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diagram being calculatedThe following calculations are needed when finding Pearson's product moment correlation coefficient or pmcc:
S_{xx} = \displaystyle \sum x^2 - \frac{(\sum x)^2}{n}
S_{yy} = \displaystyle \sum y^2 - \frac{(\sum y)^2}{n}
S_{xy} = \displaystyle \sum xy - \frac{(\sum x)(\sum y)}{n}
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Summary/Background

The pmcc can be found using:
r = \displaystyle \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }
MathsNet imageKarl Pearson FRS (27 March 1857 – 27 April 1936) established the discipline of mathematical statistics. A sesquicentenary conference was held in London on 23 March 2007, to celebrate the 150th anniversary of his birth.
In 1911 he founded the world's first university statistics department at University College London. He was a proponent of eugenics, and a protege and biographer of Sir Francis Galton. He was also a socialist. Pearson was instrumental in the development of regression and correlation theory. One of his classic data sets (originally collected by Galton) involves the regression of sons' height upon that of their fathers'. Pearson built a 3-dimensional model of this data set (which remains in the care of the Statistical Science Department) to illustrate the ideas. The Pearson product-moment correlation coefficient is named after him, and it was the first important "effect size" to be introduced into statistics.

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Glossary

coefficient

The constant value in an expression, for example in 3x the coefficient of x is 3.

correlation

The degree of relationship between two random variables, in the range -1 to 1.

moment

The turning effect of a force whose value depends on the magnitude of the force and where it is applied.

pmcc

The product moment correlation coefficient

product moment correlation coefficient

Often abbreviated to PMCC; a measure of correlation.

regression

A statistical model, whereby the expected value of a variable y is expressed in terms of known values of x.

union

The union of two sets A and B is the set containing all the elements of A and B.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AQA A-Level (UK - Pre-2017)S1Correlation and RegressionCorrelation
AQA A2 Maths 2017StatisticsCorrelation and RegressionProduct Moment Correlation Coefficient
AQA AS Further Maths 2017StatisticsExtraProduct Moment Correlation Coefficient
AQA AS/A2 Further Maths 2017StatisticsExtraProduct Moment Correlation Coefficient
AQA AS/A2 Maths 2017StatisticsCorrelation and RegressionProduct Moment Correlation Coefficient
CCEA A-Level (NI)S2Correlation and RegressionCorrelation
L Statistics - DataL2 Bivariate DataCorrelation
Edexcel A-Level (UK - Pre-2017)S1Correlation and RegressionCorrelation
Edexcel A2 Maths 2017StatisticsRegression and CorrelationProduct Moment Correlation Coefficient
Edexcel AS Further Maths 2017Further Statistics 2CorrelationProduct Moment Correlation Coefficient
Edexcel AS/A2 Further Maths 2017Further Statistics 2CorrelationProduct Moment Correlation Coefficient
Edexcel AS/A2 Maths 2017StatisticsRegression and CorrelationProduct Moment Correlation Coefficient
I.B. Higher Level7Correlation and RegressionCorrelation
OCR A-Level (UK - Pre-2017)S1Correlation and RegressionCorrelation
OCR A2 Maths 2017StatisticsUsing and Testing Correlation CoefficientProduct Moment Correlation Coefficient
OCR AS Further Maths 2017StatisticsCorrelationProduct Moment Correlation Coefficient
OCR MEI A2 Maths 2017StatisticsUsing and Testing Correlation CoefficientProduct Moment Correlation Coefficient
OCR MEI AS Further Maths 2017Statistics ACorrelationProduct Moment Correlation Coefficient
OCR-MEI A-Level (UK - Pre-2017)S2Correlation and RegressionCorrelation
Pre-U A-Level (UK)ProbCorrelation and RegressionCorrelation
Scottish (Highers + Advanced)HSCorrelation and RegressionCorrelation
Scottish HighersSCorrelation and RegressionCorrelation
Universal (all site questions)CCorrelation and RegressionCorrelation