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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

    The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations. [4]

  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. Covariance - Wikipedia

    en.wikipedia.org/wiki/Covariance

    When the covariance is normalized, one obtains the Pearson correlation coefficient, which gives the goodness of the fit for the best possible linear function describing the relation between the variables. In this sense covariance is a linear gauge of dependence.

  6. 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 productmoment correlation coefficient (also referred to as the Pearson correlation coefficient or correlation coefficient), which is usually denoted by the letter “r.” [3]

  7. Covariance matrix - Wikipedia

    en.wikipedia.org/wiki/Covariance_matrix

    An entity closely related to the covariance matrix is the matrix of Pearson product-moment correlation coefficients between each of the random variables in the random vector , which can be written as ⁡ = (⁡ ()) (⁡ ()), where ⁡ is the matrix of the diagonal elements of (i.e., a diagonal matrix of the variances of for =, …,).

  8. Financial correlation - Wikipedia

    en.wikipedia.org/wiki/Financial_correlation

    The Pearson product-moment correlation coefficient is sometimes applied to finance correlations. However, the limitations of Pearson correlation approach in finance are evident. First, linear dependencies as assessed by the Pearson correlation coefficient do not appear often in finance.

  9. Principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Principal_component_analysis

    Mean-centering is unnecessary if performing a principal components analysis on a correlation matrix, as the data are already centered after calculating correlations. Correlations are derived from the cross-product of two standard scores (Z-scores) or statistical moments (hence the name: Pearson Product-Moment Correlation).