> For the complete documentation index, see [llms.txt](https://machine-learning.paperspace.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://machine-learning.paperspace.com/wiki/logistic-regression.md).

# Logistic Regression

![Source: Technology of Computing](/files/-LwAVc1EdfmPMge5dlYC)

Logistic regression is a machine learning algorithm used for classification problems.  The term logistic is derived from the cost function (logistic function) which is a type of **sigmoid function** known for its characteristic S-shaped curve.  A logistic regression model predicts probability values which are mapped to two (binary classification) or more (multiclass classification) classes.

![Source: Analytics India Magazine](/files/-LwAYhg8-OqxqG7aWKhN)

![Formula of a sigmoid function](/files/-LwAgUAGfE21Zw1J-gnb)

Where:

* 1 = the curve's maximum value
* *S(z)*  = output between 0 and 1 (probability estimate)
* *z* = the input
* *e* = base of natural log (also known as Euler's number)

In multiclass classification with logistic regression, a **softmax function** is used instead of the sigmoid function.  

Like [linear regression](/wiki/linear-regression.md), [gradient descent](/wiki/gradient-descent.md) is typically used to optimize the values of the coefficients (each input value or column) by iteratively minimizing the loss of the model during training.  

The **decision boundary** is the acceptable threshold at which a probability can be mapped to a discrete class e.g. pass/fail or vegan/vegetarian/omnivore.  

The cost function in logistic regression is more complex than linear regression. For example, mean squared error would yield a non-convex function with many local minimums, making it difficult to optimize with gradient descent. **Cross entropy**, also called **log loss** is the cost function used with logistic regression.

**Regularization** is a technique used to prevent [overfitting ](/wiki/overfitting-vs-underfitting.md)by penalizing signals that provide too much explanatory power to a single feature.  Regularization is extremely important in logistic regression.

[Accuracy](/wiki/accuracy-and-loss.md#accuracy), a [model evaluation metric](/wiki/metrics-in-machine-learning.md), is used to measure how accurate a model's predictions are -- this is expressed as the number of true classifications divided by the total.

### Linear vs Logistic Regression

**Linear regression** predictions are continuous (e.g. test scores from 0-100).

**Logistic regression** predictions classify items where only specific values or classes are allowed (e.g. binary classification or multiclass classification). The model provides a probability score (confidence) with each prediction.


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://machine-learning.paperspace.com/wiki/logistic-regression.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.