LinearRegression

LinearRegression(
    alpha=0.0,
    l1_ratio=0.0,
    fit_intercept=True,
    max_iterations=1000,
    tolerance=1e-08,
    l1_smoothing=1e-06,
)

Linear regression estimated by direct optimization of squared loss.

The fitted model minimizes the average squared-error objective. When alpha > 0, the optimization backend switches to Frank-Wolfe over an exact L1 or L2 ball, depending on l1_ratio. For unregularized fits, both classical and robust sandwich covariance estimators are available.

Attributes

Name	Type	Description
coef_	ndarray of shape (n_features,)	Estimated slope coefficients.
intercept_	float	Estimated intercept. Equals 0.0 when fit_intercept=False.
params_	ndarray of shape (n_params,)	Full parameter vector, including the intercept when present.
std_errors_	ndarray or None	Classical standard errors for params_.
robust_std_errors_	ndarray or None	Heteroskedasticity-robust sandwich standard errors for params_.

Methods

Name	Description
confidence_intervals	Return coefficient confidence intervals.
fit	Fit the linear regression model.
predict	Predict the conditional mean response.
score	Return the coefficient of determination, R^2.
summary	Return [coef, se, ci_lb, ci_ub] for each fitted parameter.

confidence_intervals

LinearRegression.confidence_intervals(alpha=0.05, covariance_type='nonrobust')

Return coefficient confidence intervals.

Parameters

Name	Type	Description	Default
alpha	float	Two-sided significance level.	0.05
covariance_type	('nonrobust', 'robust')	Covariance estimator used to construct intervals.	"nonrobust"

Returns

Name	Type	Description
	ndarray of shape (n_params, 2)	Lower and upper confidence bounds for each fitted parameter.

fit

LinearRegression.fit(X, y)

Fit the linear regression model.

Parameters

Name	Type	Description	Default
X	ndarray of shape (n_samples, n_features)	Feature matrix.	required
y	ndarray of shape (n_samples,)	Response vector.	required

Returns

Name	Type	Description
	LinearRegression	The fitted estimator.

predict

LinearRegression.predict(X)

Predict the conditional mean response.

Parameters

Name	Type	Description	Default
X	ndarray of shape (n_samples, n_features)	Feature matrix.	required

Returns

Name	Type	Description
	ndarray of shape (n_samples,)	Predicted mean response.

score

LinearRegression.score(X, y)

Return the coefficient of determination, R^2.

Parameters

Name	Type	Description	Default
X	ndarray of shape (n_samples, n_features)	Feature matrix.	required
y	ndarray of shape (n_samples,)	Observed response vector.	required

Returns

Name	Type	Description
	float	The in-sample R^2 statistic.

summary

LinearRegression.summary(alpha=0.05, covariance_type='nonrobust')

Return [coef, se, ci_lb, ci_ub] for each fitted parameter.