OLS

from SymbolicDSGE.regression.ols import OLSResult, ols

ols(
    x: ndarray,
    y: ndarray,
    variables: list[str] | None = None,
    intercept: bool = True,
) -> OLSResult

Run Ordinary Least Squares regression on a one-dimensional response and a two-dimensional design matrix.

Inputs:

Name	Description
x	Design matrix. Shape `(n, k)`.
y	Response vector. Shape `(n,)`.
variables	Optional names for the columns of `x`. Defaults to `x0`, `x1`, ...
intercept	If `True`, prepend an intercept column to the design matrix.

Returns:

Type	Description
`OLSResult`	Regression result with common fitted diagnostics and OLS inference outputs.

@dataclass(frozen=True)
class OLSResult(RegressionResult)

OLSResult extends RegressionResult with standard errors, coefficient tests, confidence intervals, and an F-test.

Additional Fields and Methods:

Name	Type	Description
se	`ndarray`	Coefficient standard errors.
t_stat	`ndarray`	Coefficient t-statistics.
partial_r2	`ndarray`	Partial R-squared values implied by each t-statistic.
p_values	`ndarray`	Two-sided coefficient p-values under the t reference distribution.
`confidence_intervals(alpha=0.05)`	`ndarray`	Lower and upper coefficient bounds. Shape `(k, 2)`.
`summary(alpha=0.05)`	`pandas.DataFrame`	Coefficient, interval, t-statistic, p-value, and partial R-squared table.
`F_test(alpha=0.05)`	`TestResult`	Regression F-test against the relevant F reference distribution.

Rank-Deficient Designs

OLS first attempts a Cholesky solve and falls back to least squares when needed. The status field records the solver status used by the result.