Dependent and independent variables
concept in mathematical modeling, statistical modeling and experimental sciences
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are the outcome of the test they depend on, by some law or rule (e.g., by a mathematical function). Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter.
In pure mathematics
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number or set of numbers). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f(x).
It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. Functions with multiple outputs are often referred to as vector-valued functions.
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