Limitations of using linear, unilevel regression procedures in modeling student achievement are discussed. This study is a part of a broader study that is developing an empirically-based predictive model of variables associated with academic achievement from a multilevel perspective and examining the differences by which parameters are estimated in a multilevel analysis using regression-based hierarchical linear modeling. An introduction to hierarchical linear modeling is provided. The data for this study comprises the cohort of Pennsylvania elementary school students who were enrolled in grade 3 in 1986 and grade 5 in 1988 and who participated in the statewide Tests of Essential Learning Skills program in reading and mathematics. Results indicate the importance of correctly partitioning variability among schools or school districts; this finding has clear implications for educational policy research. Analyses using district-level aggregate data can only explain a finite portion of the variation in achievement. Although the individual-level model explains variation in student-level achievement, it cannot model policy manipulable district-level factors without biasing other effects in the model. Multilevel analysis, on the other hand, offers a means of improving conventional regression analyses confounded by aggregation bias and model misspecification. Four data tables are included. (TJH)