“correlation coefficient”的概念、定义、翻译、参考文献-科学参考

correlation coefficient

Statistics

Depending on context this refers either to the population correlation coefficient, or the sample correlation coefficient.

Chemical Engineering

A statistical number that represents the linear relationship between two variables or groups of variables (X and Y). The correlation has a value between −1 and +1. A positive value represents a positive linear relationship, whereas a negative value represents a negative relationship. A value of 0 represents no relationship between the variables. It is calculated from:
$R = \frac{n \sum X Y - (\sum X) (\sum Y)}{\sqrt{(n \sum X^{2} - {(\sum X)}^{2}) (n {\sum Y}^{2} - {(\sum Y)}^{2})}}$

where n is the number of values. The correlation coefficient requires that the relationship between the two variables is linear. Where this is known not to be the case, then the correlation coefficient is not useful.

Computer

See correlation.

Economics

A unit-free measure of the degree of linear relationship between two random variables, say, X and Y defined by

$ρ_{XY} = \frac{C o v (X, Y)}{\sqrt{V a r (X)} \sqrt{V a r (Y)}}$

where Cov(X, Y) is the covariance between X and Y. The correlation coefficient lies between −1 and 1, with ρ‎_XY = 1 corresponding to a perfect positive linear relationship, and ρ‎_XY = −1 corresponding to a perfect negative linear relationship between X and Y. Positive (negative) correlation means that large values of X are likely to be observed with large (small) values of Y.

单词	correlation coefficient
释义	correlation coefficient Statistics Depending on context this refers either to the population correlation coefficient, or the sample correlation coefficient. Chemical Engineering A statistical number that represents the linear relationship between two variables or groups of variables (X and Y). The correlation has a value between −1 and +1. A positive value represents a positive linear relationship, whereas a negative value represents a negative relationship. A value of 0 represents no relationship between the variables. It is calculated from: $R = \frac{n \sum X Y - (\sum X) (\sum Y)}{\sqrt{(n \sum X^{2} - {(\sum X)}^{2}) (n {\sum Y}^{2} - {(\sum Y)}^{2})}}$ where n is the number of values. The correlation coefficient requires that the relationship between the two variables is linear. Where this is known not to be the case, then the correlation coefficient is not useful. Computer See correlation. Economics A unit-free measure of the degree of linear relationship between two random variables, say, X and Y defined by $ρ_{XY} = \frac{C o v (X, Y)}{\sqrt{V a r (X)} \sqrt{V a r (Y)}}$ where Cov(X, Y) is the covariance between X and Y. The correlation coefficient lies between −1 and 1, with ρ‎_XY = 1 corresponding to a perfect positive linear relationship, and ρ‎_XY = −1 corresponding to a perfect negative linear relationship between X and Y. Positive (negative) correlation means that large values of X are likely to be observed with large (small) values of Y.
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