如何计算python线性回归模型中斜率的99%置信区间? [英] How to calculate the 99% confidence interval for the slope in a linear regression model in python?

问题描述

我们有以下线性回归:y ~ b0 + b1 * x1 + b2 * x2.我知道 Matlab 中的回归函数会计算它，但 numpy 的 linalg.lstsq 不会(https://docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html).

We have following linear regression: y ~ b0 + b1 * x1 + b2 * x2. I know that regress function in Matlab does calculate it, but numpy's linalg.lstsq doesn't (https://docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html).

推荐答案

StatsModels 的 RegressionResults 有一个 conf_int() 方法.这里有一个使用它的例子(他们的普通最小二乘法 示例):

StatsModels' RegressionResults has a conf_int() method. Here an example using it (minimally modified version of their Ordinary Least Squares example):

import numpy as np, statsmodels.api as sm

nsample = 100
x = np.linspace(0, 10, nsample)
X = np.column_stack((x, x**2))
beta = np.array([1, 0.1, 10])
e = np.random.normal(size=nsample)

X = sm.add_constant(X)
y = np.dot(X, beta) + e

mod = sm.OLS(y, X)
res = mod.fit()
print res.conf_int(0.01)   # 99% confidence interval

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