<P> In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables . The dependent variables represent the output or outcome whose variation is being studied . The independent variables represent inputs or causes, i.e., potential reasons for variation or, in the experimental setting, the variable controlled by the experimenter . Models and experiments test or determine the effects that the independent variables have on the dependent variables . Sometimes, independent variables may be included for other reasons, such as for their potential confounding effect, without a wish to test their effect directly . </P> <P> 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). 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) (\ displaystyle y = f (x)). </P>

When can a variable be considered independent and dependent
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