Much research has analyzed the relationship between class size and scholastic aptitude. Specifically, studies have focused on whether or not reducing class size contributes to improving children's scholastic aptitude. Not all research shows such an impact, with some studies showing no positive effect. These inconsistent results suggest that other factors besides class size have a major influence on scholastic aptitude. This paper not only focuses on class size but also examines the multicollinearity of select factors considered economically relevant. Data on the percentage of correct answers (by third grade public middle school students, from 2007 to 2010) by prefecture obtained from the National Survey of Scholastic Aptitude and Learning Environment were used as the dependent variable. Results of all panel data models used in the paper showed that students in smaller classes tended to answer a higher percentage of answers correctly as compared to their counterparts in larger classes. Moreover, the results clearly suggested that this effect was more pronounced for applied basic knowledge skills in mathematics. The coefficient for the household learning rate used as an explanatory variable was found to be negative, indicating that prefectures with lower levels of scholastic aptitude among public middle schools tend to have more education-oriented households that invest in education outside of school.