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Correlations02:20

Correlations

34.7K
Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
34.7K
Scatter Plot01:15

Scatter Plot

8.5K
The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either:
8.5K
Correlation01:09

Correlation

12.2K
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
12.2K
Coefficient of Correlation01:12

Coefficient of Correlation

7.7K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
7.7K
Correlation and Regression00:53

Correlation and Regression

3.8K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
3.8K
Microsoft Excel: Pearson's Correlation01:18

Microsoft Excel: Pearson's Correlation

2.9K
Microsoft Excel is a powerful tool for statistical analysis, including calculating Pearson's correlation coefficient, which measures the strength and direction of a linear relationship between two continuous variables. Pearson's correlation coefficient, often denoted as "r," ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, meaning as one variable increases, the other does too. A value close to -1 indicates a strong negative correlation, implying...
2.9K

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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Correlación de los patrones de recurrencia de los patrones de recurrencia.

Gabriel Marghoti1,2, Matheus Palmero Silva2,3, Thiago de Lima Prado1

  • 1Federal University of Paraná, Physics Department, Curitiba, Paraná 81530-015, Brazil.

Physical review. E
|February 20, 2026
PubMed
Resumen
Este resumen es generado por máquina.

Desarrollamos la correlación de patrones de recurrencia (RPC), un nuevo método para analizar datos complejos de series temporales. RPC ofrece una forma más flexible de estudiar estructuras localizadas en sistemas dinámicos que las tramas de recurrencia tradicionales (RP).

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Área de la Ciencia:

  • La dinámica no lineal es la dinámica no lineal.
  • Análisis de sistemas complejos análisis de sistemas complejos.
  • El análisis de las series temporales.

Sus antecedentes:

  • Los gráficos de recurrencia (RP) son valiosos para visualizar la dinámica de las series temporales.
  • El análisis de cuantificación de la recurrencia tradicional a menudo utiliza métricas globales, faltando estructuras localizadas.
  • Existe una brecha entre la inspección cualitativa de RP y el análisis cuantitativo.

Objetivo del estudio:

  • Introducir la correlación de patrones de recurrencia (RPC) para cerrar la brecha en el análisis de la recurrencia.
  • Desarrollar una herramienta flexible para analizar la formación de patrones en sistemas dinámicos recurrentes.
  • Medir el grado de correlación de RPs a patrones de forma y escala arbitrarias.

Principales métodos:

  • Introducir la correlación de patrones de recurrencia (RPC), inspirada en las estadísticas espaciales.
  • Aplicar RPC para visualizar colectores inestables en el mapa Logístico.
  • Disiegue el espacio de fase mixta del mapa estándar utilizando RPC.
  • Rastrear órbitas periódicas inestables en el sistema Lorenz '63.

Principales resultados:

  • RPC visualiza con éxito las estructuras localizadas que se pierden con los métodos tradicionales.
  • El método revela correlaciones entre los patrones de recurrencia y las propiedades dinámicas subyacentes.
  • RPC demuestra flexibilidad en el análisis de diversos sistemas no lineales.

Conclusiones:

  • La correlación de patrones de recurrencia (RPC) proporciona un análisis cuantitativo más matizado de los datos de series temporales.
  • Las correlaciones de largo alcance en los patrones de recurrencia codifican información crucial sobre la dinámica no lineal.
  • RPC ofrece un marco flexible para el estudio de la formación de patrones en sistemas complejos.