Correlation and Dependence
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In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling; however, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship. Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. In loose usage, correlation can refer to any departure of two or more random variables from independence, but technically it refers to any of several more specialized types of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which may exist even if one is a nonlinear function of the other). Other correlation coefficients have been developed to be more robust than the Pearson correlation – that is, more sensitive to nonlinear relationships. Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. Note that 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.From Wikipedia under the
GNU Free Documentation License Matching Results for Correlation and Dependence:Paul TillichPaul Johannes Tillich (20 August 1886 22 October 1965) was a theologian and existentialist philosopher. Tillich was one of the most influential Protestant ... Noam Chomsky The most effective way to restrict democracy is to transfer decision-making from the public arena to unaccountable institutions: kings and princes, priestly castes ... Albert Einstein A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to ... From Wikiquote under the
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Science: Chemistry: Software: Physical and ... Jan 2, 2007 ... advances in understanding the environment- dependence of (sigma) chemical ... PyVib2 - Permits the automatic correlation of vibrational ... Business: Textiles and Nonwovens: Industrial ... Aug 19, 2009 ... APDFA; Yarn Strength Dependence on Test Length - Technical paper about the evaluation of yarn strength changes, and the auto- correlation ...
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