Python实现多项式回归

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model
from sklearn.preprocessing import PolynomialFeatures
 
 
# 读取数据集
datasets_X = []
datasets_Y = []
fr = open('多项式线性回归.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]))
 
length = len(datasets_X)
datasets_X = np.array(datasets_X).reshape([length,1])
datasets_Y = np.array(datasets_Y)
 
minX = min(datasets_X)
maxX = max(datasets_X)
X = np.arange(minX,maxX).reshape([-1,1])
 
 
poly_reg = PolynomialFeatures(degree = 2)      #degree=2表示建立datasets_X的二次多项式特征X_poly。
X_poly = poly_reg.fit_transform(datasets_X)    #使用PolynomialFeatures构造x的二次多项式X_poly
lin_reg_2 = linear_model.LinearRegression()
lin_reg_2.fit(X_poly, datasets_Y)           #然后创建线性回归，使用线性模型（linear_model）学习X_poly和y之间的映射关系
 
print(X_poly)
print(lin_reg_2.predict(poly_reg.fit_transform(X)))
print('Coefficients:', lin_reg_2.coef_)      #查看回归方程系数(k)
print('intercept:', lin_reg_2.intercept_)    ##查看回归方程截距(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]))
# 图像中显示
plt.scatter(datasets_X, datasets_Y, color = 'red')  #scatter函数用于绘制数据点，这里表示用红色绘制数据点；
#plot函数用来绘制回归线，同样这里需要先将X处理成多项式特征；
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
 
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), '\n')
 
# 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), '\n')
 
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()

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 
 
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