LaTeX
\sigma(z)=\frac{1}{1+e^{-z}}Variables
- z: linear predictor
- σ(z): transformed value
How to use this formula
Maps a real-valued score to a number between zero and one.
Important notes
- A probability interpretation depends on the model and calibration.
Quick example
At z=0, σ(z)=0.5.
Applicability, worked calculation, and verification
Assumptions and domain checks
- A probability interpretation depends on the model and calibration.
- For the Logistic Sigmoid, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Logistic Sigmoid, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
At z=0, σ(z)=0.5.
Common mistakes
- When copying Logistic Sigmoid, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Logistic Sigmoid, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Logistic Sigmoid in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\sigma(z)=\frac{1}{1+e^{-z}}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Logistic Sigmoid used for?
Maps a real-valued score to a number between zero and one.
Can I copy this formula as LaTeX?
Yes. Copy \sigma(z)=\frac{1}{1+e^{-z}} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.