Using Predictive Power Score to Pinpoint Non-linear Correlations

Correlations
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense, correlation is any statistical association, although it commonly refers to the degree to which a pair of variables are related linearly.

Known examples of dependent phenomena include the correlation between the height of parents and their children and the correlation between the price of a good and the quantity that consumers are willing to buy, as represented by the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice.

For example, a electric utility may produce less energy on a warm day based on the correlation between electricity demand and climate. In this example, there is a causal relationship because extreme weather causes people to use more electricity to heat or cool themselves

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 causality). Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence. In informal language, correlation is synonymous with dependence.

Essentially, correlation is the measure of how two or more variables relate to each other. There are several correlation coefficients. The most common of these is Pearson's correlation coefficient, which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a non-linear function of the other)

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