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 l2norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=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 for n_targets > 1 and sufficient large problems.
None
means 1 unless in ajoblib.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 whenX
is dense. singular_array of shape (min(X, y),)
Singular values of
X
. Only available whenX
is dense. intercept_float or array of shape (n_targets,)
Independent term in the linear model. Set to 0.0 if
fit_intercept = False
.
See also
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
ElasticNet 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_ 3.0000... >>> 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
(X)Predict using the linear model.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.

fit
(X, y, sample_weight=None)[source]¶ Fit linear model.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
Training data
 yarraylike of shape (n_samples,) or (n_samples, n_targets)
Target values. Will be cast to X’s dtype if necessary
 sample_weightarraylike 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
(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
 Xarraylike 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 \(R^2\) of the prediction.
The coefficient \(R^2\) 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 ofy
, disregarding the input features, would get a \(R^2\) score of 0.0. Parameters
 Xarraylike 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)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator. yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
. sample_weightarraylike 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 usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

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.