人工智能-Python实现多项式回归

　　import matplotlib.pyplot as plt

　　from sklearn.preprocessing import PolynomialFeatures

　　from sklearn.pipeline import Pipeline

　　from sklearn.linear_model import LinearRegression

　　from sklearn.metrics import mean_squared_error, r2_score

　　import numpy as np

　　import pandas as pd

　　import warnings

　　warnings.filterwarnings(action="ignore", module="sklearn")

　　dataset = pd.read_csv('多项式线性回归.csv')

　　X = np.asarray(dataset.get('x'))

　　y = np.asarray(dataset.get('y'))

　　# 划分训练集和测试集

　　X_train = X[:-2]

　　X_test = X[-2:]

　　y_train = y[:-2]

　　y_test = y[-2:]

　　# fit_intercept 为 True

　　model1 = Pipeline([('poly', PolynomialFeatures(degree=2)), ('linear', LinearRegression(fit_intercept=True))])

　　model1 = model1.fit(X_train[:, np.newaxis], y_train)

　　y_test_pred1 = model1.named_steps['linear'].intercept_ + model1.named_steps['linear'].coef_[1] * X_test

　　print('while fit_intercept is True:................')

　　print('Coefficients: ', model1.named_steps['linear'].coef_)

　　print('Intercept:', model1.named_steps['linear'].intercept_)

　　print('the model is: y = ', model1.named_steps['linear'].intercept_, ' + ', model1.named_steps['linear'].coef_[1],

　　'* X')

　　# 均方误差

　　print("Mean squared error: %.2f" % mean_squared_error(y_test, y_test_pred1))

　　# r2 score，0,1之间，越接近1说明模型越好，越接近0说明模型越差

　　print('Variance score: %.2f' % r2_score(y_test, y_test_pred1), '

　　')

　　# fit_intercept 为 False

　　model2 = Pipeline([('poly', PolynomialFeatures(degree=2)), ('linear', LinearRegression(fit_intercept=False))])

　　model2 = model2.fit(X_train[:, np.newaxis], y_train)

　　y_test_pred2 = model2.named_steps['linear'].coef_[0] + model2.named_steps['linear'].coef_[1] * X_test +

　　model2.named_steps['linear'].coef_[2] * X_test * X_test

　　print('while fit_intercept is False:..........................................')

　　print('Coefficients: ', model2.named_steps['linear'].coef_)

　　print('Intercept:', model2.named_steps['linear'].intercept_)

　　print('the model is: y = ', model2.named_steps['linear'].coef_[0], '+', model2.named_steps['linear'].coef_[1], '* X + ',

　　model2.named_steps['linear'].coef_[2], '* X^2')

　　# 均方误差

　　print("Mean squared error: %.2f" % mean_squared_error(y_test, y_test_pred2))

　　# r2 score，0,1之间，越接近1说明模型越好，越接近0说明模型越差

　　print('Variance score: %.2f' % r2_score(y_test, y_test_pred2), '

　　')

　　plt.xlabel('x')

　　plt.ylabel('y')

　　# 画训练集的散点图

　　plt.scatter(X_train, y_train, alpha=0.8, color='black')

　　# 画模型

　　plt.plot(X_train, model2.named_steps['linear'].coef_[0] + model2.named_steps['linear'].coef_[1] * X_train +

　　model2.named_steps['linear'].coef_[2] * X_train * X_train, color='red',

　　linewidth=1)

　　plt.show()