Pearson correlation coefficient
E665236
The Pearson correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two continuous variables.
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
correlation coefficient
ⓘ
measure of linear association ⓘ statistical measure ⓘ |
| abbreviation | r ⓘ |
| alsoKnownAs |
Pearson product-moment correlation coefficient
NERFINISHED
ⓘ
product-moment correlation coefficient ⓘ |
| appliesTo | two continuous variables ⓘ |
| assumes |
interval or ratio scale measurement
ⓘ
linear relationship between variables ⓘ |
| canBeTestedBy | t-test for correlation ⓘ |
| category |
descriptive statistics
ⓘ
inferential statistics ⓘ |
| contrastedWith |
Kendall rank correlation coefficient
ⓘ
Spearman rank correlation coefficient ⓘ |
| dependsOn |
covariance of the two variables
ⓘ
standard deviation of each variable ⓘ |
| doesNotMeasure | nonlinear association strength ⓘ |
| field | mathematical statistics ⓘ |
| formula |
r = cov(X,Y) / (σ_X σ_Y)
ⓘ
r = Σ[(x_i - x̄)(y_i - ȳ)] / sqrt[Σ(x_i - x̄)² Σ(y_i - ȳ)²] ⓘ |
| indicates |
negative association when r < 0
ⓘ
positive association when r > 0 ⓘ |
| interpretationAt0 | no linear relationship ⓘ |
| interpretationAt1 | perfect positive linear relationship ⓘ |
| interpretationAtMinus1 | perfect negative linear relationship ⓘ |
| introducedBy | Karl Pearson NERFINISHED ⓘ |
| is | a parametric measure of correlation ⓘ |
| isDimensionless | true ⓘ |
| maximumValue | 1 ⓘ |
| measures |
direction of linear relationship between two variables
ⓘ
strength of linear relationship between two variables ⓘ |
| minimumValue | -1 ⓘ |
| neutralValue | 0 ⓘ |
| oftenAssumesForInference | bivariate normal distribution ⓘ |
| relatedTo |
coefficient of determination
ⓘ
covariance ⓘ simple linear regression ⓘ |
| requires | variables with nonzero variance ⓘ |
| sampleStatisticOf | population correlation coefficient ⓘ |
| sensitiveTo | outliers ⓘ |
| symmetricIn | its two variables ⓘ |
| undefinedWhen | either variable has zero variance ⓘ |
| usedFor |
computing coefficient of determination r² in simple linear regression
ⓘ
measuring effect size ⓘ testing linear association between variables ⓘ |
| usedIn |
data analysis
ⓘ
econometrics ⓘ machine learning feature analysis ⓘ psychometrics ⓘ statistics ⓘ |
| valueRange | -1 to 1 ⓘ |
Referenced by (1)
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