Definition:Regression

Definition

Let $X$ and $Y$ be random variables.

The regression of $Y$ on $X$ is the mapping defined and denoted as:

$\forall x \in X: \map f {Y, x} := \expect {Y \mid x}$

where $\expect {Y \mid x}$ denotes the expectation of $Y$ conditional upon $x$.

Informal Definition

A regression is a model which describes how the expectation of one random variable depends on one or more other random variables.

Cause Variable

Let $X$ and $Y$ be random variables.

Let $\map f {Y, x}$ denote the regression of $Y$ on $X$.

The random variable $X$ is known as the cause variable.

Effect Variable

Let $X$ and $Y$ be random variables.

Let $\map f {Y, x}$ denote the regression of $Y$ on $X$.

The random variable $Y$ is known as the effect variable.

Examples

Weight and Height of Babies

A function which gives the average weight of a baby given its height is an example of a regression.

Also see

• Results about regression can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): regression
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): regression