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This article is about how Python implements the ordinary least squares method. The editor thinks it is very practical, so share it with you as a reference and follow the editor to have a look.

Generalized linear regression model:

Regard as a coefficient vector (coef_); set

As intercept (intercept_)

1. Ordinary least square method (Ordinary Least Squares)

The purpose of linear regression is to minimize the sum of squares between the predicted values and the actual values:

Import matplotlib.pyplot as pltimport numpy as np# loads the dataset "datasets" from sklearn import datasets, and linear_model# gets the dataset of diabetes diabetes = datasets.load_diabetes () # using one of the features, the role of np.newaxis is to increase the dimension diabetes_X = diabetes.data [:, np.newaxis 2] # split the X variable data set into training set and test set diabetes_X_train = diabetes_X [:-20] diabetes_X_test = diabetes_X [- 20:] # split Y target variables into training set and test set diabetes_y_train = diabetes.target [:-20] diabetes_y_test = diabetes.target [- 20:] # create linear regression object regr = linear_model.LinearRegression () # use training data to train Practice the model regr.fit (diabetes_X_train) Diabetes_y_train) # View the correlation coefficient print ('Coefficients:\ nvariance, regr.coef_) # View the mean of the square of the residual (mean square error,MSE) print ("Residual sum of squares:% .2f" #% is formatted% np.mean ((regr.predict (diabetes_X_test)-diabetes_y_test) * * 2) # Explained variance score: 1 is perfect prediction# explain the variance score (R ^ 2) The best score is 1: # coefficient R ^ 2 = 1-UBV, where u is the square of residual, u = (y_true-y_pred) * * 2). Sum () # v is the sum of squares of deviations V = (y_true-y_true.mean ()) * * 2). Sum () print ('Variance score:% .2f'% regr.score (diabetes_X_test, diabetes_y_test)) # draw the test point plt.scatter (diabetes_X_test, diabetes_y_test, color='black') # draw the predicted point plt.plot (diabetes_X_test, regr.predict (diabetes_X_test), color='blue') Linewidth=3) # Delete the scale of the X axis plt.xticks (()) # delete the scale of the Y axis plt.yticks (()) plt.show ()

Computational complexity of ordinary least square method

This method calculates the solution of the least square by using the singular value decomposition (singular value decomposition,SVD) of X. If X is a matrix of (n < p), then the cost is

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