Independent variable
From Exampleproblems
In an experimental design, the independent variable (argument of the function) is the variable that is manipulated or selected by the experimenter to determine its relationship to an observed phenomenon (the dependent variable). In such an experiment, an attempt is made to find evidence that the values of the independent variable determine the values of the dependent variable (that which is being measured). 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 one 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 the dependent variable is the “presumed effect” of the independent variable.
The independent variable is also called the manipulated variable, predictor variable or exposure variable.
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Mathematics usage
When graphing a set of collected data, the independent variable is graphed on the x-axis (see Cartesian coordinates). In mathematics, and functional analysis in particular, it was traditional to define the set of independent variables as the only set of variables in a given context that can 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, x2 + y2 = R2, when computing derivatives it is nonetheless necessary to take a group of variables as “independent”, or else the derivative has no meaning).
Advertising Usage
An independent variable is what you know about the customer, or what you can observe.
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.
In measuring the acceleration of a vehicle, time is usually the independent variable and speed is the dependent variable. This is because when taking measurements, times are usually predetermined, and the resulting speed of the vehicle is recorded at those times. As far as the experiment is concerned, the speed is dependent on the time. Since the decision is made to measure the speed at certain times, time is the independent variable.
