“correlation”的概念、定义、翻译、参考文献-科学参考

correlation

Mathematics

Between two random variables, the correlation is a measure of the extent to which a change in one tends to correspond to a change in the other. The correlation is high or low depending on whether the relationship between the two is close or not. If the change in one corresponds to a change in the other in the same direction, there is positive correlation, and there is a negative correlation if the changes are in opposite directions. Independent random variables have zero correlation. One measure of correlation between the random variables X and Y is the correlation coefficient ρ‎ defined by

$ρ = \frac{Cov (X, Y)}{\sqrt{Var (X) Var (Y)}}$

(see covariance, variance). This satisfies −1 ≤ ρ‎ ≤ 1. If X and Y are linearly related, then ρ‎ = −1 or + 1.

For a sample of n paired observations (x₁, y₁), (x₂, y₂),…(x_n, y_n), the (sample) correlation coefficient is equal to

$\frac{\sum (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt{(\sum {(x_{i} - \bar{x})}^{2}) (\sum {(y_{i} - \bar{y})}^{2})}}$

Note that the existence of some correlation between two variables need not imply causation.

Statistics

A general term used to describe the fact that two (or more) variables are related. Galton, in 1869, was probably the first to use the term in this way (as ‘co-relation’). Usually the relation is not precise. For example, we would expect a tall person to weigh more than a short person of the same build, but there will be exceptions.
Although the word ‘correlation’ is used loosely to describe the existence of some general relationship, it has a more specific meaning in the context of linear relations between variables (see population correlation coefficient; sample correlation coefficient).

Computer

A measure of a tendency for two or more random variables to be associated. The formula for r, the sample correlation coefficient between two variables x and y, is
$\frac{Σ (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt [Σ {(x_{i} - \bar{x})}^{2} Σ {(y_{i} - \bar{y})}^{2}]}$
which varies between −1 and +1. Negative values or r indicate that y tends to decrease as x increases, while positive values indicate that x and y increase or decrease together. If the value of r is zero then x and y are uncorrelated.
Rank correlation measures the correlation between the ranks (or order numbers) of the variables, i.e. between the positions when the numbers are arranged in increasing order of magnitude.
Correlation does not imply causation. Variables may be correlated accidentally, or because of joint association with other unmeasured agencies such as a general upward trend with time. If the relationship is not linear the correlation coefficient may be misleading.

Electronics and Electrical Engineering

The process of comparison of signals to establish how alike they are, or the extent of correspondence so found. When two signals are compared with each other, the process is known as cross correlation, and if a signal is compared with itself it is referred to as autocorrelation. The correlation function is the result of multiplying the signals together for different values of time delay between them. A peak in the correlation function indicates a delay at which the signals have a degree of periodicity, and the delay associated with such a peak gives the time period.

Biology

In statistics, the degree of linear relationship between two or more variables. Pairs of observations can be plotted as a series of points on a graph. The correlation coefficient measures the extent to which the points on the resulting scatter diagram form a straight line. The correlation coefficient varies within the range of +1 (where an increase of one variable is associated with a corresponding increase in the other, and vice versa) to −1 (where an increase of one variable is associated with a corresponding decrease of the other); a coefficient of 0 indicates no linear relationship between the two variables. The statistical technique known as multivariate analysis can be used to investigate the relationships between several variables. See also confounding.

Geology and Earth Sciences

1. In stratigraphy, correlation is the establishment of a correspondence between stratigraphic units. It depends on the similarities that exist in terms of lithology or fossil content. Isolated stratigraphic units, or successions, may be either ‘correlated’, i.e. they were once physically continuous, or time-correlated, i.e. equated in terms of time.
2. In geostatistics, correlation is a technique used to determine the degree of association between two data sets.
3. In geophysics, the comparison of one wave-form with another in the time domain. It is analogous to coherence in the frequency domain. See auto-correlation; cross-correlation.

单词	correlation
释义	correlation Mathematics Between two random variables, the correlation is a measure of the extent to which a change in one tends to correspond to a change in the other. The correlation is high or low depending on whether the relationship between the two is close or not. If the change in one corresponds to a change in the other in the same direction, there is positive correlation, and there is a negative correlation if the changes are in opposite directions. Independent random variables have zero correlation. One measure of correlation between the random variables X and Y is the correlation coefficient ρ‎ defined by $ρ = \frac{Cov (X, Y)}{\sqrt{Var (X) Var (Y)}}$ (see covariance, variance). This satisfies −1 ≤ ρ‎ ≤ 1. If X and Y are linearly related, then ρ‎ = −1 or + 1. For a sample of n paired observations (x₁, y₁), (x₂, y₂),…(x_n, y_n), the (sample) correlation coefficient is equal to $\frac{\sum (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt{(\sum {(x_{i} - \bar{x})}^{2}) (\sum {(y_{i} - \bar{y})}^{2})}}$ Note that the existence of some correlation between two variables need not imply causation. Statistics A general term used to describe the fact that two (or more) variables are related. Galton, in 1869, was probably the first to use the term in this way (as ‘co-relation’). Usually the relation is not precise. For example, we would expect a tall person to weigh more than a short person of the same build, but there will be exceptions. Although the word ‘correlation’ is used loosely to describe the existence of some general relationship, it has a more specific meaning in the context of linear relations between variables (see population correlation coefficient; sample correlation coefficient). Computer A measure of a tendency for two or more random variables to be associated. The formula for r, the sample correlation coefficient between two variables x and y, is $\frac{Σ (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt [Σ {(x_{i} - \bar{x})}^{2} Σ {(y_{i} - \bar{y})}^{2}]}$ which varies between −1 and +1. Negative values or r indicate that y tends to decrease as x increases, while positive values indicate that x and y increase or decrease together. If the value of r is zero then x and y are uncorrelated. Rank correlation measures the correlation between the ranks (or order numbers) of the variables, i.e. between the positions when the numbers are arranged in increasing order of magnitude. Correlation does not imply causation. Variables may be correlated accidentally, or because of joint association with other unmeasured agencies such as a general upward trend with time. If the relationship is not linear the correlation coefficient may be misleading. Electronics and Electrical Engineering The process of comparison of signals to establish how alike they are, or the extent of correspondence so found. When two signals are compared with each other, the process is known as cross correlation, and if a signal is compared with itself it is referred to as autocorrelation. The correlation function is the result of multiplying the signals together for different values of time delay between them. A peak in the correlation function indicates a delay at which the signals have a degree of periodicity, and the delay associated with such a peak gives the time period. Biology In statistics, the degree of linear relationship between two or more variables. Pairs of observations can be plotted as a series of points on a graph. The correlation coefficient measures the extent to which the points on the resulting scatter diagram form a straight line. The correlation coefficient varies within the range of +1 (where an increase of one variable is associated with a corresponding increase in the other, and vice versa) to −1 (where an increase of one variable is associated with a corresponding decrease of the other); a coefficient of 0 indicates no linear relationship between the two variables. The statistical technique known as multivariate analysis can be used to investigate the relationships between several variables. See also confounding. Geology and Earth Sciences 1. In stratigraphy, correlation is the establishment of a correspondence between stratigraphic units. It depends on the similarities that exist in terms of lithology or fossil content. Isolated stratigraphic units, or successions, may be either ‘correlated’, i.e. they were once physically continuous, or time-correlated, i.e. equated in terms of time. 2. In geostatistics, correlation is a technique used to determine the degree of association between two data sets. 3. In geophysics, the comparison of one wave-form with another in the time domain. It is analogous to coherence in the frequency domain. See auto-correlation; cross-correlation.
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