`ols` – Ordinary least squares – baseline linear regression.#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.ols_fit.

Function signature#

mf.functions.ols_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> OLSFitResult

Parameters#

name	type	default	constraint	description
`X`	`np.ndarray	pd.DataFrame`	—	—
`y`	`np.ndarray	pd.Series`	—	—

Returns#

OLSFitResult — frozen dataclass with fit results.

Attribute	Type	Description
`.coef_`	`np.ndarray`	Fitted coefficient vector, shape (n_features,).
`.intercept_`	`float`	Fitted intercept scalar.
`.predict(X)`	`np.ndarray`	Predictions for new data X, shape (n_samples,).
`.summary()`	`str`	Human-readable text table of fit results.

Behavior#

Closed-form linear regression with no regularisation. Cheapest linear estimator; appropriate when p << n and predictors are well-conditioned. Returns NaN coefficients when the design matrix is rank-deficient (sklearn raises an error in that case).

When to use

Low-dimensional baselines; sanity-check sweeps.

When NOT to use

High-dimensional panels (p ≈ n) – use ridge / lasso instead.

In recipe context#

Set params.family = "ols" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: ols

References#

macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’
Greene (2018) ‘Econometric Analysis’, 8th ed., Pearson.

ols – Ordinary least squares – baseline linear regression.#