---
tag: 41FVC4P5JB
kind: concept
name: Linear regression
msc: [62J05]
specializes: [K3AMMSY8DD]
sources:
  - url: https://en.wikipedia.org/wiki/Linear_regression
same_as:
  wikidata: Q10861030
  wikipedia: Linear regression
---

## Summary

Linear regression models a response variable as a linear function of explanatory variables plus a random error.
The model is linear in the unknown coefficients, not necessarily in the explanatory variables themselves.
Its coefficients are most often estimated by [[ordinary least squares|YM708KHV2W]].
It is one of the most widely used statistical models, and the base of the [[general linear model|A06SGFCSCE]] and its extensions.

## Explanations

### L1 human

Plot the heights of children against their ages, and the points lie roughly along a line.
Linear regression describes the height as an intercept plus a slope times the age, plus a random deviation for each child.
The slope says how much height increases per year on average.
With several explanatory variables, such as age and parents' heights, the line becomes a plane or a higher-dimensional flat surface.