# Definitions for **regression toward the mean**

### This page provides all possible meanings and translations of the word **regression toward the mean**

### Princeton's WordNet

regression, simple regression, regression toward the mean, statistical regression(noun)

the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x)

### Freebase

Regression toward the mean

In statistics, regression toward the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and, paradoxically, if it is extreme on its second measurement, it will tend to be closer to the average on its first. To avoid making wrong inferences, regression toward the mean must be considered when designing scientific experiments and interpreting data. The conditions under which regression toward the mean occurs depend on the way the term is mathematically defined. Sir Francis Galton first observed the phenomenon in the context of simple linear regression of data points. However, a less restrictive approach is possible. Regression towards the mean can be defined for any bivariate distribution with identical marginal distributions. Two such definitions exist. One definition accords closely with the common usage of the term “regression towards the mean”. Not all such bivariate distributions show regression towards the mean under this definition. However, all such bivariate distributions show regression towards the mean under the other definition. Historically, what is now called regression toward the mean has also been called reversion to the mean and reversion to mediocrity.

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"regression toward the mean." *Definitions.net.* STANDS4 LLC, 2014. Web. 29 Aug. 2014. <http://www.definitions.net/definition/regression toward the mean>.