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Related Concept Videos

Correlations02:20

Correlations

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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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Correlation and Regression00:53

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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...
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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
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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. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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Coefficient of Correlation01:12

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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.
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Correlation01:09

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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:
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Quantifying direct associations between variables.

Minyuan Zhao1, Yun Chen2, Qin Liu2

  • 1Institute for Brain Sciences and Kuang Yaming Honors School, Nanjing University, Nanjing 210023, China.

Fundamental Research
|August 8, 2025
PubMed
Summary
This summary is machine-generated.

We introduce independent conditional mutual information (ICMI) to measure direct variable association. ICMI offers greater stability and reliability than traditional methods, especially in complex networks.

Keywords:
Chain graphConditional mutual informationDirect associationDirected acyclic graphIndependent conditional mutual information

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Area of Science:

  • Statistics
  • Network Analysis
  • Data Science

Background:

  • Traditional methods for quantifying direct variable association often fail to capture non-linear relationships.
  • Existing measures can be unstable when a parent variable strongly influences multiple child variables.

Purpose of the Study:

  • To propose a novel measure, independent conditional mutual information (ICMI), for quantifying direct association in three-variable networks.
  • To evaluate the stability and reliability of ICMI compared to existing measures.

Main Methods:

  • Developed the independent conditional mutual information (ICMI) metric.
  • Conducted numerical simulations comparing ICMI with unique information, conditional mutual information, and partial correlation.
  • Assessed statistical power across different functional forms.

Main Results:

  • ICMI demonstrated superior stability compared to unique information, conditional mutual information, and partial correlation in various scenarios.
  • ICMI proved more reliable across different functional forms, indicating robust performance.
  • The measure was successfully applied to analyze the interrelations within a network of family finance, social security, and senior citizen residence.

Conclusions:

  • Independent conditional mutual information (ICMI) is a stable and reliable measure for quantifying direct variable association in networks.
  • ICMI overcomes limitations of traditional methods, offering improved accuracy in complex data.
  • The proposed measure has practical applications in analyzing real-world socio-economic networks.