Least squares over runtime-length samples, in double, with R²

[Yaraslaut]

Problem

linear_least_squares fits a curve of fixed length N and evaluates only in Rational. Two common situations are not covered:

1. The number of points is data, not part of the method. A method says "all determinations of the series that meet condition X", so the count is only known at run time. observations<Q, Capacity> models exactly this for statistics, but it cannot be the input of a fit, a curve or an opaque operation (ObservationsNodeBase: "the only thing that reads it is binned").
2. The point count and precision are beyond Rational headroom. A realistic case is about 50 points with 4 decimal places, which is past the overflow sizes measured in docs/numeric-headroom.md (see Numeric headroom: 64-bit Rational overflows on realistic lab statistics — 128-bit intermediates or a wider representation? #1). There is no traced fallback in double: LinearLeastSquares::compute<double> can be called, but its result reaches neither the trace nor the page.

Wanted

• A least-squares line over observations<Q, Capacity> (domain and value observations of the same count, or pairs), with Capacity a bound as elsewhere.
• Evaluation with Rep = double through checked_evaluate_si<double>, traced like any other opaque call.
• A coefficient of determination output next to intercept and slope; methods report it and use it as an acceptance criterion.
• A degenerate set (fewer than two points, no spread in the domain) stays the fit's own DomainError.

Related: #1 would remove the overflow for the exact path, but not the fixed-length restriction.

[christianparpart]

Implemented in #7 and released in 0.2.0: linear_least_squares over two sets of raw observations gives the intercept, the slope, R² and the number of points, exactly in Rational, through rounded_output where the exact route overflows, and untraced in double. The guide is docs/opaque-and-retry.md, A line through observations.