Definition:Regression
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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