Linear Models - Scikit Learn

1. Linear Models

The target value is expected to be a linear combination of the features.

from sklearn import linear_model

reg = linear_model.LinearRegression()
reg.fit([[0, 0], [1, 1], [2, 2]], [0, 1, 2])

## LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)

reg.coef_

## array([0.5, 0.5])

2. Linear Regression Example - Diabetes Dataset

# Code source: Jaques Grobler
# License: BSD 3 clause

import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets, linear_model
from sklearn.metrics import mean_squared_error, r2_score

# Load the diabetes dataset
diabetes_X, diabetes_y = datasets.load_diabetes(return_X_y=True)

# Use only one feature
diabetes_X = diabetes_X[:, np.newaxis, 2]

# Split the data into training/testing sets
diabetes_X_train = diabetes_X[:-20]
diabetes_X_test = diabetes_X[-20:]

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

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

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

# Make predictions using the testing set

## LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)

diabetes_y_pred = regr.predict(diabetes_X_test)

# The coefficients
print('Coefficients: \n', regr.coef_)
# The mean squared error

## Coefficients: 
##  [938.23786125]

print('Mean squared error: %.2f'
      % mean_squared_error(diabetes_y_test, diabetes_y_pred))
# The coefficient of determination: 1 is perfect prediction

## Mean squared error: 2548.07

print('Coefficient of determination: %.2f'
      % r2_score(diabetes_y_test, diabetes_y_pred))

# Plot outputs

## Coefficient of determination: 0.47

plt.scatter(diabetes_X_test, diabetes_y_test,  color='black')
plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=3)

plt.xticks(())

## ([], <a list of 0 Text xticklabel objects>)

plt.yticks(())

## ([], <a list of 0 Text yticklabel objects>)

plt.show()