Final answer:
A SAS macro variable is not part of a data set but instead holds a text string and retains its value until altered. Unlike typical variables in math, which may continuously change depending on other factors, SAS macro variables are set by the user for dynamic text manipulation.
Step-by-step explanation:
The correct definition of a SAS macro variable is: b. A SAS macro variable is independent of a SAS data set and contains a text string. The value of the macro variable remains constant until you change it.
Variables in general have various applications in different fields. In mathematics, for instance, a variable represents a quantity that can take on different values, such as x or y in an equation. Variables can be numerical, where they take on values with equal units like weight in pounds, or categorical, where they represent categories, such as political party affiliation. The independent variable is one that is manipulated or controlled in an experiment, while the dependent variable responds to this manipulation. In the context of SAS programming, a macro variable's value is set by the user and does not change with each observation in a data set, distinguishing it from a data set variable. Macro variables are used to manage and manipulate text in SAS programs dynamically.