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 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 in case of sufficiently large problems, that is if firstly
n_targets > 1
and secondlyX
is sparse or ifpositive
is set toTrue
.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
.- 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.
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 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
(X)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 ofy
, 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)
, wheren_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 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.