Scikit-learn：我的线性回归不是一条直线，它是凌乱的

Question

我试图简单地绘制一条回归线，但是我得到了凌乱的线条。是因为我为模型安装了 2 个特征，所以唯一合适的可视化是 3d 平面？

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import load_boston
from sklearn.linear_model import LinearRegression

# prepare data
boston = load_boston()
X = pd.DataFrame(boston.data, columns=boston.feature_names)[['AGE','RM']]
y = boston.target

# split dataset into training and test data
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.20, random_state=33)

# apply linear regression on dataset
lm = LinearRegression()
lm.fit(X_train, y_train)
pred_train = lm.predict(X_train)
pred_test = lm.predict(X_test)

#plot relationship between RM and price
plt.scatter(X_train['RM'],
            y_train,
            c='g',
            s=40,
            alpha=0.5)
plt.plot(X_train['RM'], pred_train, color='r')
plt.title('Relationship between RM and Price')
plt.ylabel('Price')
plt.xlabel('RM')

Answer 1

你是对的。您正在训练多个功能，即 AGE 和 RM。但是你正在绘制一个只有一个特征的二维图，即 RM。尝试获得 3D 情节。通常，具有两个特征的线性回归会产生一个平面。这仍然是一个线性回归。这就是我们使用“超平面”一词的原因。它解析为单个特征的线，两个特征的平面等等。

这是 3D 的输出：

plt3d = plt.figure().gca(projection='3d')
plt3d.view_init(azim=135)
plt3d.plot_trisurf(X_train['RM'].values, X_train['AGE'].values, pred_train, alpha=0.7, antialiased=True)

Answer 2

问题在于，当您绘制时，您必须对参数进行排序。

'plt.plot(np.sort(X_train['RM']), np.sort(pred_train), color='r')'

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import load_boston
from sklearn.linear_model import LinearRegression

# prepare data
boston = load_boston()
X = pd.DataFrame(boston.data, columns=boston.feature_names)[['AGE','RM']]
y = boston.target

# split dataset into training and test data
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.20, random_state=33)

# apply linear regression on dataset
lm = LinearRegression()
lm.fit(X_train, y_train)
pred_train = lm.predict(X_train)
pred_test = lm.predict(X_test)

#plot relationship between RM and price
plt.scatter(X_train['RM'],
            y_train,
            c='g',
            s=40,
            alpha=0.5)
plt.plot(np.sort(X_train['RM']), np.sort(pred_train), color='r')
plt.title('Relationship between RM and Price')
plt.ylabel('Price')
plt.xlabel('RM')
plt.show()

结果： output-plot

如果你做一个 3d 绘图，你可能会很容易地看到协变量 RM 和年龄之间的关系3d-plot