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Fits a linear model and reports the estimates and their standard errors, without the inference table.

public static OlsEstimate Estimate(ReadOnlySpan<double> design, ReadOnlySpan<double> response, int featureCount, bool withIntercept = true)

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. featureCount is how many regressors each row carries. withIntercept says whether to fit a constant, prepended to the coefficients; true by default.

Returns — OlsEstimate: the coefficients, their standard errors and t statistics, and the residual sum of squares.

Exceptions — ArgumentOutOfRangeException when featureCount is not positive. ArgumentException when design is not a whole number of rows, when response has a different length, when no residual degrees of freedom are left, or when a column of design lies within rounding of the span of the columns before it — the collinearity Fit refuses, on the same test.

Example — the same line Fit reads, with only what a caller fitting many of them needs.

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];

OlsEstimate estimate = OrdinaryLeastSquares.Estimate(design, response, featureCount: 1);

double slope = Math.Round(estimate.Coefficients[1], 4);         // => 1.9976
double error = Math.Round(estimate.StandardErrors[1], 4);       // => 0.0278
double t = Math.Round(estimate.TStatistics[1], 4);              // => 71.8557
double residuals = Math.Round(estimate.ResidualSumOfSquares, 4);  // => 0.1948

Remarks — always the Householder reflections Fit falls back to, for a caller fitting many regressions and reading a coefficient, a t statistic or a likelihood from each — the augmented Dickey-Fuller lag search in Lodestar.Stats.TimeSeries fits one per candidate lag. It skips what Fit adds on top: p-values, intervals, R², the F test, the variance inflation factors and the robust covariances. The standard errors are the non-robust ones; a robust covariance is Fit's. Where Fit took the normal equations the two agree to rounding rather than to the bit: 1.9976190476190478 here against Fit's 1.9976190476190496 on the example above.

Applies to — net10.0, netstandard2.0.

See also — OlsEstimate, OrdinaryLeastSquares.Fit, the Python equivalence table.