Three Regression Models: Their Relative Usefulness in Predicting College Achievement

Statement and Significance of the Problem: The primary concern of this study was methodological, while a secondary concern was substantive The methodological concern was an investigation of three methods for developing.predictive equations. The three regression models employed raw scores, and two reduced-rank methods of computing "factor" scores as predictors The reduced-rank predictors were orthogonally computed component scores, and saumative scale scores. The substantive concein was an investigation of a guidance and placement test battery used in a community college, the Comparative Guidance and Placement battery (CGP) A review of the literature indicated that -when reduced-rank methods were used in predictor reduction, the largest principal component method was the most efficient. The present study capitalized on these research findings by investigating the combinetion of stepwise regression with the largest principal components in an attempt to establish an optimal prediction method. Thus, the focus of this study was the development and cross-validation of a multivaiiate prediction mode'.! which will maximize the effectiveness of a guidance and placement instrument used in a community college. Methods and Procedures: The CGP was administered to all incoming freshman students at a Connecticut community coilogs during the Springs of 1971 find 1972. Two curricular groups were identified and extracted for investigation:Liberal-Studies (n = 395) and Business-Technical career programs (n = 291) Tne regression techniques used with the community college groups were replicated on a sample of 171+ students admitted in an associate degree nursing program at Purdue University in I9S8. End-of-year grade point average (GPA) v/as used as the criterion in all analyses. The data from the tv/o community college curricular groups on the CGP battery were submitted separately to a principal component analysis; alpha scale reliabilities were computed on the derived components. The three regression models were then carried out on each curricular group. Comparisons of cross-validation coefficients for the complete data sets and optimal data subsets selected by stepwise regression were made for all three models. Finally, to examine the generalizability of the regression techniques the methodological procedures were duplicated on the Purdue nursing data. In a separate analysis, the CGP self-reported high school grades .in English and mathematics were found to be poor estimates of the students’ actual grades and were removed from the study. In light of these results, the incremental validity of school-reported grades in predicting college GPA, when added to the CGP variables, was investigated using a sample from each curricular group. Results and Conclusions: The principal component analyses were found to be meaningful and consistent with previous research. The resulting CGP dimensions achieved moderate alpha reliabilities. Results indicated that the CGP is useful in making differential curricular predictions. However, further attempts should be made to use predictors with higher reliabilities, and to find additional variables to increase the level of predictive efficiency established by the CGP battery. High school English and mathematics grades were found to significantly increase the prediction of college GPA when added to the Business-Technical predictor variables. This increment did not occur with a sample of Liberal-Studies students. Comparison of the community college and Purdue nursing data results indicated that the reduced-rank models were superior to the raw score model in maximizing the predictability of the criterion in the cross-validation samples. Further, the reduced-rank models achieved multiple correlations close to the raw score model while using fewer numbers of predictors. There were no apparent differences between the results obtained in the two reduced-rank models. The context of the research may ultimately decide the usefulness of the three predictor models. For efficiency, the use of raw scores was suggested; for understanding or theory development the vise of reduced rank scores was proposed.