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Variables used in an experiment or modelling can be divided into three types: "dependent variable", "independent variable", or other. The "dependent variable" represents the output or effect, or is tested to see if it is the effect. The "independent variables" represent the inputs or causes, or are tested to see if they are the cause. Other variables may also be observed for various reasons.
In calculus, a function is a map whose action is specified on variables. Take x and y to be two variables. A function f may map x to some expression in x. Assigning gives a relation between y and x. If there is some relation specifying y in terms of x, then y is known as a dependent variable (and x is an independent variable).
In mathematical modelling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In the simple stochastic linear model the term is the i th value of the dependent variable and is i th value of the independent variable. The term is known as the "error" and contains the variability of the dependent variable not explained by the independent variable.
With multiple independent variables, the expression is: , where n is the number of independent variables.
In simulation, the dependent variable is changed in response to changes in the independent variables.
An independent variable is also known as a "predictor variable", "regressor", "controlled variable", "manipulated variable", "explanatory variable", "exposure variable" (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or an "input variable."
Independent variable(s) may be of these kinds: continuous variable(s), binary/dichotomous variable(s), nominal categorical variable(s), ordinal categorical variable(s), among others.
A dependent variable is also known as a "response variable", "regressand", "measured variable", "responding variable", "explained variable", "outcome variable", "experimental variable", and "output variable".
A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that variable will be kept constant or monitored to try to minimise its effect on the experiment. Such variables may be called a "controlled variable" or "control variable" or "extraneous variable".
Extraneous variables, if included in a regression as independent variables, may aid a researcher with accurate response parameter estimation, prediction, and goodness of fit, but are not of substantive interest to the hypothesis under examination. For example, in a study examining the effect of post-secondary education on lifetime earnings, some extraneous variables might be gender, ethnicity, social class, genetics, intelligence, age, and so forth. A variable is extraneous only when it can be assumed (or shown) to influence the dependent variable. If included in a regression, it can improve the fit of the model. If it is excluded from the regression and if it has a non-zero covariance with one or more of the independent variables of interest, its omission will bias the regression's result for the effect of that independent variable of interest. This effect is called confounding or omitted variable bias; in these situations, design changes and/or statistical control is necessary.
Extraneous variables are often classified into three types:
In quasi-experiments, differentiating between dependent and other variables may be downplayed in favour of differentiating between those variables that can be altered by the researcher and those that cannot. Variables in quasi-experiments may be referred to as "extraneous variables", "subject variables", "experimental variables", "situational variables", "pseudo-independent variables", "ex post facto variables", "natural group variables" or "non-manipulated variables".
In modelling, variability that is not covered by the explanatory variable is designated by and is known as the "residual", "side effect", "error", "unexplained share", "residual variable", or "tolerance".
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