correlation coefficient

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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.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.

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.
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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.

Collins Dictionary of Economics, 4th ed. © C. Pass, B. Lowes, L. Davies 2005
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The highest significant correlation coefficient for standard germination was calculated in second day germination percentage of standard germination test (r=0.936**), followed by the cold (r=0.838**) and the cool (r=0.792**) tests.
1) and also the correlation coefficients between Vitr - Inert and Cat.
[28] developed MCDM strategies based on correlation coefficient and Jaccard similarity measures, respectively in BNS environment.
From Figures 12 and 13, it can be seen that the Pearson correlation coefficient between D and PSV is higher than the Pearson correlation coefficient between [R.sub.q] and PSV in the early stage of the polishing process, and the macrotexture has a greater influence on PSV.
It is interesting to note that the model performs very well in simulating the spatial distribution of latent heat flux in South China during both summer and winter with the correlation coefficients of 0.86 and 0.93, respectively, but the corresponding RMSEs are also very high, with the value of 35.5 W/[m.sup.2] and 26.1 W/[m.sup.2] for winter and summer.
The visually close cohesion of the French WAP and HPI in Figure 2 (Appendix) is remarkable (even though both have different scales), which can be affirmed by a correlation coefficient of 0.975.
The estimates of genotypic correlation coefficient between eight characters showed close parallelism in direction with their corresponding phenotypic correlation coefficient.
ix and iy for selection intensity of trait x and y, rg for genetic correlation coefficient of trait x and y; Hx and Hy for evolution of heritability of trait x and y.
The correlation coefficients obtained between (a *) and the other parameters are shown in Table 4.

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