Variable

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function  are  and . A function having a single variable is said to be univariate, one having two variables is said to be bivariate, and one having two or more variables is said to be multivariate. In a polynomial, the variables correspond to the base symbols themselves stripped of coefficients and any powers or products.

In literature, one often distinguishes between dependent and independent variables, the latter of which usually represents the inputs or quantities whose causality is being tested experimentally while the former generally represents the output whose values are altered by causal phenomena. Similar to the multivariate example mentioned above, the equation  has  as a dependent variable due to the fact that its value depends on what values and  are plugged into ;  and  are both independent variables due to their having no dependences within the equation.

The variables in a polynomial can be extracted using the Wolfram Language command Variables[poly].

In general, mathematical functions may have a number of arguments. Arguments that are typically varied when plotting, performing mathematical operations, etc., are termed "variables," while those that are not explicitly varied in situations of interest are termed "parameters." For example, in the standard equation of an ellipse

 and  are generally considered variables and  and  are considered parameters. The decision on which arguments to consider variables and which to consider parameters may be historical or may be based on the application under consideration. However, the nature of a mathematical function may change depending on which choice is made. For example, the above equation is quadratic in  and , but if  and  are instead considered as variables, the resulting equation

is quartic in  and .

REFERENCES:

Dodge, Y.; Cox, D.; Commenges, D.; Davidson, A; Solomon, P.; and Wilson, S. (Eds.). The Oxford Dictionary of Statistical Terms, 6th Edition. New York: Oxford University Press, 2006.