Dependent variables and independent variables refer to values that change in relationship to each other. The dependent variables are those that are observed to change in response to the independent variables. The independent variables are those that are deliberately manipulated to invoke a change in the dependent variables. In short, "if x is given, then y occurs", where x represents the independent variables and y represents the dependent variables. Image File history File links Question_book-3. ...

Depending on the context, independent variables are also known as predictor variables, regressors, controlled variables, manipulated variables, or explanatory variables.

The dependent variable is also known as the response variable, the regressand, the measured variable, the responding variable, the explained variable, or the outcome variable.

Mathematics

In mathematics, an independent variable is any of the arguments, i.e. "inputs", to a function. These are contrasted with the dependent variable, which is the value, i.e. the "output", of the function. Thus if we have a function f(x), then x is an independent variable, and f(x) is a dependent variable. The dependent variable depends on the independent variables; hence the names. For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Look up argument in Wiktionary, the free dictionary. ... This article is about functions in mathematics. ...

When there is only one independent variable and its values and those of the dependent variable are real numbers, then one conventionally draws the graph of the function with values of the independent variable on the horizontal axis—the x-axis—and the values of the dependent variable on the vertical axis—the y-axis (see Cartesian coordinates). In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... relation graph theory In mathematics, the graph of a function f is the collection of all ordered pairs (x,f(x)). In particular, graph means the graphical representation of this collection, in the form of a curve or surface, together with axes, etc. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

In calculus, the identification of the independent and dependent variable is significant, since the rate of change, or derivative, of the dependent variable is calculated with respect to the independent variable. For other uses, see Calculus (disambiguation). ... For other uses, see Derivative (disambiguation). ...

Experiments

In the design of experiments, independent variables are those whose values are controlled 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. The dependent variable on the other hand, usually cannot be directly controlled. The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. ... For other uses, see Observation (disambiguation). ...

Controlled variables are also important to identify in experiments. They are the variables that are kept constant to prevent their influence on the effect of the independent variable on the dependent. Every experiment has a controlling variable, and it is necessary to not change it, or the results of the experiment won't be valid.

In summary:

• The independent variable answers the question "What do I change?".
• The dependent variable answers the question "What do I observe?".
• The controlled variable answers the question "What do I keep the same?".

Examples

• If one were to measure the influence of different quantities of fertilizer on plant growth, the independent variable would be the amount of fertilizer used (the changing factor of the experiment). The dependent variables would be the growth in height and/or mass of the plant (the factors that are influenced in the experiment) and the controlled variables would be the type of plant, the type of fertilizer, the amount of sunlight the plant gets, the size of the pots, etc. (the factors that would otherwise influence the dependent variable if they were not controlled).

• In a study of how different doses of a drug affect the severity of symptoms, a researcher could compare the frequency and intensity of symptoms (the dependent variables) when different doses (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.

• In measuring the amount of color removed from beetroot samples at different temperatures, the dependent variable would be the amount of pigment removed, because it is depending on the temperature (which is the independent variable).

• In sociology, in measuring the effect of education on income or wealth, the dependent variable could be a level of income or wealth measured in monetary units (United States Dollars for example), and an independent variable could be the education level of the individual(s) who compose(s) the household (i.e. academic degrees).

In pharmacology an effective dose is the amount of drug that produces a therapeutic response in 50% of the people taking it. ... This article does not cite any references or sources. ... A symptom is a manifestation of a disease, indicating the nature of the disease, which is noticed by the patient. ... Sociology (from Latin: socius, companion; and the suffix -ology, the study of, from Greek λόγος, lógos, knowledge [1]) is the scientific or systematic study of society, including patterns of social relationships, social interaction, and culture[2]. Areas studied in sociology can range from the analysis of brief contacts between anonymous...

See also

• Variable
• Attribute
• Empirical method
• Test method
• Statistical independence