Definition:Independent Variable

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Real Function

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

Let $\map f x = y$.

Then $x$ is referred to as an independent variable.

Complex Function

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

Let $\map f z = w$.

Then $z$ is referred to as an independent variable (of $f$).

Also known as

An independent variable can also be referred to as an argument.

In the context of regressions, the independent variable is often called the cause variable.

Also see

  • Results about independent 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 $x$.