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The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
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.
The package hermiter [20] computes fast batch estimates of the Spearman correlation along with sequential estimates (i.e. estimates that are updated in an online/incremental manner as new observations are incorporated). Stata implementation: spearman varlist calculates all pairwise correlation coefficients for all variables in varlist.
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 .
Weighted correlation network analysis, also known as weighted gene co-expression network analysis (WGCNA), is a widely used data mining method especially for studying biological networks based on pairwise correlations between variables.
Consequently, the correlation is a dimensionless quantity that can be used to compare the linear relationships between pairs of variables in different units. If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ XY is near +1 (or −1).
the constant-correlation model, where the sample variances are preserved, but all pairwise correlation coefficients are assumed to be equal to one another; the two-parameter matrix, where all variances are identical, and all covariances are identical to one another (although not identical to the variances);
A bivariate correlation is a measure of whether and how two variables covary linearly, that is, whether the variance of one changes in a linear fashion as the variance of the other changes. Covariance can be difficult to interpret across studies because it depends on the scale or level of measurement used.