Variate and Variable

noun

• A variable quantity that is random.
  • synonyms: random variable, variant, stochastic variable, chance variable

variate is a single item in a group.

noun

• Something that is likely to vary; something that is subject to variation.
  • usage: "the weather is one variable to be considered"
• A quantity that can assume any of a set of values.
  • synonyms: variable quantity
• A star that varies noticeably in brightness.
  • synonyms: variable star
• A symbol (like x or y) that is used in mathematical or logical expressions to represent a variable quantity.

adjective

• Liable to or capable of change.
  • usage: "rainfall in the tropics is notoriously variable"; "variable winds"; "variable expenses"
• Marked by diversity or difference.
  • usage: "the varying angles of roof slope"; "nature is infinitely variable"
  • synonyms: varying
• Used of a device) designed so that a property (as e. G. Light) can be varied. (
  • usage: "a variable capacitor"; "variable filters in front of the mercury xenon lights"

• (n.) Those parts of the sea where a steady wind is not expected, especially the parts between the trade-wind belts.
• (n.) That which is variable; that which varies or is subject to change.
• (a.) Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
• (n.) A quantity which may increase or decrease; a quantity which admits of an infinite number of values in the same expression; a variable quantity; as, in the equation x2 - y2 = R2, x and y are variables.
• (a.) Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
• (n.) A shifting wind or one that varies in force.

Variable is an element in a model. For example, in the model RS&Pt+1 = a + b Tbill t + et, where RS&Pt+1 is the return on the S&P in month t+1 and Tbill is the Tbill return at month t, both RS&P and Tbill are "variables" because they change through time; i. E., they are not constant.