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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...
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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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Updated: May 5, 2026

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

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繰り返しのパターンの相関関係

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
まとめ
この要約は機械生成です。

私たちは,複雑なタイムシリーズデータを分析するための新しい方法である再帰パターン相関 (RPC) を開発しました. RPCは,従来の再帰プロット (RP) よりも,動的システムにおける局所構造を研究するためのより柔軟な方法を提供します.

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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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科学分野:

  • 非線形ダイナミクス 非線形ダイナミクス
  • 複雑なシステムの分析分析
  • タイムシリーズの分析

背景:

  • リキュアンスプロット (RP) は,タイムシリーズのダイナミクスを視覚化するのに価値があります.
  • 伝統的な再発量定量分析は,しばしばグローバルメトリックを使用し,局所化された構造が欠落しています.
  • 定性的なRP検査と定量的な分析の間にギャップがあります.

研究 の 目的:

  • 再発パターン相関 (RPC) を導入し,再発分析のギャップを埋める.
  • 繰り返しの動的システムにおけるパターン形成を分析するための柔軟なツールを開発する.
  • 任意の形状とスケールのパターンのRPの相関度を測定します.

主な方法:

  • 空間統計からインスパイアされた再発パターン相関 (RPC) を導入する.
  • ロジスティックマップで不安定なマニホールドを視覚化するためにRPCを適用します.
  • RPCを使用して標準マップの混合相空間を剖析する.
  • ローレンツ63系における不安定な周期軌道を追跡する.

主要な成果:

  • RPCは,従来の方法では見逃された局所的な構造を視覚化することに成功しました.
  • この方法は,再発パターンと基礎となる動的性質の間の相関を明らかにします.
  • RPCは,多様な非線形系を分析する際の柔軟性を示しています.

結論:

  • 再帰パターン相関 (RPC) は,タイムシリーズデータのより微妙な定量分析を提供します.
  • 繰り返しのパターンの長距離相関は,非線形動力学に関する重要な情報を暗号化しています.
  • RPCは,複雑なシステムにおけるパターン形成を研究するための柔軟な枠組みを提供します.