## 5 Results  
As shown in Figure 3, the coefficients of each significant variable at a level of 0.05 are presented for all years. To better visualize the difference of the coefficients over time, they were separated into three different ranges: from 2009 to 2012, 2013 to 2015, and 2016 to 2018. Variables with lower variance in the period must have coefficients close to zero, regardless of whether they are school success determinants. One interesting aspect of the model is the substantial impact of demographic variables, such as those related to race, on performance. These variables are well-known as related to performance in Brazil, but it was expected that their coefficient would be close to zero, as their values tend to remain stable over time. However, they were highlighted as significant in various periods. This suggests that Brazilian students may be changing how they self-declare their race, which is consistent with findings from a recent longitudinal study by INEP at the student level [73]. Some variables, such as faculty education and father's education, have coefficients with different signals across different time periods. This calls for caution in the analysis, as models with a small time window tend to be low in information due to the expected lack of variance in the contextual variables. Figure 4 demonstrates the performance of the models by plotting their AUC_ROC values alongside their respective confidence intervals. The results indicate a significant decrease in AUC_ROC as the time window narrows. The best models are those starting in 2011, 2012, and 2013, respectively. Table 3 displays the coefficients of the top variables in the best model (2011-2019). To evaluate consistency, the number of times each variable was significant in the top seven with higher effects, regardless of the direction, is depicted, as well as their averages within parentheses. Figure 4: AUC_ROC for all models. Figure 3: Significant coefficients (\(p\)-value \(<\) 0.05) for all periods. Income per capita, faculty education, faculty work overload, and mother's education were the four most important positive variables during the period of 2011-2019. The relationship between students' socioeconomic status and educational outcomes is well-established in the literature [74; 75; 76], including previous research using this same dataset with a slightly different methodology [3]. Nevertheless, our methodology can provide new insights into the relationship between socioeconomic status and educational outcomes. Our model suggests variations in this effect concerning the top quartile, which opens the path for further research to explore whether these variations lead to a narrowing or widening of socioeconomic inequalities. Regarding parents' education, as expected, the mother's education is directly linked to good performance, while father's education has a negative coefficient. This negative effect on the period of 2011-2019 is not consistent with other periods in which father's education was significant into the top seven, since having a positive average. This can also be observed in Figure 3, in which father's education has positive effects for some periods. Therefore, this adverse effects interpretation requires caution, as there is no theoretical evidence to support it. Interestingly, we found that faculty education and faculty work overload, which had little relevance in our previous investigation of this same dataset [77] without causal reasoning, received higher coefficients. Faculty education is a school index that accounts for the average teacher education level, with weights based on years of schooling. Faculty work overload is the ratio of teachers to subjects offered in the school and aims to measure the volume of work. In Brazilian public secondary education, there is a low rate of teachers with additional years of education beyond graduation, particularly those with advanced degrees (in 2019, only 4.8% of teachers had an M.S., and 1.1% had a Ph.D). Additionally, teachers often have heavy schedules.