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Multiple Regression and Validity Estimation in One Sample.
Peer reviewed Peer reviewed
Claudy, John G. – Applied Psychological Measurement, 1979
Equations for estimating the value of the multiple correlation coefficient in the population underlying a sample and the value of the population validity coefficient of a sample regression equation were investigated. Results indicated that cross-validation may no longer be necessary for certain purposes. (Author/MH)
Descriptors: Correlation, Mathematical Formulas, Multiple Regression Analysis, Predictor Variables
Comparison of Different Shrinkage Formulas in Estimating Population Multiple Correlation Coefficients.
Peer reviewed Peer reviewed
Carter, David S. – Educational and Psychological Measurement, 1979
There are a variety of formulas for reducing the positive bias which occurs in estimating R squared in multiple regression or correlation equations. Five different formulas are evaluated in a Monte Carlo study, and recommendations are made. (JKS)
Descriptors: Comparative Analysis, Correlation, Mathematical Formulas, Multiple Regression Analysis
Formula Estimation of Cross-Validated Multiple Correlation.
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Schmitt, Neal – 1982
A review of cross-validation shrinkage formulas is presented which focuses on the theoretical and practical problems in the use of various formulas. Practical guidelines for use of both formulas and empirical cross-validation are provided. A comparison of results using these formulas in a range of situations is then presented. The result of these…
Descriptors: Correlation, Estimation (Mathematics), Mathematical Formulas, Mathematical Models
Estimators of the Squared Cross-Validity Coefficient: A Monte Carlo Investigation.
Peer reviewed Peer reviewed
And Others; Drasgow, Fritz – Applied Psychological Measurement, 1979
A Monte Carlo experiment was used to evaluate four procedures for estimating the population squared cross-validity of a sample least squares regression equation. One estimator was particularly recommended. (Author/BH)
Descriptors: Correlation, Least Squares Statistics, Mathematical Formulas, Multiple Regression Analysis
A Monte Carlo Evaluation of Estimated Parameters of Five Shrinkage Estimate Formuli.
Newman, Isadore; And Others – 1979
A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample…
Descriptors: Correlation, Mathematical Formulas, Monte Carlo Methods, Multiple Regression Analysis
A Monte Carlo Evaluation of Estimated Parameters of Five Shrinkage Estimate Formuli.
Peer reviewed Peer reviewed
Newman, Isadore; And Others – Multiple Linear Regression Viewpoints, 1979
A Monte Carlo simulation was employed to determine the accuracy with which the shrinkage in R squared can be estimated by five different shrinkage formulas. The study dealt with the use of shrinkage formulas for various sample sizes, different R squared values, and different degrees of multicollinearity. (Author/JKS)
Descriptors: Computer Programs, Correlation, Goodness of Fit, Mathematical Formulas
Estimates of Multiple Correlation Coefficient Shrinkage.
Cummings, Corenna C. – 1982
The accuracy and variability of 4 cross-validation procedures and 18 formulas were compared concerning their ability to estimate the population multiple correlation and the validity of the sample regression equation in the population. The investigation included two types of regression, multiple and stepwise; three sample sizes, N = 30, 60, 120;…
Descriptors: Correlation, Error of Measurement, Mathematical Formulas, Multiple Regression Analysis