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  2. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Pearson_correlation...

    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. Spearman's rank correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Spearman's_rank_correlation...

    The most common of these is the Pearson product-moment correlation coefficient, which is a similar correlation method to Spearman's rank, that measures the “linear” relationships between the raw numbers rather than between their ranks.

  6. Proportionate reduction of error - Wikipedia

    en.wikipedia.org/wiki/Proportionate_reduction_of...

    Its square root is Pearson's product-moment correlation. There are several other correlation coefficients that have PRE interpretation and are used for variables of different scales: predict

  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. 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).

  9. Karl Pearson - Wikipedia

    en.wikipedia.org/wiki/Karl_Pearson

    Karl Pearson FRS FRSE [1] (/ ˈ p ɪər s ə n /; born Carl Pearson; 27 March 1857 – 27 April 1936 [2]) was an English biostatistician and mathematician. [ 3 ] [ 4 ] He has been credited with establishing the discipline of mathematical statistics .