An independent variable is a variable whose values don't depend on changes in other variables. This is in contrast to the definition of dependent variable.
As with dependent variables, the notion of an independent variable comes up in a variety of contexts. In the case of univariate
functions 
,
the input variable 
is an independent variable. Similarly, 
are all independent variables in the case of the
multivariate function 
.
In experimental settings, the independent variable usually represents the inputs or quantities whose causality is being tested. As a result, independent variables are also known by a variety of synonyms including explanatory variable, predictor variable, controlled variable, manipulated variable, and input variable.
Worth noting is that the term independent variable has nothing to do with statistical or probabilistic independence.
