correlation

Also known as correlation and dependence, dependence, positive correlation, negative correlation, association, correlation of data

thumb|400px|right|Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. 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.

AI overview

Correlation measures how closely two variables move together in a linear fashion, telling you both the strength and direction of their relationship. It matters because it helps you quickly identify whether two things tend to rise and fall together or move in opposite directions, though it won't tell you how steep that relationship is or whether the connection is actually caused by one variable affecting the other.

AI-generated from the Wikipedia summary — may contain errors.

Research

2,679,331 papers

Psychological correlates of university students' academic performance: a systematic review and meta-analysis.Psychological bulletin · 2012Richardson M, Abraham C, Bond RDOI: 10.1037/a0026838
Inclusion body myositis: correlation of clinical outcomes with histopathology, electromyography and laboratory findings.ReviewRheumatology (Oxford, England) · 2022Pinto MV, Laughlin RS, Klein CJ et al.DOI: 10.1093/rheumatology/keab754
Correlation between magnetic resonance imaging and clinical outcomes after cartilage repair surgery in the knee: a systematic review and meta-analysis.The American journal of sports medicine · 2013Blackman AJ, Smith MV, Flanigan DC et al.DOI: 10.1177/0363546513485931
CORRELATION STUDY BETWEEN DRUSEN MORPHOLOGY AND FUNDUS AUTOFLUORESCENCE.Retina (Philadelphia, Pa.) · 2021Flores R, Carneiro A, Serra J et al.DOI: 10.1097/IAE.0000000000002881
Correlation of telomere length in brain tissue with peripheral tissues in living human subjects.Frontiers in molecular neuroscience · 2024Carver AJ, Hing B, Elser BA et al.DOI: 10.3389/fnmol.2024.1303974
Clinical Correlation Between Vertical Gaze Palsy and Midbrain Volume in Progressive Supranuclear Palsy.Journal of neuro-ophthalmology : the official journal of the North American Neuro-Ophthalmology Society · 2022Buch KA, Bouffard MA, Kardon RH et al.DOI: 10.1097/WNO.0000000000001393
Correlation of Body Mass Index with Epidermal Biophysical Properties Varies with Gender in Chinese.Skin pharmacology and physiology · 2022Ye L, Lai Q, Wen S et al.DOI: 10.1159/000524295
Correlation between trait emotional intelligence and prefrontal activation during a verbal fluency task: A functional near-infrared spectroscopy study.Medicine · 2023Fukumoto T, Amitani H, Nishi R et al.DOI: 10.1097/MD.0000000000034418

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Wikidata facts

Image: Correlation examples2.svg

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Commons category: Correlation
Stack Exchange tag: stats.stackexchange.com/tags/correlation

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~26 min read

Article

20 sections

Contents

Coefficients
Pearson's product-moment coefficient
Correlation and independence
Sample correlation coefficient
Example
Rank correlation coefficients
Common misconceptions
Correlation and causality
Simple linear correlations
Properties
Uncorrelatedness and independence of stochastic processes
Sensitivity to the data distribution
Correlation matrices
Nearest valid correlation matrix
Bivariate normal distribution
Other measures of association among random variables{{anchor|Other measures of dependence among random variables}}
See also
References
Further reading
External links

In statistics, correlation is a kind of statistical relationship between two random variables or bivariate data. Usually it refers to the degree to which a pair of variables are linearly related. In statistics, more general relationships between variables are called an association, the degree to which some of the variability of one variable can be accounted for by the other.