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Related Concept Videos

Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
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Methodological and computational considerations for multiple correlation analysis.

Gwowen Shieh1, Cmen-Feng Kung

  • 1Department of Management Science, National Chiao Tung University, Hsinchu, Taiwan. gwshieh@mail.nctu.edu.tw

Behavior Research Methods
|January 11, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces methods for testing the substantive significance of the squared multiple correlation coefficient, a key measure of linear regression model fit. It provides practical Excel tools for researchers to assess effect sizes and conduct power analyses.

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • The squared multiple correlation coefficient (R²) is crucial for assessing linear regression model fit.
  • Existing literature extensively covers inferential statistics for multinormal correlation models.
  • However, testing substantive significance using a nonzero-effect null hypothesis for R² is underexplored.

Purpose of the Study:

  • To highlight the importance of evaluating R² against predefined standards for substantive significance.
  • To develop practical tools for implementing significance tests for R².
  • To provide computational routines for interval estimation, power calculation, and sample size determination.

Main Methods:

  • Development of Excel worksheets for significance testing of R².
  • Implementation of statistical routines for interval estimation, power, and sample size.
  • Focus on the nonzero-effect null hypothesis for R².

Main Results:

  • Provided user-friendly Excel tools for assessing the substantive significance of R².
  • Developed computer routines for essential statistical analyses related to R².
  • Facilitated practical application and pedagogical use of R² significance testing.

Conclusions:

  • The proposed methods and tools enhance the assessment of linear regression model fit.
  • The developed resources support both academic instruction and psychological research applications.
  • Emphasizes practical significance testing for R² beyond mere statistical significance.