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# `sklearn.linear_model`.LinearRegression

class sklearn.linear_model.LinearRegression(*, fit_intercept=True, copy_X=True, n_jobs=None, positive=False)

  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, 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).

    copy_X bool, default=True

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

    n_jobs int, 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 secondly `X` is sparse or if `positive` is set to `True`. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    positive bool, 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 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 (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_metadata_routing`() | Get metadata routing of this object.
  `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_fit_request`(*[, sample_weight]) | Request metadata passed to the `fit` method.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.

  fit(X, y, sample_weight=None)

    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.

        New in version 0.17: parameter sample_weight support to LinearRegression.

    Returns:
      self object

        Fitted Estimator.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    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 dict

        Parameter names mapped to their values.

  predict(X)

    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.

  score(X, y, sample_weight=None)

    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 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 with 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)` w.r.t. `y`.

    Notes

    The \(R^2\) score used when calling `score` on a regressor uses `multioutput='uniform_average'` from version 0.23 to keep consistent with default value of `r2_score`. This influences the `score` method of all the multioutput regressors (except for `MultiOutputRegressor`).

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

    Request metadata passed to the `fit` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `fit` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `fit`.

    - `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 the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `fit`.

    Returns:
      self object

        The updated object.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

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

    Request metadata passed to the `score` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `score` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `score`.

    - `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 the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `score`.

    Returns:
      self object

        The updated object.

## Examples using `sklearn.linear_model.LinearRegression`

Principal Component Regression vs Partial Least Squares Regression

Principal Component Regression vs Partial Least Squares Regression

Plot individual and voting regression predictions

Plot individual and voting regression predictions

Comparing Linear Bayesian Regressors

Comparing Linear Bayesian Regressors

Linear Regression Example

Linear Regression Example

Logistic function

Logistic function

Non-negative least squares

Non-negative least squares

Ordinary Least Squares and Ridge Regression Variance

Ordinary Least Squares and Ridge Regression Variance

Quantile regression

Quantile regression

Robust linear estimator fitting

Robust linear estimator fitting

Robust linear model estimation using RANSAC

Robust linear model estimation using RANSAC

Sparsity Example: Fitting only features 1 and 2

Sparsity Example: Fitting only features 1 and 2

Theil-Sen Regression

Theil-Sen Regression

Failure of Machine Learning to infer causal effects

Failure of Machine Learning to infer causal effects

Face completion with a multi-output estimators

Face completion with a multi-output estimators

Isotonic Regression

Isotonic Regression

Metadata Routing

Metadata Routing

Plotting Cross-Validated Predictions

Plotting Cross-Validated Predictions

Underfitting vs. Overfitting

Underfitting vs. Overfitting

Using KBinsDiscretizer to discretize continuous features

Using KBinsDiscretizer to discretize continuous features