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Related Concept Videos

Correlation01:09

Correlation

11.5K
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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Correlation and Regression00:53

Correlation and Regression

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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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Correlation of Experimental Data01:23

Correlation of Experimental Data

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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
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Time-Series Graph00:54

Time-Series Graph

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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Correlations02:20

Correlations

32.2K
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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Coefficient of Correlation01:12

Coefficient of Correlation

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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.
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...
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Expected correlation in time-series analysis.

Theodore MacMillan1, James P Hilditch2, Nicholas T Ouellette1

  • 1Stanford University, Department of Civil and Environmental Engineering, Stanford, California 94305, USA.

Physical Review. E
|March 19, 2025
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Summary
This summary is machine-generated.

Predictability in time-series analysis increases with system size when viewed across multiple time scales. Aggregated time-series data inherently shows higher correlations, a previously underestimated bias.

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Area of Science:

  • Data Science
  • Statistical Analysis
  • Time-Series Modeling

Background:

  • Time-series analysis frequently assesses order and predictability, linked to internal structure and autocorrelation.
  • Understanding these qualities is crucial for accurate data interpretation and modeling.

Purpose of the Study:

  • To investigate a new algorithm for density prediction tasks.
  • To demonstrate how viewing systems across multiple time scales impacts predictability.
  • To establish bounds on expected structure and autocorrelation functions for multi-scale time series.

Main Methods:

  • Analysis of a recently proposed density prediction algorithm.
  • Derivation of bounds for the second-order structure function and autocorrelation function.
  • Introduction of a lower bound for the expected correlation time.

Main Results:

  • Expected order and predictability increase with system size when multiple observation scales are available.
  • Established bounds on the second-order structure function and autocorrelation function.
  • Quantified an inevitable degree of correlation induced by data aggregation.

Conclusions:

  • Multi-scale analysis reveals inherent predictability that grows with system size.
  • Data aggregation introduces a bias towards higher correlations, a factor previously overlooked.
  • The derived lower bound on correlation time highlights this induced correlation effect.