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Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of Y is zero.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
Correlogram. A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram.
In statistics, the correlation ratio is a measure of the curvilinear relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation. The context here is the same as that of ...
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them.
correlation. so that. where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as ...
Administering one form of the test to a group of individuals. At some later time, administering an alternate form of the same test to the same group of people. Correlating scores on form A with scores on form B. The correlation between scores on the two alternate forms is used to estimate the reliability of the test.