sklearn.linear model.LinearRegression

A sklearn.linear model.LinearRegression is a linear least-squares regression system within sklearn.linear_model class.

AKA: LinearRegression, linear model.LinearRegression.
Context
- Usage:

1) Import Linear Regression model from scikit-learn : from sklearn.linear_model import LinearRegression

2) Create a design matrix X and response vector Y

3) Create a Lasso Regression object: model=LinearRegression([fit_intercept=True, normalize=False, copy_X=True, n_jobs=1])

4) Choose method(s):

Fit model with coordinate descent: model.fit(X, Y[, check_input]))(supervised learning) or model.fit(X) (unsupervised learning)
Predict Y using the linear model with estimated coefficients: Y_pred = model.predict(X)
Return coefficient of determination (R^2) of the prediction: model.score(X,Y[, sample_weight=w])
Get estimator parameters: model.get_params([deep])
Set estimator parameters: model.set_params(**params)

Example(s):
- 10-fold sklearn Boston data evaluation [1]

Input:	Output:
from sklearn.linear_model import LinearRegression from sklearn.model_selection import cross_val_predict from sklearn.datasets import load_boston from sklearn.metrics import explained_variance_score, mean_squared_error import numpy as np import pylab as pl boston = load_boston() #Loading boston datasets x = boston.data # Creating Regression Design Matrix y = boston.target # Creating target dataset linreg = LinearRegression() # Create linear regression object linreg.fit(x,y) <span style="font-weight:italic; color:gray; # Fit linear regression yp = linreg.predict(x) # predicted values yp_cv = cross_val_predict(linreg, x, y, cv=10) #Calculation 10-Fold CV	(blue dots correspond to 10-Fold CV)
#Calculaton of RMSE and Explained Variances Evariance=explained_variance_score(y,yp) Evariance_cv=explained_variance_score(y,yp_cv) RMSE =np.sqrt(mean_squared_error(y,yp)) RMSECV =sqrt(mean_squared_error(y,yp_cv)_	Method: Linear Regression RMSE on the dataset: 4.6795 RMSE on 10-fold CV: 5.8819 Explained Variance Regression Score on the dataset : 0.7406 Explained Variance Regression 10-fold CV: 0.5902

Counter-Example(s)
See: Linear Regression Task, Ordinary Least Squares Linear Regression System, Estimation Task, Coordinate Descent Algorithm.

References

2017a

http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
- QUOTE: Ordinary least squares Linear Regression.
  class sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1)[source]

2017b

http://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html
- QUOTE:

# Split the targets into training/testing sets 
diabetes_y_train = diabetes.target[:-20]
diabetes_y_test = diabetes.target[-20:]


# Create linear regression object
regr = linear_model.LinearRegression()


# Train the model using the training sets
regr.fit(diabetes_X_train, diabetes_y_train)

2017D

(Mobasher,2017) ⇒ Bamshad Mobasher (2017). Example of Regression Analysis Using the Boston Housing Data Set. Retrieved 2017-10-01

2017 e.

(Scipy Lectures, 2017) ⇒ http://www.scipy-lectures.org/packages/scikit-learn/#supervised-learning-regression-of-housing-data
- QUOTE: 3.6.4.2. Predicting Home Prices: a Simple Linear Regression
  Now we'll use scikit-learn to perform a simple linear regression on the housing data. There are many possibilities of regressors to use. A particularly simple one is LinearRegression: this is basically a wrapper around an ordinary least squares calculation.

from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(data.data, data.target) from sklearn.linear_model import LinearRegression clf = LinearRegression() clf.fit(X_train, y_train) predicted = clf.predict(X_test) expected = y_test print("RMS: %s" % np.sqrt(np.mean((predicted - expected) ** 2)))

We can plot the error: expected as a function of predicted:

plt.scatter(expected, predicted)

2016

(Thiebaut) ⇒ D. Thiebaut (2016). SKLearn Tutorial: Linear Regression on Boston Data