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Related Concept Videos

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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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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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Calibration Curves: Correlation Coefficient01:10

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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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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Calculating and Interpreting the Linear Correlation Coefficient01:11

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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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Establishing a Competing Risk Regression Nomogram Model for Survival Data
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[Correlation coefficient-based classification method of hydrological dependence variability: With auto-regression

Yu Xi Zhao1, Ping Xie1,2, Yan Fang Sang3

  • 1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China.

Ying Yong Sheng Tai Xue Bao = the Journal of Applied Ecology
|May 5, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new method to evaluate hydrological dependence variability using correlation coefficients and auto-regression models. It helps researchers understand the complex temporal dynamics in water systems.

Keywords:
auto-regression modelcorrelation coefficientdependencehydrological variabilitystochastic process

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Area of Science:

  • Hydrology
  • Time Series Analysis
  • Statistical Modeling

Background:

  • Hydrological process evaluation is complicated by temporal dependence and data inconsistency.
  • Variability in hydrological dependence poses challenges for water research.

Purpose of the Study:

  • To propose a novel correlation coefficient-based method for evaluating the significance of hydrological dependence.
  • To address the challenges posed by temporal dependence in hydrological time series analysis.

Main Methods:

  • Developed a method based on auto-regression models to assess hydrological dependence significance.
  • Calculated correlation coefficients between original series and dependence components.
  • Classified dependence significance into five levels: no, weak, mid, strong, and drastic variability.
  • Deduced the relationship between correlation coefficient and auto-correlation coefficients.

Main Results:

  • The proposed method effectively classifies the significance of hydrological dependence.
  • Correlation coefficients are primarily determined by auto-correlation coefficients of lower orders.
  • Monte-Carlo experiments validated the deduced formulas for first and second-order auto-regression models.
  • Analysis of observed hydrological time series revealed the coexistence of stochastic and dependence characteristics.

Conclusions:

  • The developed method provides a robust framework for analyzing hydrological time series.
  • Understanding hydrological dependence variability is crucial for accurate water resource management.
  • The findings highlight the inherent complexity of hydrological processes, combining random and dependent behaviors.