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  2. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/.../Pearson_correlation_coefficient

    Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.

  3. Correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Correlation_coefficient

    A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.

  4. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    The most familiar measure of dependence between two quantities is the Pearson product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by taking the ratio of the covariance of the two variables in question of our numerical dataset, normalized to ...

  5. Bivariate analysis - Wikipedia

    en.wikipedia.org/wiki/Bivariate_analysis

    For this reason, covariance is standardized by dividing by the product of the standard deviations of the two variables to produce the Pearson product–moment correlation coefficient (also referred to as the Pearson correlation coefficient or correlation coefficient), which is usually denoted by the letter “r.” [3]

  6. Covariance and correlation - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_correlation

    [1] [2] Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μ X and μ Y and standard deviations σ X and σ Y, respectively, then their covariance and correlation are as follows: covariance

  7. Coefficient of multiple correlation - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_multiple...

    The coefficient of multiple correlation is known as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been ...

  8. Distribution of the product of two random variables - Wikipedia

    en.wikipedia.org/wiki/Distribution_of_the...

    The approximate distribution of a correlation coefficient can be found via the Fisher transformation. Multiple non-central correlated samples. The distribution of the product of correlated non-central normal samples was derived by Cui et al. [11] and takes the form of an infinite series of modified Bessel functions of the first kind.

  9. Estimation of covariance matrices - Wikipedia

    en.wikipedia.org/wiki/Estimation_of_covariance...

    The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. [1]