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Related Concept Videos

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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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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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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Correlation of Experimental Data01:23

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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.
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Correlation01:09

Correlation

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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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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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Parametric Dependencies of Sliding Window Correlation.

Sadia Shakil, Jacob C Billings, Shella D Keilholz

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    Sliding window correlation (SWC) results for functional connectivity (FC) analysis are sensitive to signal parameters. This study highlights SWC limitations in resting-state fMRI (rsfMRI) due to unknown signal properties and parameter dependencies.

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    Area of Science:

    • Neuroimaging
    • Signal Processing
    • Network Science

    Background:

    • Sliding window correlation (SWC) is crucial for analyzing functional connectivity (FC) dynamics in resting-state fMRI (rsfMRI).
    • rsfMRI signals possess complex amplitudes, frequencies, and phases, whose exact values remain unknown.
    • Previous research investigated the impact of window length and frequency on SWC, but further exploration is needed.

    Purpose of the Study:

    • To investigate the parametric dependencies of SWC on signal characteristics.
    • To evaluate the reliability of SWC for studying FC network dynamics with unknown signal parameters.
    • To extend previous findings on window length and frequency effects using deterministic and real rsfMRI data.

    Main Methods:

    • Utilized deterministic signals with varying amplitudes, frequencies, and phases to assess SWC.
    • Introduced nonstationarity by modulating one signal.
    • Examined the influence of window length and frequency bands on SWC using real rsfMRI data.

    Main Results:

    • SWC accurately estimated stationary correlation for deterministic signals with specific frequency relationships.
    • Undesirable frequency components were mitigated under certain conditions for dynamic relationships.
    • SWC results for rsfMRI data demonstrated variability dependent on frequency and window length.

    Conclusions:

    • SWC's reliability in studying FC dynamics is questionable for rsfMRI data due to unknown ground truth parameters.
    • The study underscores the parametric dependencies and limitations of SWC in analyzing FC network dynamics.