Overview
Logistic Regression is a regression technique which fits a logistic function to a set of data. It is used primarily to model dichotomous data, that is, data where the response variable can take one of only two values.
Logistic Regression is used to model situations where the response variable is dichotomous, i.e. can take on two values. These types of models occur frequently across several fields. In medicine, the response variable could be presence of a disease. In insurance, the response could be the occurence of the modeled event (such as death). In finance, logistic regression is often used to model loan default.
The Logistic and Sigmoid Functions
The sigmoid function is the function that is fitted to the data
{% sigmoid(x) = 1 / (1 - \exp(x)) %}
The logistic function is the inverse of the sigmoid function.
{% Logit(x) = log(\frac{x}{1-x}) %}
Topics
- Fitting the Model is typically done using Newtons algorithm.
- Model Diagnostics - shows ways to test the effectiveness of the regression.
- Logistic Regression and Machine Learning - discusses the use of logistic regression within the context of machine learning classification.
- Multinomial Regression