A comparison of: four multiple prediction selection techniques, mathematical and empirical estimation of weight validity, and the quality of prediction of three different combinations of a real life data set

摘要

The present study investigated the performance of four multiple regression techniques: stepwise, forward, backward and Maximizing Weight Validity (MWV) in predicting the success of freshman students, as measured by Freshman GPA, in the college of science at Yarmouk University, Irbid-Jordan, from the grades of five academic subjects selected by an exploratory analysis from eight available subjects taken from the General Secondary Education Certificate Examination (GSECE). The shrinkage in the squared validity coefficient (R(\u272)) was compared with the corresponding values calculated from the three mathematical shrinkage formulas (Wherry, Lord-Nicholson and Stein-Darlington). The original eight variables were numerically reduced by three techniques (judgment, factor analysis and regression). The quality of prediction from the reduced variables utilizing the three techniques was investigated. The data were collected from the records of 344 freshman (220 males and 124 females) which were available in the Admission and Registration Department of the University. The data of males and females were treated separately and the whole data set was also treated as a single group. The superiority of the prediction techniques and the estimated shrinkage in R(\u272) were investigated for three sample sizes, small, intermediate and large. The validity of the prediction equation was tested over a two year period. The results indicated the equality of the performance of the MWV technique and the traditional techniques for samples of small ratios. The results of the analysis applied to intermediate and large ratios indicated the superiority of the MWV prediction equation. The findings indicated that females were consistently more predictable than males. The results revealed that the amount of shrinkage was underestimated differentially by the three mathematical shrinkage formulas. The highest underestimation was obtained from the Wherry formula. The best estimation for large and intermediate sample ratios was obtained from the Stein-Darlington formula. According to Schmitt\u27s criterion, the shrinkage was underestimated by all three formulas in the case of small sample sizes. The results of testing the validity of the prediction equation over time indicated the invalidity of the prediction equations. The quality of prediction of the three reduced models was judged by four indices (R(\u272)%, MAE, P and shrinkage of R(\u272)). The results indicated that the factor score model had better quality of prediction than the other two reduced models.