate.

using Lodestar.Stats.Regression;

double[] design = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0];
double[] response = [2.1, 3.9, 6.2, 7.8, 10.1, 12.2, 13.8, 16.1];

OlsSummary ninetyFive = OrdinaryLeastSquares.Fit(design, response, featureCount: 1);
OlsSummary ninetyNine = OrdinaryLeastSquares.Fit(
    design, response, featureCount: 1, new OlsOptions { ConfidenceLevel = 0.99 });

double narrow = ninetyFive.ConfidenceLower[1];  // => 1.929593811075316
double wide = ninetyNine.ConfidenceLower[1];    // => 1.894550901538726

Remarks — turning the intercept off does more than drop a coefficient. OlsSummary.RSquared becomes the uncentred one, measured against zero rather than against the response's mean, and the overall F test gains a degree of freedom. Both follow statsmodels. On the data above, the centred R-squared is 0.9988 and the uncentred one 0.9998: the second is larger not because the model is better but because it is being scored against a lower bar.

Applies to — net10.0, netstandard2.0.

See also — OrdinaryLeastSquares.Fit, OlsSummary, CovarianceType.