## Logistic regression §

### What is logistic regression? §

• Logistic regression is a method for classification
• It helps classification: either 0 or 1
• It’s a specific type of generalized linear model(GLM)

### Why to use logistic regression, and not liner regression §

1. Because normal linear regression model on binary groups
1. Result is either 0 or 1, while linear regression is a continuous line which can go beyond 0 or 1 (beyond limit)
2. It poorly fits the data
2. Logistic regression is a transformed form of linear regression

### Sigmoid Function/Logistic Function §

#### What is Sigmoid Function (Logistic function) ? §

A function to transform any value to be between 0 and 1

#### How to use it in evaluation? §

We can set cutoff point at 0.5:

1. Below 0.5 belongs to 0
2. Above 0.5 belongs to 1
##### How to interpret when the point is in 0.5? §

There’s a 50/50 chance that the result is either 0 or 1.

#### Explain the math: where does it comes from? §

Linear regression model:

Transformed to Logistic regression model:

## Evaluate the model §

Using Confusion matrix

### Simple example of confusion matrix §

A simple example to predict disease:

n=165Predicted: NPredicted: Y
Actual: N50 (TN)10 (FP=Type-I)60
Actual: Y5 (FN=Type-II)100 (TP)105
55110

### Terminology §

• True Positives (TP)
• True Negatives (TN)
• False Positives (FP): Type-I error
• False Negatives (FN): Type-II error

In the example:

In the example: