Python 普通最小二乘法(OLS)进行多项式拟合的方法

import numpy as np
import pandas as pd
#import statsmodels.api as sm #方法一
import statsmodels.formula.api as smf #方法二
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
 
df = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
X = df[['TV', 'radio']]
y = df['sales']
 
#est = sm.OLS(y, sm.add_constant(X)).fit() #方法一
est = smf.ols(formula='sales ~ TV + radio', data=df).fit() #方法二
y_pred = est.predict(X)
 
df['sales_pred'] = y_pred
print(df)
print(est.summary()) #回归结果
print(est.params) #系数
 
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d') #ax = Axes3D(fig)
ax.scatter(X['TV'], X['radio'], y, c='b', marker='o')
ax.scatter(X['TV'], X['radio'], y_pred, c='r', marker='+')
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()

import numpy as np
import pandas as pd
import statsmodels.formula.api as smf
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
 
df = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
X = df['TV']
y = df['sales']
 
est = smf.ols(formula='sales ~ TV ', data=df).fit()
y_pred = est.predict(X)
print(est.summary())
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(X, y, c='b')
ax.plot(X, y_pred, c='r')
plt.show()

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn import linear_model
from mpl_toolkits.mplot3d import Axes3D
 
df = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
X = np.asarray(df[['TV', 'radio']])
y = np.asarray(df['sales'])
 
clf = linear_model.RidgeCV(alphas=[i+1 for i in np.arange(200.0)]).fit(X, y)
y_pred = clf.predict(X)
df['sales_pred'] = y_pred
print(df)
print("alpha=%s, 常数=%.2f, 系数=%s" % (clf.alpha_ ,clf.intercept_,clf.coef_))
 
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(df['TV'], df['radio'], y, c='b', marker='o')
ax.scatter(df['TV'], df['radio'], y_pred, c='r', marker='+')
ax.set_xlabel('TV')
ax.set_ylabel('radio')
ax.set_zlabel('sales')
plt.show()