Covariate

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect. In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect. In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f ( x ) {displaystyle y=f(x)} . It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f ( x , y ) {displaystyle z=f(x,y)} , where z is a dependent variable and x and y are independent variables. Functions with multiple outputs are often referred to as vector-valued functions. In an experiment, a variable, manipulated by an experimenter, is called an independent variable. The dependent variable is the event expected to change when the independent variable is manipulated. In data mining tools (for multivariate statistics and machine learning), the dependent variable is assigned a role as target variable (or in some tools as label attribute), while an independent variable may be assigned a role as regular variable. Known values for the target variable are provided for the training data set and test data set, but should be predicted for other data. The target variable is used in supervised learning algorithms but not in unsupervised learning. In mathematical modeling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In the simple stochastic linear model y i = a + b x i + e i {displaystyle y_{i}=a+bx_{i}+e_{i}} the term y i {displaystyle y_{i}} is the i th value of the dependent variable and x i {displaystyle x_{i}} is the i th value of the independent variable. The term e i {displaystyle e_{i}} is known as the 'error' and contains the variability of the dependent variable not explained by the independent variable. With multiple independent variables, the model is y i = a + b x i , 1 + b x i , 2 + ⋯ + b x i , n + e i {displaystyle y_{i}=a+bx_{i,1}+bx_{i,2}+cdots +bx_{i,n}+e_{i}} , where n is the number of independent variables. In simulation, the dependent variable is changed in response to changes in the independent variables. Depending on the context, an independent variable is sometimes called a 'predictor variable', regressor, covariate, 'controlled variable', 'manipulated variable', 'explanatory variable', exposure variable (see reliability theory), 'risk factor' (see medical statistics), 'feature' (in machine learning and pattern recognition) or 'input variable.'In econometrics, the term 'control variable' is usually used instead of 'covariate'.