Univariate

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The mathematical term univariate describes the dependence on only one variable . In statistics , the term is used in a related sense.

Use in math

In mathematics, univariate denotes an equation , expression, or function that only depends on one variable. In contrast, the term multivariate is used when an expression depends on more than one variable, in the special case of two variables sometimes also bivariate .

example

A function is univariate if it contains exactly one indefinite variable (e.g. ). ${\displaystyle f(x)=5x+\sin(x)}$

A function is bivariate if it contains exactly two indefinite variables (e.g. ). ${\displaystyle f(x,y)=3x^{2}+y+y^{3}}$

A function is multivariate when it contains several indefinite variables (e.g. ). ${\displaystyle f(x,y,z)=y^{2}+z-x^{2}}$

Use in statistics

Within statistics , univariate expresses that the measured variable under consideration is one-dimensional, even if it depends on several variables. This is particularly the case when the measured variable is the one-dimensional dependent variable of a random experiment or the characteristic value of a one-dimensional random variable . The observations can then be displayed individually.

Accordingly, multivariate expresses that the measured variable is multidimensional ( multivariate distribution , multivariate method ), and bivariate that the measured variable is two-dimensional ( bivariate distribution ). The observations can then be represented either in the form of a vector or using several one-dimensional measured variables.

In statistics, the term univariate is used for relationships with only one criterion, regardless of the number of predictors that predict this criterion. The term multivariate , on the other hand, describes relationships with several criteria, but also independent of the number of predictors that predict the criteria. In addition to the question of scaling , a criterion ( variable ) in univariate statistics can be described by two important measures (also key figures or parameters ): location and scatter . Measures of position (e.g. mode , median , arithmetic mean ) describe the area in which the data are centrally arranged. Scatter measures (e.g. range , interquartile range , standard deviation ) describe how similar or differently the data are scattered.

example

Consider the case that one measures the height and weight of different test subjects.

If one examines these two variables separately, for example by calculating the mean value of the weight or the mean value of the body height of all test persons, then this is a univariate analysis.

If, on the other hand, you consider the height and weight of each person together and would like to describe them using a bivariate distribution, for example, then this is a bivariate analysis, since the measured variable (height together with weight) is two-dimensional.