Editing Pearson correlation coefficient (section)

{{Short description|Measure of linear correlation}}
{{Distinguish|Coefficient of determination}}
{{Use dmy dates|date=August 2022}}
[[File:Correlation examples2.svg|thumb|400px|right|Several sets of (''x'',&nbsp;''y'') points, with the correlation coefficient of ''x'' and ''y'' for each set. The correlation reflects the strength 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.]]

In [[statistics]], the '''Pearson correlation coefficient''' ('''PCC'''){{efn|Also known as '''Pearson's ''r''''', the '''Pearson product-moment correlation coefficient''' ('''PPMCC'''), the '''bivariate correlation''',<ref>{{cite web |url=http://libguides.library.kent.edu/SPSS/PearsonCorr |title=SPSS Tutorials: Pearson Correlation}}</ref> or simply the unqualified '''correlation coefficient'''<ref>{{cite web|url=https://www.statisticshowto.com/probability-and-statistics/correlation-coefficient-formula/|title=Correlation Coefficient: Simple Definition, Formula, Easy Steps|website=Statistics How To}}</ref>}} is a [[correlation coefficient]] that measures [[linear]] correlation between two sets of data. It is the ratio between the [[covariance]] of two variables and the product of their [[standard deviation]]s; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear [[correlation]] of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).