Pearson correlation coefficient (original) (raw)
في الإحصاء، معامل الارتباط لبيرسون (بالإنجليزية: Pearson correlation coefficient) أو معامل الارتباط لبرافي بيرسون (Bravais-Pearson) هو قياس الارتباط بين متغيرين اثنين. سمي هذ المعامل هكذا نسبة إلى عالم الرياضيات الإنجليزي كارل بيرسون الذي طوره معتمدا في ذلك على فكرة تعود إلى عالم الرياضيات الإنجليزي فرانسيس غالتون في ثمانينات القرن التاسع عشر.
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| dbo:abstract | في الإحصاء، معامل الارتباط لبيرسون (بالإنجليزية: Pearson correlation coefficient) أو معامل الارتباط لبرافي بيرسون (Bravais-Pearson) هو قياس الارتباط بين متغيرين اثنين. سمي هذ المعامل هكذا نسبة إلى عالم الرياضيات الإنجليزي كارل بيرسون الذي طوره معتمدا في ذلك على فكرة تعود إلى عالم الرياضيات الإنجليزي فرانسيس غالتون في ثمانينات القرن التاسع عشر. (ar) Dins l'entorn de l'estadística, el coeficient de correlació de Pearson és un índex que mesura la relació lineal entre dues variables quantitatives. A diferència de la covariància, la correlació de Pearson és independent de l'escala de mesura de les variables. (ca) Der Korrelationskoeffizient, auch Produkt-Moment-Korrelation, ist ein Maß für den Grad des linearen Zusammenhangs zwischen zwei mindestens intervallskalierten Merkmalen, das nicht von den Maßeinheiten der Messung abhängt und somit dimensionslos ist. Er kann Werte zwischen und annehmen. Bei einem Wert von (bzw. ) besteht ein vollständig positiver (bzw. negativer) linearer Zusammenhang zwischen den betrachteten Merkmalen. Wenn der Korrelationskoeffizient den Wert 0 aufweist, hängen die beiden Merkmale überhaupt nicht linear voneinander ab. Allerdings können diese ungeachtet dessen in nichtlinearer Weise voneinander abhängen. Damit ist der Korrelationskoeffizient kein geeignetes Maß für die (reine) stochastische Abhängigkeit von Merkmalen. Das Quadrat des Korrelationskoeffizienten stellt das Bestimmtheitsmaß dar. Der Korrelationskoeffizient wurde erstmals vom britischen Naturforscher Sir Francis Galton (1822–1911) in den 1870er Jahren verwendet. Karl Pearson lieferte schließlich eine formal-mathematische Begründung für den Korrelationskoeffizienten. Da er von Auguste Bravais und Pearson populär gemacht wurde, wird der Korrelationskoeffizient auch Pearson-Korrelation oder Bravais-Pearson-Korrelation genannt. Je nachdem, ob der lineare Zusammenhang zwischen zeitgleichen Messwerten zweier verschiedener Merkmale oder derjenige zwischen zeitlich verschiedenen Messwerten eines einzigen Merkmals betrachtet wird, spricht man entweder von der Kreuzkorrelation oder von der Kreuzautokorrelation (siehe auch Zeitreihenanalyse). Korrelationskoeffizienten wurden mehrfach – so schon von Ferdinand Tönnies – entwickelt, heute wird allgemein jener von Pearson verwendet. (de) Estatistikan, Pearsonen korrelazio koefiziente linealak edo, labur, korrelazio koefizienteak bi aldagai kuantitatiboren arteko korrelazio linealaren norabidea eta sendotasuna neurtzen duen adierazle bat da. Kobariantzatik eratortzen den koefizientea da: jatorrizko datuez kalkulaturiko kobariantza dimentsionatua izanik, korrelazioaren sendotasuna neurtzeko egokia ez denez, jatorrizko datuak estandarizatu eta datu estandarizatu hauekin kobariantza kalkulatuz lortzen da Pearsonen korrelazio koefizientearen formula. Azpimarratu behar da Pearsonen korrelazio koefiziente linealak korrelazio lineala neurtzen duela eta ez dituela antzematen aldagaien artean izan daitezkeen bestelako erlazio motak. (eu) En estadística, el coeficiente de correlación de Pearson