Dependent and independent variables

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question.[lower-alpha 1] In this sense, some common independent variables are time, space, density, mass, fluid flow rate,[1][2] and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable).[3]

Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that the experimenter manipulates[clarification needed] can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.

In single variable calculus, a function is typically graphed with the horizontal axis representing the independent variable and the vertical axis representing the dependent variable.[4] In this function, y is the dependent variable and x is the independent variable.