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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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Regression Analysis01:11

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Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
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Residuals and Least-Squares Property01:11

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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
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
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Spearman's Rank Correlation Test01:20

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Spearman's rank correlation test, also known as Spearman's rho, is a nonparametric method for assessing the strength and direction of association between two variables. This test is particularly valuable when the data distribution is unknown or when the assumption of normality does not hold. Named after the English psychologist and statistician Dr. Charles Edward Spearman, it serves as the nonparametric counterpart to Pearson's correlation coefficient.
Spearman's test calculates correlation by...
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Residual Plots01:07

Residual Plots

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A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
When the residual values are plotted against the variable x, it is called a residual...
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Introduction to Test of Independence01:21

Introduction to Test of Independence

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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
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Related Experiment Video

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Disturbance Term Regression Test Procedures for Recursive and Nonrecursive Models: Solution From Intercorrelation

C E Lance

    Multivariate Behavioral Research
    |February 2, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study reviews disturbance term regression tests for structural models. The test is mathematically equivalent to part correlation in simple mediational cases, offering a way to assess model consistency.

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    Area of Science:

    • Structural Equation Modeling
    • Statistical Methods
    • Psychometrics

    Background:

    • Structural models are crucial for understanding complex relationships.
    • Assessing the logical consistency of these models is vital for valid inferences.
    • Existing methods for evaluating model fit have limitations.

    Purpose of the Study:

    • To review the logic and procedures of disturbance term regression tests.
    • To demonstrate the mathematical equivalence of this test to part correlation in specific cases.
    • To provide practical procedures for applying these tests in research.

    Main Methods:

    • Review of disturbance term regression test principles.
    • Mathematical analysis for recursive and nonrecursive designs.
    • Demonstration of equivalence to part correlation in a three-variable mediational model.
    • Outline of procedures using intercorrelation matrices.

    Main Results:

    • The disturbance term regression test is mathematically equivalent to part correlation in a simple, complete mediational case.
    • Procedures are presented for conducting these tests using only intercorrelation matrices.
    • Generalizable methods are provided for testing mediation and cross-effects.

    Conclusions:

    • Disturbance term regression offers a valuable tool for assessing structural model consistency.
    • The outlined procedures facilitate the application of these tests in both recursive and nonrecursive models.
    • This approach provides an alternative or complement to other model fit indices.