Definition

logistic regression

Contributor(s): Linda Rosencrance, Ed Burns

Logistic regression is a statistical analysis method used to predict a data value based on prior observations of a data set. Logistic regression has become an important tool in the discipline of machine learning. The approach allows an algorithm being used in a machine learning application to classify incoming data based on historical data. As more relevant data comes in, the algorithm should get better at predicting classifications within data sets. Logistic regression can also play a role in data preparation activities by allowing data sets to be put into specifically predefined buckets during the extract, transform, load (ETL) process in order to stage the information for analysis.

A logistic regression model predicts a dependent data variable by analyzing the relationship between one or more existing independent variables. For example, a logistic regression could be used to predict whether a political candidate will win or lose an election or whether a high school student will be admitted to a particular college.

The resulting analytical model can take into consideration multiple input criteria. In the case of college acceptance, the model could consider factors such as the student’s grade point average, SAT score and number of extracurricular activities. Based on historical data about earlier outcomes involving the same input criteria, it then scores new cases on their probability of falling into a particular outcome category.

Purpose and examples of logistic regression

Logistic regression is one of the most commonly used machine learning algorithms for binary classification problems, which are problems with two class values, including predictions such as “this or that,” “yes or no” and “A or B.”

The purpose of logistic regression is to estimate the probabilities of events, including determining a relationship between features and the probabilities of particular outcomes.

One example of this is predicting if a student will pass or fail an exam when the number of hours spent studying is provided as a feature and the variables for the response has two values: pass and fail.

Organizations can use insights from logistic regression outputs to enhance their business strategies so they can achieve their business goals, including reducing expenses or losses and increasing ROI in marketing campaigns, for example.

An e-commerce company that mails expensive promotional offers to customers would like to know whether a particular customer is likely to respond to the offers or not. For example, they’ll want to know whether that consumer will be a “responder” or a “non responder.” In marketing, this is called propensity to respond modeling.

Likewise, a credit card company develops a model to decide whether to issue a credit card to a customer or not will try to predict whether the customer is going to default or not on the credit card based on such characteristics as annual income, monthly credit card payments and number of defaults. In banking parlance, this is known as default propensity modeling.

Uses of logistic regression

Logistic regression has become particularly popular in online advertising, enabling marketers to predict the likelihood of specific website users who will click on particular advertisements as a yes or no percentage.

Logistic regression can also be used in:

  • Healthcare to identify risk factors for diseases and plan preventive measures.
  • Weather forecasting apps to predict snowfall and weather conditions.
  • Voting apps to determine if voters will vote for a particular candidate.
  • Insurance to predict the chances that a policy holder will die before the term of the policy expires based on certain criteria, such as gender, age and physical examination.
  • Banking to predict the chances that a loan applicant will default on a loan or not, based on annual income, past defaults and past debts.

Logistic regression vs. linear regression

The main difference between logistic regression and linear regression is that logistic regression provides a constant output, while linear regression provides a continuous output.

In logistic regression, the outcome, such as a dependent variable, only has a limited number of possible values. However, in linear regression, the outcome is continuous, which means that it can have any one of an infinite number of possible values. 

Logistic regression is used when the response variable is categorical, such as yes/no, true/false and pass/fail. Linear regression is used when the response variable is continuous, such as number of hours, height and weight.

For example, given data on the time a student spent studying and that student’s exam scores, logistic regression and linear regression can predict different things.

With logistic regression predictions, only specific values or categories are allowed. Therefore, logistic regression can predict whether the student passed or failed. Since linear regression predictions are continuous, such as numbers in a range, it can predict the student’s test score on a scale of 0 -100.

This was last updated in May 2019

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