es una medida de dependencia lineal entre dos variables aleatorias cuantitativas. A diferencia de la covarianza, la correlación de Pearson es independiente de la escala de medida de las variables. De manera menos formal, podemos definir el coeficiente de correlación de Pearson como un índice que puede utilizarse para medir el grado de relación de dos variables siempre y cuando ambas sean cuantitativas y continuas. (es) In statistics, the Pearson correlation coefficient (PCC, pronounced /ˈpɪərsən/) ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; 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 teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). (en) In statistica, l'indice di correlazione di Pearson (anche detto coefficiente di correlazione lineare o coefficiente di correlazione di Pearson o coefficiente di correlazione di Bravais-Pearson) tra due variabili statistiche è un indice che esprime un'eventuale relazione di linearità tra esse. Secondo la disuguaglianza di Cauchy-Schwarz ha un valore compreso tra e dove corrisponde alla perfetta correlazione lineare positiva, corrisponde a un'assenza di correlazione lineare e corrisponde alla perfetta correlazione lineare negativa. Fu sviluppato da Karl Pearson da un'idea introdotta da Francis Galton nel 1880; la formula matematica fu derivata e pubblicata da Auguste Bravais nel 1844. La denominazione del coefficiente è anche un esempio della legge di Stigler. (it) 통계학에서 , 피어슨 상관 계수(Pearson Correlation Coefficient ,PCC)란 두 변수 X 와 Y 간의 선형 상관 관계를 계량화한 수치다. 피어슨 상관 계수는 코시-슈바르츠 부등식에 의해 +1과 -1 사이의 값을 가지며, +1은 완벽한 양의 선형 상관 관계, 0은 선형 상관 관계 없음, -1은 완벽한 음의 선형 상관 관계를 의미한다. 일반적으로 상관관계는 피어슨 상관관계를 의미하는 상관계수이다. (ko) Een correlatiecoëfficiënt is een maat voor de correlatie tussen twee stochastische grootheden (of stochastische variabelen). Meestal spreekt men van correlatie als er tussen de beide grootheden een zekere samenhang is, in die zin dat waarden van de beide grootheden dezelfde of een tegengestelde tendens vertonen. Zo is er sprake van correlatie tussen de grootheden lengte en gewicht bij (volwassen) mensen. Met toenemende lengte neemt gemiddeld gezien ook het gewicht toe. Correlatie kan, maar hoeft niet op een causaal verband te duiden. Zo is er correlatie tussen sociale klasse en inkomen, berustend op de genoten opleiding. Ook is er de zogenaamde nonsenscorrelatie, zoals tussen de schade bij een brand en het aantal ingezette brandweerlieden. Afhankelijk van de soort grootheden zijn er verschillende correlatiecoëfficiënten om de correlatie te meten. Ook dient weer goed onderscheid gemaakt te worden tussen populatie en steekproef. Bij enkelvoudige lineaire regressie is het kwadraat van de correlatiecoëfficiënt gelijk aan de determinatiecoëfficiënt (veelal aangeduid met ). (nl) Współczynnik korelacji liniowej Pearsona – współczynnik określający poziom zależności liniowej między zmiennymi losowymi. Został opracowany przez Karla Pearsona. (pl) Em estatística descritiva, o coeficiente de correlação de Pearson, também chamado de "coeficiente de correlação produto-momento" ou simplesmente de "ρ de Pearson" mede o grau da correlação (e a direcção dessa correlação - se positiva ou negativa) entre duas variáveis de escala métrica (intervalar ou de rácio/razão). Este coeficiente, normalmente representado por ρ assume apenas valores entre -1 e 1. * Significa uma correlação perfeita positiva entre as duas variáveis. * Significa uma correlação negativa perfeita entre as duas variáveis - Isto é, se uma aumenta, a