Dependent and independent variables
In experimental design an independent variable is that variable which is measured, manipulated, or selected by the experimenter to determine its relationship to an observed phenomenon (the dependent variable). In other words, the experiment will attempt to find evidence that the values of the independent variable determine the values of the dependent variable. The independent variable can be changed as required, and its values do not represent a problem requiring explanation in an analysis, but are taken simply as given.
More generally, the independent variable is the thing that someone actively controls/changes; while the dependent variable is the thing that changes as a result. In other words, the independent variable is the "presumed cause", while dependent variable is the "presumed effect" of the independent variable.
This format is most used in Standard scientific experiments to help understand what is going on.
Examples
In a study of how different dosages of a drug are related to the severity of symptoms of a disease, a researcher could compare the frequency and intensity of varying symptoms (the dependent variables) when varying dosages (the independent variable) are administered, and attempt to draw a conclusion.
The independent variable is also called the predictor variable. Independent variable is the most common name given for this item.
Mathematics usage
When graphing a set of collected data, the independent variable is graphed on the x-axis (see Cartesian coordinates).
In mathematics, in functional analysis, it was traditional to define the set of independent variables as the only set of variables in a given context which could be altered. For, even though any function defines a bilateral relation between variables, and it's even true that two variables might be connected by an implicit equation (for instance, cf. the definition of a circle, ), when computing derivatives it is nonetheless necessary to take a group of variables as "independent", or else the derivative has no meaning.
