Multiple linear regression (two or more regressors) with singular-design detection

[Yaraslaut]

Problem

Methods determine model parameters by a multiple linear regression: one value fitted against two (or more) regressors plus a constant term, y = c0 + c1·x1 + c2·x2. least_squares.hpp has only the straight line, so this has to live outside the library, untraced, with its outputs entered into the formulas as if they were measurements.

Wanted

• An opaque operation, e.g. formula::multiple_least_squares, over runtime-length samples (see Least squares over runtime-length samples, in double, with R² #4), with outputs for the constant term, each coefficient and the coefficient of determination.
• The dimension of each coefficient derived from the value and the regressor it multiplies, as slope is today.
• A singular design is an error, not a number. If a regressor is constant, or two are collinear, the normal equations are singular. Spreadsheet solvers answer with arbitrary coefficients in this case. The operation should return DomainError, so the method can say why no parameters were determined.
• Evaluation in double (see Numeric headroom: 64-bit Rational overflows on realistic lab statistics — 128-bit intermediates or a wider representation? #1 for the exact path's headroom).

Open points

• A fixed number of regressors as a template parameter, or a variadic list of regressor samples?
• Should the trace list the sample count that entered the fit? Methods report it next to the coefficients.

[christianparpart]

Implemented in #7 and released in 0.2.0: multiple_least_squares(regressors(x1, ..., xK), y, citation) for one to eight regressors. A singular design is refused exactly, by a zero pivot, as the fit's own DomainError. The guide is docs/opaque-and-retry.md, Several regressors.