Home › Stats-Regression › Ordinary least squares

OlsSummary

What a fitted ordinary least-squares model reports: the estimates, and how sure it is of each of them.

public sealed class OlsSummary

Properties — the per-coefficient lists are parallel and in the design's own order, intercept first when one was fitted: Coefficients, StandardErrors, TStatistics, PValues, ConfidenceLower and ConfidenceUpper. VarianceInflationFactors carries one entry per regressor, so it is shorter by one whenever HasIntercept is true. The whole-model figures are RSquared, AdjustedRSquared, FStatistic, FPValue, ResidualDegreesOfFreedom and ResidualStandardError, and ConfidenceLevel says what the two interval lists were computed at. CovarianceType echoes the estimator that produced the standard errors, and is what tells a reader holding only this summary whether TStatistics and PValues are t against Student's or z against the normal.

Example — the whole-model half of the table.

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 summary = OrdinaryLeastSquares.Fit(design, response, featureCount: 1);

double explained = summary.RSquared;              // => 0.9988392866011389
double residualError = summary.ResidualStandardError;  // => 0.18016747059421467
int degreesOfFreedom = summary.ResidualDegreesOfFreedom;  // => 6
double overall = summary.FPValue;                 // => 4.88893361255519E-10

Remarks — there is no public constructor. A summary is what OrdinaryLeastSquares.Fit returns, and the arithmetic between the lists is the invariant that makes it one: TStatistics[j] is Coefficients[j] / StandardErrors[j] and each interval is centred on its estimate.

FStatistic and FPValue test every slope at once, not the intercept. With a fitted intercept the null is that all featureCount slopes are zero; without one the intercept is not there to exclude and the test gains a degree of freedom. FPValue reads the F on ResidualDegreesOfFreedom denominator degrees of freedom, except under CovarianceType.Cluster, where it reads the cluster count less one, as statsmodels' df_resid_inference does; ResidualDegreesOfFreedom itself stays rows less parameters.

A VIF is not a p-value's replacement. It says how much of a regressor the others already explain — 1 when nothing does, and unbounded as two regressors converge on saying the same thing. A single regressor fitted with no intercept has no other column to be explained by, and its entry is NaN: statsmodels raises there, and this returns the whole table with the one undefined diagnostic marked rather than refusing a fit that is otherwise sound.

Applies to — net10.0, netstandard2.0.

See also — OrdinaryLeastSquares, OlsOptions.