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_intercept : bool, 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).

normalize : bool, 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 :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on an estimator with ``normalize=False``.

copy_X : bool, optional, default True If True, X will be copied; else, it may be overwritten.

n_jobs : int 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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` 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.)

Fit linear model.

Parameters ---------- X : array-like, sparse matrix of shape (n_samples, n_features) Training data

y : array-like of shape (n_samples,) or (n_samples, n_targets) Target values. Will be cast to X's dtype if necessary

sample_weight : array-like of shape (n_samples,), default=None Individual weights for each sample

.. versionadded:: 0.17 parameter *sample_weight* support to LinearRegression.

Returns ------- self : returns an instance of self.

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

Predict using the linear model.

Parameters ---------- X : array_like or sparse matrix, shape (n_samples, n_features) Samples.

Returns ------- C : array, shape (n_samples,) Returns predicted values.

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 ---------- X : array-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.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) True values for X.

sample_weight : array-like of shape (n_samples,), default=None Sample weights.

Returns ------- score : float 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 :func:`~sklearn.metrics.r2_score`. This will influence the ``score`` method of all the multioutput regressors (except for :class:`~sklearn.multioutput.MultiOutputRegressor`). To specify the default value manually and avoid the warning, please either call :func:`~sklearn.metrics.r2_score` directly or make a custom scorer with :func:`~sklearn.metrics.make_scorer` (the built-in scorer ``'r2'`` uses ``multioutput='uniform_average'``).

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 ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

Attribute coef_: see constructor for documentation

Attribute rank_: see constructor for documentation

Attribute singular_: see constructor for documentation

Attribute intercept_: see constructor for documentation

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.