Definition:Dependent Variable

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This page is about dependent variable. For other uses, see dependent.

Definition

Real Function

Let $f: \R \to \R$ be a real function.

Let $\map f x = y$.

Then $y$ is referred to as a dependent variable.


Complex Function

Let $f: \C \to \C$ be a complex function.

Let $\map f z = w$.


Then $w$ is referred to as the dependent variable (of $f$).


Statistics

In the field of statistics, the concept has a more specialized definition:


Context: statistics.

A variable which is believed to be possibly influenced by certain other explanatory variables is referred to as a dependent variable.

In regression, a relationship is sought between the dependent variable and the explanatory variables.

The purpose is usually to enable the value of the dependent variable to be predicted from the given values of the explanatory variables.


Also known as

A dependent variable can also be referred to as a response variable.

The particular value taken by the dependent variable for a specific value of the independent variable is called the image.


Also see

  • Results about dependent variables can be found here.


Linguistic Note

The terms independent variable and dependent variable arise from the idea that it is usual to consider that $x$ can be chosen independently of $y$, but having chosen $x$, the value of $y$ then depends on the value of $x$.


Sources

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