outra sempre diminui. * Significa que as duas variáveis não dependem linearmente uma da outra. No entanto, pode existir uma dependência não linear. Assim, o resultado deve ser investigado por outros meios. (pt) Коефіцієнт кореляції Пірсона (позначають «r») — в статистиці, показник кореляції (лінійної залежності) між двома змінними X та Y, який набуває значень від −1 до +1 включно. Він широко використовується в науці для вимірювання ступеня лінійної залежності між двома змінними. Показник був розроблений Карлом Пірсоном (Karl Pearson) зі схожої ідеї, представленої Френсісом Гальтоном в 1880-х рр. (uk) 在统计学中，皮尔逊积矩相关系数（英語：Pearson product-moment correlation coefficient，缩写：PPMCC，或PCCs，有时简称相关系数）用于度量兩組數據的变量X和Y之间的線性相關的程度。它是兩個變量的協方差與其標準差的乘積之比； 因此，它本質上是協方差的歸一化度量，因此結果始終具有介於-1和1之間的值。與協方差本身一樣，該度量只能反映變量的線性相關性，而忽略了許多其他類型的關係或相關性。舉個簡單的例子，可以預期高中青少年樣本的年齡和身高的皮尔逊积矩相关系数顯著大於0，但小於1（因為1表示不切實際的完美相關性）。 (zh) |
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| dbp:date | February 2015 (en) |
| dbp:reason | suboptimal in what sense? (en) |
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| rdfs:comment | في الإحصاء، معامل الارتباط لبيرسون (بالإنجليزية: Pearson correlation coefficient) أو معامل الارتباط لبرافي بيرسون (Bravais-Pearson) هو قياس الارتباط بين متغيرين اثنين. سمي هذ المعامل هكذا نسبة إلى عالم الرياضيات الإنجليزي كارل بيرسون الذي طوره معتمدا في ذلك على فكرة تعود إلى عالم الرياضيات الإنجليزي فرانسيس غالتون في ثمانينات القرن التاسع عشر. (ar) Dins l'entorn de l'estadística, el coeficient de correlació de Pearson és un índex que mesura la relació lineal entre dues variables quantitatives. A diferència de la covariància, la correlació de Pearson és independent de l'escala de mesura de les variables. (ca) En estadística, el coeficiente de correlación de Pearson es una medida de dependencia lineal entre dos variables aleatorias cuantitativas. A diferencia de la covarianza, la correlación de Pearson es independiente de la escala de medida de las variables. De manera menos formal, podemos definir el coeficiente de correlación de Pearson como un índice que puede utilizarse para medir el grado de relación de dos variables siempre y cuando ambas sean cuantitativas y continuas. (es) In statistica, l'indice di correlazione di Pearson (anche detto coefficiente di correlazione lineare o coefficiente di correlazione di Pearson o coefficiente di correlazione di Bravais-Pearson) tra due variabili statistiche è un indice che esprime un'eventuale relazione di linearità tra esse. Secondo la disuguaglianza di Cauchy-Schwarz ha un valore compreso tra e dove corrisponde alla perfetta correlazione lineare positiva, corrisponde a un'assenza di correlazione lineare e corrisponde alla perfetta correlazione lineare negativa. Fu sviluppato da Karl Pearson da un'idea introdotta da Francis Galton nel 1880; la formula matematica fu derivata e pubblicata da Auguste Bravais nel 1844. La denominazione del coefficiente è anche un esempio della legge di Stigler. (it) 통계학에서 , 피어슨 상관 계수(Pearson Correlation Coefficient ,PCC)란 두 변수 X 와 Y 간의 선형 상관 관계를 계량화한 수치다. 피어슨 상관 계수는 코시-슈바르츠 부등식에 의해 +1과 -1 사이의 값을 가지며, +1은 완벽한 양의 선형 상관 관계, 0은 선형 상관 관계 없음, -1은 완벽한 음의 선형 상관 관계를 의미한다. 