# sklearn.linear_model.LinearRegression¶

class sklearn.linear_model.LinearRegression(*, fit_intercept=True, normalize='deprecated', copy_X=True, n_jobs=None, positive=False)[source]

Ordinary least squares Linear Regression.

LinearRegression fits a linear model with coefficients w = (w1, …, wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.

Parameters
fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e. data is expected to be centered).

normalizebool, default=False

This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.

Deprecated since version 1.0: normalize was deprecated in version 1.0 and will be removed in 1.2.

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

n_jobsint, default=None

The number of jobs to use for the computation. This will only provide speedup in case of sufficiently large problems, that is if firstly n_targets > 1 and secondly X is sparse or if positive is set to True. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

positivebool, default=False

When set to True, forces the coefficients to be positive. This option is only supported for dense arrays.

New in version 0.24.

Attributes
coef_array of shape (n_features, ) or (n_targets, n_features)

Estimated coefficients for the linear regression problem. If multiple targets are passed during the fit (y 2D), this is a 2D array of shape (n_targets, n_features), while if only one target is passed, this is a 1D array of length n_features.

rank_int

Rank of matrix X. Only available when X is dense.

singular_array of shape (min(X, y),)

Singular values of X. Only available when X is dense.

intercept_float or array of shape (n_targets,)

Independent term in the linear model. Set to 0.0 if fit_intercept = False.

n_features_in_int

Number of features seen during fit.

New in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

New in version 1.0.

Ridge

Ridge regression addresses some of the problems of Ordinary Least Squares by imposing a penalty on the size of the coefficients with l2 regularization.

Lasso

The Lasso is a linear model that estimates sparse coefficients with l1 regularization.

ElasticNet

Elastic-Net is a linear regression model trained with both l1 and l2 -norm regularization of the coefficients.

Notes

From the implementation point of view, this is just plain Ordinary Least Squares (scipy.linalg.lstsq) or Non Negative Least Squares (scipy.optimize.nnls) wrapped as a predictor object.

Examples

>>> import numpy as np
>>> from sklearn.linear_model import LinearRegression
>>> X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
>>> # y = 1 * x_0 + 2 * x_1 + 3
>>> y = np.dot(X, np.array([1, 2])) + 3
>>> reg = LinearRegression().fit(X, y)
>>> reg.score(X, y)
1.0
>>> reg.coef_
array([1., 2.])
>>> reg.intercept_
3.0...
>>> reg.predict(np.array([[3, 5]]))
array([16.])


Methods

 fit(X, y[, sample_weight]) Fit linear model. get_params([deep]) Get parameters for this estimator. Predict using the linear model. score(X, y[, sample_weight]) Return the coefficient of determination of the prediction. set_params(**params) Set the parameters of this estimator.
fit(X, y, sample_weight=None)[source]

Fit linear model.

Parameters
X{array-like, sparse matrix} of shape (n_samples, n_features)

Training data.

yarray-like of shape (n_samples,) or (n_samples, n_targets)

Target values. Will be cast to X’s dtype if necessary.

sample_weightarray-like of shape (n_samples,), default=None

Individual weights for each sample.

New in version 0.17: parameter sample_weight support to LinearRegression.

Returns
selfobject

Fitted Estimator.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

predict(X)[source]

Predict using the linear model.

Parameters
Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.

Returns
Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None)[source]

Return the coefficient of determination of the prediction.

The coefficient of determination $$R^2$$ is defined as $$(1 - \frac{u}{v})$$, where $$u$$ is the residual sum of squares ((y_true - y_pred)** 2).sum() and $$v$$ is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a $$R^2$$ score of 0.0.

Parameters
Xarray-like of shape (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns
scorefloat

$$R^2$$ of self.predict(X) wrt. y.

Notes

The $$R^2$$ score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

Estimator parameters.

Returns
selfestimator instance

Estimator instance.