LaTeX
b_0=\bar y-b_1\bar xVariables
- b0: intercept
- b1: slope
- x̄,ȳ: sample means
How to use this formula
Computes the intercept of a fitted simple regression line.
Important notes
- The intercept may have little practical meaning when x=0 is outside the data range.
- Use the same slope and means from the fitted sample.
Quick example
The fitted line is ŷ=b0+b1x.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The intercept may have little practical meaning when x=0 is outside the data range.
- For the Simple Regression Intercept, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
The fitted line is ŷ=b0+b1x.
Common mistakes
- Do not substitute sample and population quantities interchangeably in Simple Regression Intercept; map every symbol to its definition first.
- For the Simple Regression Intercept, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Simple Regression Intercept 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
b_0=\bar y-b_1\bar x. - 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 Simple Regression Intercept used for?
Computes the intercept of a fitted simple regression line.
Can I copy this formula as LaTeX?
Yes. Copy b_0=\bar y-b_1\bar x 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.