일반적으로 상관관계는 피어슨 상관관계를 의미하는 상관계수이다. (ko) Współczynnik korelacji liniowej Pearsona – współczynnik określający poziom zależności liniowej między zmiennymi losowymi. Został opracowany przez Karla Pearsona. (pl) Коефіцієнт кореляції Пірсона (позначають «r») — в статистиці, показник кореляції (лінійної залежності) між двома змінними X та Y, який набуває значень від −1 до +1 включно. Він широко використовується в науці для вимірювання ступеня лінійної залежності між двома змінними. Показник був розроблений Карлом Пірсоном (Karl Pearson) зі схожої ідеї, представленої Френсісом Гальтоном в 1880-х рр. (uk) 在统计学中，皮尔逊积矩相关系数（英語：Pearson product-moment correlation coefficient，缩写：PPMCC，或PCCs，有时简称相关系数）用于度量兩組數據的变量X和Y之间的線性相關的程度。它是兩個變量的協方差與其標準差的乘積之比； 因此，它本質上是協方差的歸一化度量，因此結果始終具有介於-1和1之間的值。與協方差本身一樣，該度量只能反映變量的線性相關性，而忽略了許多其他類型的關係或相關性。舉個簡單的例子，可以預期高中青少年樣本的年齡和身高的皮尔逊积矩相关系数顯著大於0，但小於1（因為1表示不切實際的完美相關性）。 (zh) Der Korrelationskoeffizient, auch Produkt-Moment-Korrelation, ist ein Maß für den Grad des linearen Zusammenhangs zwischen zwei mindestens intervallskalierten Merkmalen, das nicht von den Maßeinheiten der Messung abhängt und somit dimensionslos ist. Er kann Werte zwischen und annehmen. Bei einem Wert von (bzw. ) besteht ein vollständig positiver (bzw. negativer) linearer Zusammenhang zwischen den betrachteten Merkmalen. Wenn der Korrelationskoeffizient den Wert 0 aufweist, hängen die beiden Merkmale überhaupt nicht linear voneinander ab. Allerdings können diese ungeachtet dessen in nichtlinearer Weise voneinander abhängen. Damit ist der Korrelationskoeffizient kein geeignetes Maß für die (reine) stochastische Abhängigkeit von Merkmalen. Das Quadrat des Korrelationskoeffizienten stellt d (de) Estatistikan, Pearsonen korrelazio koefiziente linealak edo, labur, korrelazio koefizienteak bi aldagai kuantitatiboren arteko korrelazio linealaren norabidea eta sendotasuna neurtzen duen adierazle bat da. Kobariantzatik eratortzen den koefizientea da: jatorrizko datuez kalkulaturiko kobariantza dimentsionatua izanik, korrelazioaren sendotasuna neurtzeko egokia ez denez, jatorrizko datuak estandarizatu eta datu estandarizatu hauekin kobariantza kalkulatuz lortzen da Pearsonen korrelazio koefizientearen formula. (eu) In statistics, the Pearson correlation coefficient (PCC, pronounced /ˈpɪərsən/) ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; 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 teenagers from a high school to h (en) Een correlatiecoëfficiënt is een maat voor de correlatie tussen twee stochastische grootheden (of stochastische variabelen). Meestal spreekt men van correlatie als er tussen de beide grootheden een zekere samenhang is, in die zin dat waarden van de beide grootheden dezelfde of een tegengestelde tendens vertonen. Zo is er sprake van correlatie tussen de grootheden lengte en gewicht bij (volwassen) mensen. Met toenemende lengte neemt gemiddeld gezien ook het gewicht toe. (nl) Em estatística descritiva, o coeficiente de correlação de Pearson, também chamado de "coeficiente de correlação produto-momento" ou simplesmente de "ρ de Pearson" mede o grau da correlação (e a direcção dessa correlação - se positiva ou negativa) entre duas variáveis de escala métrica (intervalar ou de rácio/razão). Este coeficiente, normalmente representado por ρ assume apenas valores entre -1 e 1. (pt) |
| rdfs:label | معامل الارتباط لبيرسون (ar) Coeficient de correlació de Pearson (ca) Korrelationskoeffizient (de) Korrelazio-koefiziente (eu) Coeficiente de correlación de Pearson (es) Indice di correlazione di Pearson (it) 피어슨 상관 계수 (ko) Correlatiecoëfficiënt (nl) Pearson correlation coefficient (en) Współczynnik korelacji Pearsona (pl) Coeficiente de correlação de Pearson (pt) 皮尔逊积矩相关系数 (zh) Коефіцієнт кореляції Пірсона (uk) |
| rdfs:seeAlso | dbr:Correlation dbr:Dependence |
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