Statistics 简明教程

Statistics - Logistic Regression

逻辑回归是一种用于分析数据集中一个或多个独立变量决定结果的统计方法。该结果用二值变量（其中只有两个可能结果）测量。

Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. The outcome is measured with a dichotomous variable (in which there are only two possible outcomes).

Formula

其中——

Where −

  1. Response - Presence/Absence of characteristic.

  2. Predictor - Numeric variable observed for each case

  3. ${\beta = 0 \Rightarrow }$ P (Presence) is the same at each level of x.

  4. ${\beta \gt 0 \Rightarrow }$ P (Presence) increases as x increases

  5. ${\beta = 0 \Rightarrow }$ P (Presence) decreases as x increases.

Example

Problem Statement:

Problem Statement:

求解偏头痛的利扎曲坦的以下问题的逻辑回归

Solve the logistic regression of the following problem Rizatriptan for Migraine

响应 - 两小时内完全缓解疼痛（是/否）。

Response - Complete Pain Relief at 2 hours (Yes/No).

预测变量 - 剂量（毫克）：安慰剂 (0)、2.5、5、10

Predictor - Dose (mg): Placebo (0), 2.5,5,10

Dose

#Patients

#Relieved

%Relieved

0

67

2

3.0

2.5

75

7

9.3

5

130

29

22.3

10

145

40

27.6

Solution:

Solution:

有 ${\alpha = -2.490} 和 ${\beta = .165}, 我们有以下数据：

Having ${\alpha = -2.490} and ${\beta = .165}, we’ve following data:

Dose(${x}$)

${\pi(x)}$

0

0.03

2.5

0.09

5

0.23

10

0.29
logistic regression