Correlation Coefficient
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Correlation coefficient (English)
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Definition (advanced level)
The correlation coefficient measures how closely two variables or sets of data agree. For variables X and Y it is defined as:
If it is equal to 1 or -1, the two variables have a straight-line relationship. If it is equal to zero, then the two variables are uncorrelated (not necessarily independent).
For two samples of equal size xi, yi, the correlation coefficient is r = [( ∑i ( xi − [(x)] )( yi − [(y)] ) )/( √{ ( ∑i ( xi − [(x)] ) 2 ) ( ∑i ( yi − [(y)] ) 2 ) })] .
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If it is equal to 1 or -1, the two variables have a straight-line relationship. If it is equal to zero, then the two variables are uncorrelated (not necessarily independent).
For two samples of equal size xi, yi, the correlation coefficient is r = [( ∑i ( xi − [(x)] )( yi − [(y)] ) )/( √{ ( ∑i ( xi − [(x)] ) 2 ) ( ∑i ( yi − [(y)] ) 2 ) })] .
Relations
- broader:
- (en) Statistic
- narrower:
- (en) Pearson's coefficient
- (en) Rank correlation
- references:
- (en) Correlation
- (en) Covariance
- (en) Variance
- referenced:
- (en) Goodness of fit
- (en) Rho
- see also:
- (en) Regression
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