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Logistic Regression

TL;DR

Section titled “TL;DR”
  • Predicts the probability of a binary event (two possible outcomes) from input variables.
  • Uses a logistic (sigmoid) function to map input effects to probabilities between 0 and 1.
  • A probability threshold is applied to convert the estimated probability into a binary class.

Definition

Section titled “Definition”

Logistic regression is a type of statistical analysis used to predict the outcome of a binary event by modeling the relationship between a binary dependent variable and one or more independent variables using a logistic function.

Explanation

Section titled “Explanation”

Logistic regression models the probability that a binary-dependent variable takes one of two outcomes (for example, 0 or 1) based on independent variables such as age, gender, or usage metrics. The model uses a logistic function, which has the shape of a sigmoid curve, to produce probabilities ranging from 0 to 1 as the independent variables change. Those estimated probabilities can then be converted into a binary prediction by applying a chosen threshold. Unlike regression techniques for continuous outcomes, logistic regression uses a logistic (nonlinear) function rather than a linear function and is therefore appropriate for binary classification tasks.

Examples

Section titled “Examples”

Predicting disease

Section titled “Predicting disease”

The dependent variable is whether or not a patient will develop the disease (binary outcome). Independent variables can include age, gender, and medical history. Logistic regression provides a probability that the patient will develop the disease, supporting early intervention and treatment.

Predicting customer churn

Section titled “Predicting customer churn”

The dependent variable is whether or not a customer will churn (binary outcome). Independent variables can include customer satisfaction, length of time as a customer, and product usage. Logistic regression yields a probability of churn, allowing a business to target and retain high-risk customers.

Use cases

Section titled “Use cases”
  • Healthcare
  • Finance
  • Marketing

Notes or pitfalls

Section titled “Notes or pitfalls”
  • Logistic regression is used for predicting binary outcomes, whereas other regression techniques are used for predicting continuous outcomes.
  • The distinction stems from using a logistic (sigmoid) function for binary outcomes instead of a linear function.
Section titled “Related terms”
  • Logistic function
  • Sigmoid curve
  • Binary outcome
  • Linear regression