sklearn.linear_model.LinearRegression  
class sklearn.linear_model.LinearRegression(*, fit_intercept=True, normalize=False, 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 use StandardScaler before calling fit on an estimator with normalize=False.  
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 a joblib.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 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.      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_
3.0000...
>>> 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{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 
 
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 
 
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 \(R^2\) 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 of y, 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), where n_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 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_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.     
 
 Examples using sklearn.linear_model.LinearRegression
 
  Principal Component Regression vs Partial Least Squares Regression  

  Plot individual and voting regression predictions  

  Ordinary Least Squares and Ridge Regression Variance  

  Logistic function  

  Non-negative least squares  

  Linear Regression Example  

  Robust linear model estimation using RANSAC  

  Sparsity Example: Fitting only features 1 and 2  

  Theil-Sen Regression  

  Robust linear estimator fitting  

  Automatic Relevance Determination Regression (ARD)  

  Bayesian Ridge Regression  

  Isotonic Regression  

  Face completion with a multi-output estimators  

  Plotting Cross-Validated Predictions  

  Underfitting vs. Overfitting  

  Using KBinsDiscretizer to discretize continuous features