Let $f: \R \to \R$ be a real function.
Let $\map f x = y$.
Then $y$ is referred to as a dependent variable.
Let $f: \C \to \C$ be a complex function.
Let $\map f z = w$.
Then $w$ is referred to as the dependent variable (of $f$).
Also known as
A dependent variable can also be referred to as a response variable.
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 $x$.
- 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 1$. Introduction
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Functions
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: response variable