![]() ![]() In informal parlance, correlation is synonymous with dependence. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation).įormally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. ![]() For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In the broadest sense correlation is any statistical association, though it actually refers to the degree to which a pair of variables are linearly related.įamiliar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.Ĭorrelations are useful because they can indicate a predictive relationship that can be exploited in practice. In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. 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. 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). Several sets of ( x, y) points, with the Pearson correlation coefficient of x and y for each set. ![]()
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