使用numpy/pandas的回归直线的斜率

import numpy as np
import pandas as pd

# 创建示例数据
data = {
    'X': [1, 2, 3, 4, 5],
    'Y': [2, 3, 5, 6, 8]
}
df = pd.DataFrame(data)

# 计算回归直线的斜率
X = df['X'].values.reshape(-1, 1)
Y = df['Y'].values.reshape(-1, 1)

# 使用numpy的线性代数模块计算斜率
X_mean = np.mean(X)
Y_mean = np.mean(Y)

numerator = np.sum((X - X_mean) * (Y - Y_mean))
denominator = np.sum((X - X_mean) ** 2)
slope = numerator / denominator

print(f"回归直线的斜率是: {slope[0][0]}")

from scipy import stats

# 计算Z-score
z_scores = np.abs(stats.zscore(df['Y']))

# 去除Z-score大于3的数据点
df_cleaned = df[(z_scores < 3)]

# 重新计算斜率
X_cleaned = df_cleaned['X'].values.reshape(-1, 1)
Y_cleaned = df_cleaned['Y'].values.reshape(-1, 1)

numerator_cleaned = np.sum((X_cleaned - np.mean(X_cleaned)) * (Y_cleaned - np.mean(Y_cleaned)))
denominator_cleaned = np.sum((X_cleaned - np.mean(X_cleaned)) ** 2)
slope_cleaned = numerator_cleaned / denominator_cleaned

print(f"去除异常值后的回归直线斜率是: {slope_cleaned[0][0]}")