Global and local regression analysis of factors of american college test (act) score for public high schools in the state of Missouri
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.
Geography, Geology, and Planning
American college test, Geographically weighted regression, Global regression, Local regression, Ordinary least squares, Weighted least squares
Qiu, Xiaomin, and Shuo-sheng Wu. "Global and local regression analysis of factors of American College Test (ACT) score for public high schools in the state of Missouri." Annals of the Association of American Geographers 101, no. 1 (2011): 63-83.
Annals of the Association of American Geographers