A COMPARISON OF UNBIASED, BIASED, AND WEIGHTED MULTIPLE LINEAR REGRESSION APPROACHES TO SUPPORT EDUCATIONAL POLICY IN THE IDENTIFICATION OF OUTLIER SCHOOLS (RIDGE REGRESSION, PREDICTION, RESIDUAL, EXPLANATION, NEEDS, ASSESSMENT

The purpose of this study was to illuminate strengths and limitations of four popular multiple regression approaches which are frequently applied in non-experimental contexts to support educational policy decisions.;The database contained information about over 30 variables collected on 99 public elementary schools during the school years 1972 through 1976.;The multiple regression applications included: (1) OLS--Ordinary least squares, (2) RIDGE--Ridge regression utilizing the Lawless and Wang algorithm for the k-weights, (3) FACTOR--reduced-rank models containing four composite predictors and (4) UNIT--models containing a single standardized composite predictor. These regression models were developed from two, four-year replications of student performance and school/district resource variables averaged by school.;The procedure included: (1) weighting adjustments of the samples to improve the reliability of the observations, (2) selection of the variables to use in the regression models, (3) comparisons of the importance and stability of the regression coefficients, (4) double cross-validation to determine predictive power, (5) and analyses of residual patterns for contrasts in school outliers.;Major findings from the study were: (1) Weighting adjustments to the samples produced more stable OLS regression coefficients than each regression application to the unweighted samples. (2) RIDGE regression was more effective than OLS, FACTOR, or UNIT regression in estimating true regression coefficients in the unweighted samples. (3) RIDGE regression produced more precise estimates of average student performance for new datasets than did the OLS, FACTOR and UNIT regression approaches when applied to both the unweighted and weighted datasets. (4) RIDGE and OLS approaches produced similar school outlier patterns; FACTOR and UNIT regression produced divergent outlier patterns. (5) The reliability of variables in the samples placed constraints upon the validity of information about the importance of predictors derived from each regression approach. (6) The use of composite variables as predictors altered the meaning of the original relationship of the contributing variables to the criterion.