sklearn.linear_model.LinearRegression

class sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=None)[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, optional, 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, optional, 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

copy_Xbool, optional, default True

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

n_jobsint or None, optional (default=None)

The number of jobs to use for the computation. This will only provide speedup for n_targets > 1 and sufficient large problems. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

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 of (n_targets,)

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

See also

sklearn.linear_model.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.

sklearn.linear_model.Lasso

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

sklearn.linear_model.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) 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_
3.0000...
>>> reg.predict(np.array([[3, 5]]))
array([16.])

Methods

fit(self, X, y[, sample_weight])

Fit linear model.

get_params(self[, deep])

Get parameters for this estimator.

predict(self, X)

Predict using the linear model.

score(self, X, y[, sample_weight])

Return the coefficient of determination R^2 of the prediction.

set_params(self, \*\*params)

Set the parameters of this estimator.
__init__(self, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None)[source]

Initialize self. See help(type(self)) for accurate signature.

fit(self, 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
selfreturns an instance of self.
get_params(self, 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
paramsmapping of string to any

Parameter names mapped to their values.

predict(self, 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(self, X, y, sample_weight=None)[source]

Return the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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, 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 R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). 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
selfobject

Estimator instance.