Univariate
Encyclopedia
In mathematics, univariate refers to an expression
Expression (mathematics)
In mathematics, an expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Symbols can designate numbers , variables, operations, functions, and other mathematical symbols, as well as punctuation, symbols of grouping, and other syntactic...

, equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

, function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

 or polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

 of only one variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

. Objects of any of these types but involving more than one variable may be called multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for instance the study of roots of a polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

 only has a meaning in the univariate case.

The term is commonly used in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 to distinguish a distribution
Frequency distribution
In statistics, a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of...

 of one variable from a distribution of several variables, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar
Scalar (mathematics)
In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector....

 component. In time series analysis, the term is applied with a whole time series as the object referred to: thus a univariate time series refers to the set of values over time of a single quantity. Correspondingly, a "multivariate time series" refers to the changing values over time of several quantities. Thus there is a minor conflict of terminology since the values within a univariate time series may be treated using certain types of multivariate statistical analyses
Multivariate statistics
Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis...

 and may be represented using multivariate distributions.

See also

  • Univariate analysis
    Univariate analysis
    Univariate analysis is the simplest form of quantitative analysis. The analysis is carried out with the description of a single variable and its attributes of the applicable unit of analysis...

  • Univariate distribution
    Univariate distribution
    In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector.-Further reading:...

  • Univariate binary model
  • Multivariate statistics
    Multivariate statistics
    Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis...

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