covariance

(noun)

A measure of how much two random variables change together.

Related Terms

Examples of covariance in the following topics:

  • Additional Properties of the Binomial Distribution

    • In this section, we'll look at the median, mode, and covariance of the binomial distribution.
    • If two binomially distributed random variables X and Y are observed together, estimating their covariance can be useful.
    • Using the definition of covariance, in the case n = 1 (thus being Bernoulli trials) we have .

  • Models with Both Quantitative and Qualitative Variables

    • A regression model that contains a mixture of quantitative and qualitative variables is called an Analysis of Covariance (ANCOVA) model.
    • They are the statistic control for the effects of quantitative explanatory variables (also called covariates or control variables).
    • Covariance is a measure of how much two variables change together and how strong the relationship is between them.
    • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
    • However, even with the use of covariates, there are no statistical techniques that can equate unequal groups.

  • Two Regression Lines

    • ANCOVA can be used to compare regression lines by testing the effect of a categorial value on a dependent variable, controlling the continuous covariate.
    • A method known as analysis of covariance (ANCOVA) can be used to compare two, or more, regression lines by testing the effect of a categorial value on a dependent variable while controlling for the effect of a continuous covariate.
    • Covariance is a measure of how much two variables change together and how strong the relationship is between them.
    • Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression.
    • ANCOVA evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV), while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV).

  • Making Risk Adjustments

    • The beta coefficient, expressed as a covariance, is the risk of a new project in relation to the risk of the market as a whole.
    • The beta of an investment is equal to the covariance between the rate of return of the investment, r(a), and that of the portfolio, r(p).

  • Multivariate Testing

    • Because measures of this type are usually highly correlated, it is not advisable to conduct separate univariate $t$-tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis (type I error).
    • where $n$ is the sample size, $\bar { x }$ is the vector of column means and $S$ is a $m \times m$ sample covariance matrix.

  • Tensors

    • We can find similar results for mixed tensors and covariant tensors.
    • Right now, we can build a contravariant vector by taking a set of coordinates $x^i$ for a event in spacetime and we can construct a covariant vector by applying the metric $\eta_{\mu\nu}$ to lower the index of the vector.
    • How else can we make a covariant vector?
    • Because transforms as a contravariant vector and doesn't transform, must transform as a covariant vector.

  • Two-mode correspondence analysis

    • Factoring methods operate on the variance/covariance or correlation matrices among actors and events.
    • When the connections of actors to events is measured at the binary level (which is very often the case in network analysis) correlations may seriously understate covariance and make patterns difficult to discern.

  • Making Inferences About the Slope

    • Specifically, the interpretation of $m$ is the expected change in $y$ for a one-unit change in $x$ when the other covariates are held fixed—that is, the expected value of the partial derivative of $y$ with respect to $x$.
    • This may imply that some other covariate captures all the information in $x$, so that once that variable is in the model, there is no contribution of $x$ to the variation in $y$.
    • This would happen if the other covariates explained a great deal of the variation of $y$, but they mainly explain said variation in a way that is complementary to what is captured by $x$.

  • Attribution

    • Two of the most well-known models are the covariation model and the three-dimensional model.
    • The covariation principle states that people attribute behavior to the factors that covary with that behavior.

  • Summary

    • In simple structures (such as the star, circle, or line), these advantages tend to covary.