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Related Concept Videos

Variation01:19

Variation

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An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
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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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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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Multiple Regression01:25

Multiple Regression

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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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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.
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Related Experiment Video

Updated: Mar 26, 2026

An R-Based Landscape Validation of a Competing Risk Model
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Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models.

Gwowen Shieh1

  • 1a Department of Management Science , National Chiao Tung University .

Multivariate Behavioral Research
|January 23, 2016
PubMed
Summary
This summary is machine-generated.

This study enhances statistical methods for squared cross-validity coefficients, crucial for predicting future research outcomes. New exact methods, adapted from squared multiple correlation, improve interval estimation, power calculation, and sample size determination in regression analysis.

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Area of Science:

  • Statistics
  • Social Sciences
  • Psychometrics

Background:

  • Population validity and cross-validity are key in regression analysis.
  • Inference procedures for squared multiple correlation are well-developed.
  • Statistical methods for squared cross-validity coefficients are incomplete.

Purpose of the Study:

  • To define squared cross-validity coefficient as a transformation of squared multiple correlation.
  • To extend existing exact methods for squared multiple correlation to squared cross-validity.
  • To provide practical methodologies for cross-validation in social science research.

Main Methods:

  • Defined squared cross-validity coefficient through a direct connection to squared multiple correlation.
  • Modified and extended exact methods for interval estimation, power calculation, and sample size determination.
  • Evaluated methods using a Monte Carlo study and presented empirical examples.

Main Results:

  • Established a distinct expression for squared cross-validity coefficient.
  • Successfully extended exact statistical methods for squared multiple correlation.
  • Demonstrated practical applications in psychology and management research.

Conclusions:

  • The proposed methodologies facilitate the analysis of squared cross-validity coefficients.
  • These advancements support the recommended practice of cross-validation in research.
  • Enhanced statistical tools improve the predictive effectiveness of regression equations in future studies.