OLS

Ordinary least squares with robust covariance options

from _api_doc_utils import *

1 Where it fits

Group: Regression

OLS estimates the linear projection

\[ y_i = \alpha + x_i'\beta + u_i \]

by least squares. The class stores the fitted intercept and coefficient vector and exposes the common linear-model covariance surface: classical, HC1, Newey-West, and cluster-robust standard errors.

2 Python API

Constructor: cm.OLS

Use fit(x, y) for the standard estimator, fit_weighted(x, y, sample_weight) for weighted least squares, and fit_sketch(x, y, sketch_size, seed=None) when a randomized row sketch is acceptable for a large tall design. predict(x) returns fitted values. bootstrap(B, seed=None) returns bootstrap draws with the intercept in the first column.

print(inspect.signature(cm.OLS))

()

cls = cm.OLS
display(HTML(html_table(["Public method"], public_methods(cls))))

Public method
bootstrap(self, /, n_bootstrap, seed=None)
fit(self, /, x, y)
fit_sketch(self, /, x, y, sketch_size, seed=None)
fit_weighted(self, /, x, y, sample_weight)
predict(self, /, x)
summary(self, /, vcov='hc1', lags=None, clusters=None)

3 Minimal example

rng = np.random.default_rng(1)
x = rng.normal(size=(200, 3))
y = 0.5 + x @ np.array([1.0, -0.7, 0.25]) + rng.normal(scale=0.3, size=200)
model = cm.OLS()
model.fit(x, y)
clusters = np.repeat(np.arange(20, dtype=np.int64), 10)
print(model.summary(vcov="hc1")["coef"])
print(model.summary(vcov="cluster", clusters=clusters)["coef_se"])
print(model.predict(x[:3]))

[ 1.00664118 -0.70425283  0.224367  ]
[0.02367873 0.0222344  0.0228217 ]
[ 0.29427264 -1.39837835 -0.41709421]

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

rng = np.random.default_rng(101)
x = rng.normal(size=(80, 3))
y = 0.5 + x @ np.array([1.0, -0.7, 0.25]) + rng.normal(scale=0.3, size=80)
model = cm.OLS(); model.fit(x, y)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))

summary() key	shape
intercept	()
coef	(3,)
intercept_se	()
coef_se	(3,)
vcov_type	()