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Related Concept Videos

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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The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
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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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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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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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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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Updated: Apr 29, 2026

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
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Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.

Min Jin Ha1, Wei Sun1,2

  • 1Department of Biostatistics, UNC Chapel Hill, North Carolina, U.S.A.

Biometrics
|May 22, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new statistical method to build gene co-expression networks by estimating partial correlation matrices. Our approach accurately identifies gene interactions, outperforming existing methods like Graphic Lasso in yeast gene expression data analysis.

Keywords:
Co‐expression networkEmpirical null distributionGraphical modelPartial correlation matrixRidge regression

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Area of Science:

  • Bioinformatics
  • Statistical Genetics
  • Computational Biology

Background:

  • Gene co-expression networks are crucial for understanding gene function.
  • Estimating high-dimensional partial correlation matrices is challenging.
  • Existing methods like Graphic Lasso have limitations.

Purpose of the Study:

  • To propose a robust statistical framework for estimating high-dimensional partial correlation matrices.
  • To improve the construction of gene co-expression networks.
  • To address the challenge of establishing null distributions in penalized estimates.

Main Methods:

  • A three-step approach involving penalized estimation (ridge penalty), hypothesis testing for non-zero entries, and re-estimation of coefficients.
  • Empirical estimation of the null distribution for test statistics derived from penalized estimates.
  • Application to yeast cell cycle gene expression data.

Main Results:

  • The proposed method demonstrates good performance in extensive simulation studies.
  • The method successfully estimates the partial correlation matrix in high dimensions.
  • It provides better predictions of protein-protein interactions compared to Graphic Lasso on yeast data.

Conclusions:

  • The novel statistical framework offers an effective approach for gene co-expression network construction.
  • The method overcomes limitations in estimating null distributions for penalized estimates.
  • It shows superior performance in predicting gene interactions, particularly in biological applications like yeast gene expression analysis.