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  2. Uncorrelatedness (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Uncorrelatedness...

    A set of two or more random variables , …, is called uncorrelated if each pair of them is uncorrelated. This is equivalent to the requirement that the non-diagonal elements of the autocovariance matrix K X X {\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} of the random vector X = [ X 1 …

  3. Multivariate random variable - Wikipedia

    en.wikipedia.org/wiki/Multivariate_random_variable

    The observations on the dependent variable are stacked into a column vector y; the observations on each independent variable are also stacked into column vectors, and these latter column vectors are combined into a design matrix X (not denoting a random vector in this context) of observations on the independent variables. Then the following ...

  4. Seemingly unrelated regressions - Wikipedia

    en.wikipedia.org/wiki/Seemingly_unrelated...

    where y i and ε i are R×1 vectors, X i is a R×k i matrix, and β i is a k i ×1 vector. Finally, if we stack these m vector equations on top of each other, the system will take the form [ 4 ] : eq. (2.2)

  5. Pairwise independence - Wikipedia

    en.wikipedia.org/wiki/Pairwise_independence

    Pairwise independent random variables with finite variance are uncorrelated. A pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) , (,) satisfies , (,) = (),

  6. Propagation of uncertainty - Wikipedia

    en.wikipedia.org/wiki/Propagation_of_uncertainty

    When the errors on x are uncorrelated, the general expression simplifies to =, where = is the variance of k-th element of the x vector. Note that even though the errors on x may be uncorrelated, the errors on f are in general correlated; in other words, even if Σ x {\displaystyle {\boldsymbol {\Sigma }}^{x}} is a diagonal matrix, Σ f ...

  7. Design of experiments - Wikipedia

    en.wikipedia.org/wiki/Design_of_experiments

    Example of orthogonal factorial design Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal.

  8. Multivariate normal distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_normal...

    In general, random variables may be uncorrelated but statistically dependent. But if a random vector has a multivariate normal distribution then any two or more of its components that are uncorrelated are independent. This implies that any two or more of its components that are pairwise independent are independent.

  9. Multicollinearity - Wikipedia

    en.wikipedia.org/wiki/Multicollinearity

    In a linear regression, the true parameters are =, = which are reliably estimated in the case of uncorrelated and (black case) but are unreliably estimated when and are correlated (red case). Perfect multicollinearity refers to a situation where the predictors are linearly dependent (one can be written as an exact linear function of the others ...