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.

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 ?
Genetic correlation coefficient is not influenced by environmental factors, it truly reflects the heritable relationship between quantitative traits, therefore, it is better in the breeding selection than phenotypic correlation coefficient (Wang et al., 2007).
Meanwhile, for some bands, spectral derivative algorithms were able to increase the correlation coefficient between [EC.sub.1:5] and spectral reflectance (R) and other mathematical transforms.
The correlation coefficients obtained between the Luminosity (L*) and the other parameters within the contaminated Annona Muricata are shown in
The standard correlation coefficients reported on table 1 are in all cases calculated using information that covers two variables for each coefficient.
Of 33 pleural fluid samples analysed, excellent agreement was found when counting WBCs by both the methods with a correlation coefficient being 0.96 (p =.000 < .001, HS) Figure 3.
Correlation coefficients are useful tools to determine first if a correlation exists and second to determine whether the correlation is a positive or negative relationship.
In engineering, the envelope correlation coefficient is calculated from the measured complex quantities [E.sub.[theta],1]([theta], [phi]), [E.sub.[phi],1] ([theta], [phi]) and [E.sub.[theta],2]([theta],< [phi]), [E.sub.[phi],2]([theta], [phi]).
By the differentiation method, we can find the maximum and minimum values of the correlation coefficient function [r.sub.xy].
Extraordinary position of the Czech Republic within the main cluster may be caused by relatively high value of the correlation coefficient (r = 0.929) between GDP and a value of the stock market index.
The simple correlation coefficient bilateral (two-tail) Align and retain talent Organizational Commitment Pearson's correlation coefficient 0.778 Significant level.
Source: Research called: "Fifth Systemic Helix--FSH" IMAGE 5 INTERPRETATION OF THE CORRELATION COEFFICIENT14 Coefficient Interpretation 0 to 0.20 Practically null correlation 0.21 to 0.40 Low correlation 0.41 to 0.70 Moderate correlation 0.71 to 0.90 High correlation 0.91 to 1 Very high correlation Result of the Spearman coefficient CHART 6 RESULTS OF SPEARMAN CORRELATIONS IN DEPENDENT VARIABLES Dependent Variables Independent Variables Spearman's rho PG2 General Questions The capacities PG1 Correlation Coefficient -.406 ** (a) installed and Sig.
If the value of the strength of the correlation needs to be determined then the selective coefficient (also called Pearson's correlation coefficient) is calculated based on the relationship (De Roover et al.