# Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models

@article{Shieh2009ExactAO, title={Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models}, author={Gwowen Shieh}, journal={Multivariate Behavioral Research}, year={2009}, volume={44}, pages={105 - 82} }

In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference procedures of the squared multiple correlation coefficient have been extensively developed. In contrast, a full range of statistical methods for the…

## 2 Citations

Sample size calculations for model validation in linear regression analysis

- MathematicsBMC Medical Research Methodology
- 2019

The results show that the exact approach has a distinct advantage over the current method with greater accuracy and high robustness.

## References

SHOWING 1-10 OF 43 REFERENCES

Improved Shrinkage Estimation of Squared Multiple Correlation Coefficient and Squared Cross-Validity Coefficient

- Mathematics
- 2008

The sample squared multiple correlation coefficient is widely used for describing the usefulness of a multiple linear regression model in many areas of science. In this article, the author considers…

Methodology Review: Estimation of Population Validity and Cross-Validity, and the Use of Equal Weights in Prediction

- Business
- 1997

In multiple regression, optimal linear weights are obtained using an ordinary least squares (OLS) procedure. However, these linear weighted combinations of predictors may not optimally predict the…

Estimating R 2 Shrinkage in Multiple Regression: A Comparison of Different Analytical Methods

- Mathematics
- 2001

Abstract The effectiveness of various analytical formulas for estimating R 2 shrinkage in multiple regression analysis was investigated. Two categories of formulas were identified: estimators of the…

Cross-Validation Sample Sizes

- Psychology
- 2000

The squared cross-validity coefficient is a measure of the predictive validity of a sample linear prediction equation. It provides a more realistic assessment of the usefulness of the equation than…

PREDICTIVE VALIDITY OF A LINEAR REGRESSION EQUATION

- Mathematics
- 1975

The squared correlation coefficient, w2, between an empirically chosen linear function of predictors, B0 + B′x, and a criterion, y, is employed as a measure of predictive precision. This coefficient…

Accuracy of Population Validity and Cross-Validity Estimation: An Empirical Comparison of Formula-Based, Traditional Empirical, and Equal Weights Procedures

- Psychology
- 1999

An empirical monte carlo study was performed using predictor and criterion data from 84,808 U.S. Air Force enlistees. 501 samples were drawn for each of seven sample size conditions: 25, 40, 60, 80,…

Confidence Intervals, Power Calculation, and Sample Size Estimation for the Squared Multiple Correlation Coefficient under the Fixed and Random Regression Models: A Computer Program and Useful Standard Tables

- Mathematics
- 2001

In this article, the authors introduce a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple…

Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis

- Mathematics
- 2006

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed…

Sample Size Tables for Correlation Analysis with Applications in Partial Correlation and Multiple Regression Analysis

- MathematicsMultivariate behavioral research
- 2003

SAS and SPSS computer programs are made available to permit researchers to select sample size for levels of accuracy, probabilities, and parameter values and for Type I error rates other than those used in constructing the tables.

Cost-Benefit Considerations in Choosing among Cross-Validation Methods.

- Economics
- 1984

There are two general methods of cross-validation: (a) empirical estimation, and (b) formula estimation. In choosing a specific cross-validation procedure, one should consider both costs (eg.…