Global and Local Regression Analysis of Factors of American College Test (ACT) Score for Public High Schools in the State of Missouri

• Published in: Annals of the Association of American Geographers Vol. 101; no. 1; pp. 63 - 83
• Main Authors: Qiu, Xiaomin, Wu, Shuo-sheng
• Format: Journal Article
• Language: English
• Published: Washington, DC Taylor & Francis Group 01.01.2011; Association of American Geographers; Taylor & Francis Ltd
• Subjects: Academic achievement; ACT; ACT assessment; America; American College Test; Bgi / Prodig; Education systems; Family income; geographically weighted regression; global regression; High school students; High schools; local regression; Methods, Models, and GIS; Metropolitan areas; Missouri; Modeling; mínimos cuadrados ordinarios; mínimos cuadrados ponderados; ordinary least squares; Parent's education; Prueba de Ingreso a la Universidad; regresión geográficamente ponderada; regresión global; regresión local; Regression analysis; Regression coefficients; School districts; School environment; Secondary schools; Standardized tests; Statistical methods; Teachers; U.S.A; United States of America; weighted least squares; West North Central; 全局回归; 加权最小二乘; 地理加权回归; 局部回归; 普通最小二乘法; 美国大学入学考试（ACT）; United States of America; Missouri; Higher education; Education; Secondary education; Test; Neighbourhood; Multivariate analysis; Spatial variation; Applied geography
• ISSN: 0004-5608; 2469-4452; 1467-8306; 2469-4460
• DOI: 10.1080/00045608.2010.518020

This study aims to improve the conceptual understanding of the interrelationships among individual-level and school-level factors of academic performance by presenting a context-based conceptual framework of academic performance and articulating relationships among the factors. In addition, this study intends to advance the statistical methodology of local regression analysis through a case study analyzing predictor variables of American College Test (ACT) score for 447 public high schools in Missouri. A school-level statistical model of ACT score with nine predictor variables relevant to student, teacher, and school characteristics is tested. Ordinary least squares (OLS) global regression analysis derives a model of five predictor variables, showing that schools with higher parent income and education levels, more double-parent family background, larger class size, and more experienced teachers tend to have higher ACT scores. Geographically weighted regression (GWR) local regression analysis is conducted using the five globally verified predictor variables to minimize violations of regression assumptions, particularly multicollinearity, in local models. Geographic distributions of local regression coefficients are examined at a series of local regression neighborhoods to draw integral conclusions of variable effects for local areas. Analyses show that using globally verified predictor variables in GWR effectively avoids multicollinearity that would otherwise appear. The results highlight critical local regression neighborhoods at which certain local areas start to show opposite local variable effects from the global variable effects.