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An independent variable is presumed to cause or determine a dependent variable. It 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. Thus independent variables act as catalysts for dependent variables. In other words, the independent variable is the "presumed cause", while dependent variable is the "presumed effect" of the independent variable.
In experimental design, an independent variable is a random variable used to define treatment groups.
Examples
1 The wages of an employee depend on the time worked. Time is the independent variable that varies among employees, but once a specific time is given, the amount of wages is set by a calculation, and one is not free to choose its value because its value is dependent on the time chosen.
2 In a study of how different dosages of a drug are related to the severity of symptoms of a disease, a measure of the severity of the symptoms of the disease is a dependent variable and the administration of the drug in specified doses is the independent variable. Researcher will compare the different values of the dependant variable (severity of the symptoms) and attempt to draw a conclusion.
3 Someone is having a problem with an over amount of saliva build up. The saliva build up would be the dependent variable. The dependant variable will change according to how to independent variable is used on it. The drug given to a person for their saliva problem, will be the independent variable. The independent variable can be changed in terms of (dosage, amount, frequency, intake, etc.) So with the proper amount of the independent variable, the dependent variable will change for the better, or perhaps worse if all goes wrong. The independent variable acts as a catalyst which alters the current state of the saliva build up within the individual's body.
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, 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.
See also
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