Regression Results

from SymbolicDSGE.regression import RegressionResult
from SymbolicDSGE.regression.ols import MCRegressionResult

 

@dataclass(frozen=True)
class RegressionResult(
    variables: list[str],
    coefficients: ndarray,
    y: ndarray,
    X: ndarray,
    status: RegressionStatus,
)

RegressionResult is the shared result abstraction for standard linear regression outputs. Concrete result types inherit the common fitted-data diagnostics and add method-specific quantities.

Fields and Properties:

Name	Type	Description
variables	list[str]	Names of the design columns represented in coefficients.
coefficients	ndarray	Estimated coefficient vector. Shape (k,).
y	ndarray	Response vector. Shape (n,).
X	ndarray	Design matrix used by the regression. Shape (n, k).
x	ndarray	Alias for X.
status	RegressionStatus	Solver status.
n	int	Number of observations.
k	int	Number of design columns.
y_hat	ndarray	Fitted response vector.
residuals	ndarray	Response residuals, y - y_hat.
ssr	float64	Sum of squared residuals.
sst	float64	Total sum of squares around the sample mean of y.
mse	float64	Mean squared error, ssr / n.
rmse	float64	Root mean squared error.
r2	float64	Coefficient of determination.
r2_adj	float64	Adjusted coefficient of determination.
to_dict()	dict	Dataclass dictionary representation.

Shape Contract

RegressionResult expects a one-dimensional response vector and a two-dimensional design matrix. Multivariate response regressions should be represented as separate result objects.

 

@dataclass(frozen=True)
class MCRegressionResult(
    variables: list[str],
    results: tuple[RegressionResult, ...],
)

MCRegressionResult aggregates per-replication RegressionResult objects produced by Monte Carlo regression steps.

Fields and Properties:

Name	Type	Description
variables	list[str]	Shared variable ordering across replications.
results	tuple[RegressionResult, ...]	Per-replication regression outputs.
coef_trace	ndarray	Coefficients stacked by replication. Shape (n_rep, k).
coefficients	ndarray	Alias for coef_trace.
status_trace	tuple[RegressionStatus, ...]	Solver status for each replication.
n_rep	int	Number of stored regression results.
n	int	Shared number of observations per replication.
k	int	Shared number of design columns.
y_trace	ndarray	Response vectors stacked by replication.
x_trace	ndarray	Design matrices stacked by replication.
y_hat_trace	ndarray	Fitted responses stacked by replication.
residual_trace	ndarray	Residual vectors stacked by replication.
ssr_trace	ndarray	Per-replication SSR values.
sst_trace	ndarray	Per-replication SST values.
mse_trace	ndarray	Per-replication MSE values.
rmse_trace	ndarray	Per-replication RMSE values.
r2_trace	ndarray	Per-replication R-squared values.
r2_adj_trace	ndarray	Per-replication adjusted R-squared values.
summary(alpha=0.05)	pandas.DataFrame	Coefficient trace summary. OLS results include inference columns.
to_dict()	dict	Compact dictionary representation.

OLS-Only Aggregate Diagnostics:

Name	Type	Description
se_trace	ndarray	OLS standard-error trace.
t_stat_trace	ndarray	OLS t-statistic trace.
partial_r2_trace	ndarray	OLS partial R-squared trace.
pval_trace	ndarray	OLS coefficient p-value trace.
F_stat_trace	ndarray	OLS F-statistic trace.
F_pval_trace	ndarray	OLS F-test p-value trace.
confidence_intervals(alpha=0.05)	ndarray	Per-replication OLS coefficient intervals.
F_test(alpha=0.05)	MCResult	Aggregate F-test result container.

OLS-Specific Diagnostics

OLS aggregate diagnostics require every stored result to be an OLSResult. For ridge, lasso, and elastic-net aggregates, summary() returns coefficient traces without OLS inference columns.