correlation coefficient


Also found in: Dictionary, Thesaurus, Medical, Legal, Encyclopedia, Wikipedia.

Correlation coefficient

A standardized statistical measure of the dependence of two random variables, defined as the covariance divided by the product of the standard deviations of two variables.

Correlation Coefficient

A measure of whether and by how much two variables are related. A correlation coefficient may be between -1 and +1. Suppose there are two variables, A and B, with -A and -B indicating their opposites. A correlation coefficient of -1 indicates that A and -B are correlated and vice versa. On the other hand, a correlation coefficient of +1 means that A and B are correlated.

correlation coefficient

a statistical term (usually denoted by r) that measures the strength of the association between two variables.

Where two variables are completely unrelated, then their correlation coeffcient will be zero; where two variables are perfectly related, then their correlation would be one. A high correlation coefficient between two variables merely indicates that the two generally vary together - it does not imply causality in the sense of changes in one variable causing changes in the other.

Where high values of one variable are associated with high values of the other (and vice-versa), then they are said to be positively correlated. Where high values of one variable are associated with low values of the other (and vice-versa), then they are said to be negatively correlated. Thus correlation coefficients can range from +1 for perfect positive association to -1 for perfect negative association, with zero representing the case where there is no association between the two.

The correlation coefficient also serves to measure the goodness of fit of a regression line (see REGRESSION ANALYSIS) which has been fitted to a set of sample observations by the technique of ordinary least squares. A large positive correlation coefficient will be found when the regression line slopes upward from left to right and fits closely with the observations; a large negative correlation coefficient will be found when the regression line slopes downward from left to right and closely matches the observations. Where the regression equation contains two (or more) independent variables, a multiple correlation coefficient can be used to measure how closely the three-dimensional plane, representing the multiple regression equation, fits the set of data points.

References in periodicals archive ?
Unadjusted Pearson correlation coefficients from the interrater analysis ranged from .
Figure 2 shows that the correlation coefficient was largely positive during four distinct periods: (i) the early 1880s, (ii) the long period from 1907 through 1944, (iii) 1958-1959, and (iv) 1981-1985.
The correlation coefficients for the regression of dynamic MOE by a magnetic driver and static MOE for Sitka spruce and red pine finger-jointed wood specimens were 0.
Correlation coefficient of variables x and y shows how strongly the values of these variables are related to one another.
The correlation coefficient is useful for comparing the impulse response curves in a rough-and-ready way.
Fig 8, 11 and 13 show the representation of correlation coefficient of three depth layers of 61 districts of Bangladesh.
It is also an increasing function of the correlation coefficient, [rho].
In terms of self-confidence, the evidence favoring the ARS-2 is less convincing, although when the male and female samples are pooled, it does exhibit the largest correlation coefficient.
The simple correlation coefficient bilateral (two-tail) Talent development Organizational Commitment Pearson's correlation coefficient 0.
Image 5 displays the interpretation of the correlation coefficient.
The estimates of the genetic correlation coefficient of ELP with RCP was strong and positive (+0.
If the common tendency of appearance of the values of certain entities is being observed, a so-called correlation coefficient is used (Tenenhaus, A.