LinearRegression #

classsklearn.linear_model.LinearRegression(*,fit_intercept=True,copy_X=True,tol=1e-06,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 inthe dataset, and the targets predicted by the linear approximation.

Parameters:

fit_interceptbool, default=True

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

copy_Xbool, default=True

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

tolfloat, default=1e-6

The precision of the solution (coef_) is determined bytol whichspecifies a different convergence criterion for thelsqr solver.tol is set asatol andbtol ofscipy.sparse.linalg.lsqr whenfitting on sparse training data. This parameter has no effect when fittingon dense data.

Added in version 1.7.

n_jobsint, default=None

The number of jobs to use for the computation. This will only providespeedup in case of sufficiently large problems, that is if firstlyn_targets>1 and secondlyX is sparse or ifpositive is settoTrue.None means 1 unless in ajoblib.parallel_backend context.-1 means using allprocessors. SeeGlossary for more details.

positivebool, default=False

When set toTrue, forces the coefficients to be positive. Thisoption is only supported for dense arrays.

For a comparison between a linear regression model with positive constraintson the regression coefficients and a linear regression without such constraints,seeNon-negative least squares.

Added 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), thisis a 2D array of shape (n_targets, n_features), while if onlyone target is passed, this is a 1D array of length n_features.
rank_int: Rank of matrixX. Only available whenX is dense.
singular_array of shape (min(X, y),): Singular values ofX. Only available whenX is dense.
intercept_float or array of shape (n_targets,): Independent term in the linear model. Set to 0.0 iffit_intercept=False.
n_features_in_int: Number of features seen duringfit.
Added in version 0.24.
feature_names_in_ndarray of shape (n_features_in_,): Names of features seen duringfit. Defined only whenXhas feature names that are all strings.
Added in version 1.0.

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: 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 OrdinaryLeast Squares (scipy.linalg.lstsq) or Non Negative Least Squares(scipy.optimize.nnls) wrapped as a predictor object.

Examples

>>>importnumpyasnp>>>fromsklearn.linear_modelimportLinearRegression>>>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_np.float64(3.0)>>>reg.predict(np.array([[3,5]]))array([16.])

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.
Added in version 0.17:parametersample_weight support to LinearRegression.

Returns:

selfobject: Fitted Estimator.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest: AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained 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]#

Returncoefficient of determination on test data.

The coefficient of determination,$R^2$, is defined as$(1 - \frac{u}{v})$, where$u$ is the residualsum 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 themodel can be arbitrarily worse). A constant model that always predictsthe expected value ofy, disregarding the input features, would geta$R^2$ score of 0.0.

Parameters:

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputedkernel matrix or a list of generic objects instead with shape(n_samples,n_samples_fitted), wheren_samples_fittedis the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True values forX.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: $R^2$ ofself.predict(X) w.r.t.y.

Notes

The$R^2$ score used when callingscore on a regressor usesmultioutput='uniform_average' from version 0.23 to keep consistentwith default value ofr2_score.This influences thescore method of all the multioutputregressors (except forMultiOutputRegressor).

set_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→LinearRegression[source]#

Configure whether metadata should be requested to be passed to thefit method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

True: metadata is requested, and passed tofit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it tofit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter infit.

Returns:

selfobject: The updated object.

set_params(**params)[source]#

Set the parameters of this estimator.

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

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

set_score_request(*,sample_weight:bool|None|str='$UNCHANGED$')→LinearRegression[source]#

Configure whether metadata should be requested to be passed to thescore method.

The options for each parameter are:

True: metadata is requested, and passed toscore if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it toscore.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter inscore.

Returns: