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# 2.1.12.1.Logistic regression Theory

## 1. Introduction

* Logistic regression是一種用來做classification的方式
  * Logistic regression讓我們可以解決預測離散類別 (discrete categories)的分類問題
  * 傳統的二元分類問題有0或1兩個種類
* 我們不可以用Linear regression來做二元分類
  * 擬合後會出現小於0或大於1的值
  * Logistic function (Sigmoid function)的值域介於0跟1之間, 因此一般會使用Logistic regression

## 2.Model evaluation

* 在使用training data訓練完Logistic regression的模型後, 將會使用testing data來評估模型的performance
* Confusion matrix

    ![](/files/-M4M0UyWMzPBH4Irb0kf)

  * 真正的精度 (accuracy)的算法：
    * (TP + TN)/total = 150/165 = 0.91
  * Misclassification rate: 
    * (FP + FN)/total = 15/165 = 0.09
  * False Positive: Type 1 error 
  * False Negative: Type 2 error


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