如何在由任意函数创建的 seaborn 散点图中添加一条线

Question

我希望能够在 python 中创建以下绘图（取自https://en.wikipedia.org/wiki/Logistic_regression#Logistic_model）

数据为：

hours = [
    0.50,
    0.75,
    1.00,
    1.25,
    1.50,
    1.75,
    1.75,
    2.00,
    2.25,
    2.50,
    2.75,
    3.00,
    3.25,
    3.50,
    4.00,
    4.25,
    4.50,
    4.75,
    5.00,
    5.50,
]

passed = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]
df = pd.DataFrame({"hours_study": hours, "passed": passed})

散点图很容易用以下方法创建：

sns.scatterplot(df.hours_study, df.passed)

给予

但我不确定如何在绘图中添加线条（在本例中为逻辑曲线）。

Answer 1

Matplotlib 的绘图可以在任何现有绘图上绘制曲线。要绘制逻辑函数，只需绘制1 / (1 + exp(-beta0 - beta1 * x))，其中 beta0 和 beta1 是对给定数据拟合逻辑函数的结果。 Scikit Learn的LogisticRegression是一个可以拟合这样一个函数并返回参数的函数：

import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
import seaborn as sns
import pandas as pd
import numpy as np

def draw_logistic_regression_curve(beta0, beta1, x, **kwargs):
    y = 1 / (1 + np.exp(-beta0 - beta1 * x))
    plt.plot(x, y, '-', **kwargs)


hours = np.array([0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 1.75, 2.00, 2.25, 2.50, 2.75,
                  3.00, 3.25, 3.50, 4.00, 4.25, 4.50, 4.75, 5.00, 5.50])
passed = np.array([0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1])
df = pd.DataFrame({"hours_study": hours, "passed": passed})
sns.scatterplot(df.hours_study, df.passed)

clf = LogisticRegression().fit(hours.reshape(-1, 1), passed)
beta0 = clf.intercept_ # -3.13952411
beta1 = clf.coef_[0] # 1.14860386
x = np.linspace(min(hours) - 0.5, max(hours) + 0.5, 500)
draw_logistic_regression_curve(beta0, beta1, x, color='crimson', label="Sklearn's default estimate")
draw_logistic_regression_curve(-4.0777, 1.5046, x, color='limegreen', label="Wikipedia's estimate")
plt.legend(loc='center right')
plt.show()