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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 .
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.
Intuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully opposed for a ...
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 ...
Diametrically opposed points represent a correlation of –1 = cos(π), called anti-correlation. Any two points not in the same hemisphere have negative correlation. An example would be a negative cross-sectional relationship between illness and vaccination, if it is observed that where the incidence of one is higher than average, the incidence ...
Stock correlation describes the relationship that exists between two stocks and their respective price movements. It can also refer to the relationship between stocks and other asset classes, such ...
The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors. [3] [4]
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.