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A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...
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.
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 probability and statistics, the term cross-correlations refers to the correlations between the entries of two random vectors and , while the correlations of a random vector are the correlations between the entries of itself, those forming the correlation matrix of . If each of and is a scalar random variable which is realized repeatedly in a ...
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. [citation needed]
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation ...
Partial correlation. In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. When determining the numerical relationship between two variables of interest, using their correlation coefficient will give misleading ...