import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model
from sklearn.preprocessing import PolynomialFeatures
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# 讀取數(shù)據(jù)集
datasets_X = []
datasets_Y = []
fr = open('多項(xiàng)式線性回歸.csv','r')
lines = fr.readlines()
for line in lines:
? ? items = line.strip().split(',')
? ? datasets_X.append(int(items[0]))
? ? datasets_Y.append(int(items[1]))
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length = len(datasets_X)
datasets_X = np.array(datasets_X).reshape([length,1])
datasets_Y = np.array(datasets_Y)
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minX = min(datasets_X)
maxX = max(datasets_X)
X = np.arange(minX,maxX).reshape([-1,1])
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poly_reg = PolynomialFeatures(degree = 2) ? ? ?#degree=2表示建立datasets_X的二次多項(xiàng)式特征X_poly。
X_poly = poly_reg.fit_transform(datasets_X) ? ?#使用PolynomialFeatures構(gòu)造x的二次多項(xiàng)式X_poly
lin_reg_2 = linear_model.LinearRegression()
lin_reg_2.fit(X_poly, datasets_Y) ? ? ? ? ? #然后創(chuàng)建線性回歸，使用線性模型（linear_model）學(xué)習(xí)X_poly和y之間的映射關(guān)系
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print(X_poly)
print(lin_reg_2.predict(poly_reg.fit_transform(X)))
print('Coefficients:', lin_reg_2.coef_) ? ? ?#查看回歸方程系數(shù)(k)
print('intercept:', lin_reg_2.intercept_) ? ?##查看回歸方程截距(b)
print('the model is y={0}+({1}*x)+({2}*x^2)'.format(lin_reg_2.intercept_,lin_reg_2.coef_[0],lin_reg_2.coef_[1]))
# 圖像中顯示
plt.scatter(datasets_X, datasets_Y, color = 'red') ?#scatter函數(shù)用于繪制數(shù)據(jù)點(diǎn)，這里表示用紅色繪制數(shù)據(jù)點(diǎn)；
#plot函數(shù)用來(lái)繪制回歸線，同樣這里需要先將X處理成多項(xiàng)式特征；
plt.plot(X, lin_reg_2.predict(poly_reg.fit_transform(X)), color = 'blue')
plt.xlabel('Area')
plt.ylabel('Price')
plt.show()

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
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warnings.filterwarnings(action="ignore", module="sklearn")
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dataset = pd.read_csv('多項(xiàng)式線性回歸.csv')
X = np.asarray(dataset.get('x'))
y = np.asarray(dataset.get('y'))
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# 劃分訓(xùn)練集和測(cè)試集
X_train = X[:-2]
X_test = X[-2:]
y_train = y[:-2]
y_test = y[-2:]
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# fit_intercept 為 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')
# 均方誤差
print("Mean squared error: %.2f" % mean_squared_error(y_test, y_test_pred1))
# r2 score，0,1之間，越接近1說(shuō)明模型越好，越接近0說(shuō)明模型越差
print('Variance score: %.2f' % r2_score(y_test, y_test_pred1), '\n')
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# fit_intercept 為 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')
# 均方誤差
print("Mean squared error: %.2f" % mean_squared_error(y_test, y_test_pred2))
# r2 score，0,1之間，越接近1說(shuō)明模型越好，越接近0說(shuō)明模型越差
print('Variance score: %.2f' % r2_score(y_test, y_test_pred2), '\n')
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plt.xlabel('x')
plt.ylabel('y')
# 畫(huà)訓(xùn)練集的散點(diǎn)圖
plt.scatter(X_train, y_train, alpha=0.8, color='black')
# 畫(huà)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()

while fit_intercept is True:................
Coefficients: ?[ 0.00000000e+00 -3.70858180e-04 ?2.78609637e-05]
Intercept: 204.25470490804574
the model is: y = ?204.25470490804574 ?+ ?-0.00037085818009180454 * X
Mean squared error: 26964.95
Variance score: -3.61?
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while fit_intercept is False:..........................................
Coefficients: ?[ 2.04254705e+02 -3.70858180e-04 ?2.78609637e-05]
Intercept: 0.0
the model is: y = ?204.2547049080572 + -0.0003708581801012066 * X + ?2.7860963722809286e-05 * X^2
Mean squared error: 7147.78
Variance score: -0.22?