# JorGPT: Instructor-Aided Grading of Programming Assignments with Large Language Models (LLMs)
## 4 Results
### Quantitative: Final Grades
#### 4.1.3 Regression Models  
To determine the most effective approach for predicting instructor-assigned student grades using AI-generated scores, several multiple linear regression models were developed. The initial model includes all AI-generated assessments found to be statistically significant in the previous analysis, as summarized in Table 1.  
Based on these results, three additional models were developed:  
1. A reduced model that includes only the most statistically significant predictors from the initial regression (DeepSeek, GPT 4o, o3_mini, and Qwen), aiming to minimize the number of variables while maintaining predictive performance.
2. Two simplified models, each using a single AI predictor--DeepSeek and GPT 4o, respectively--to explore the impact of individual systems.  
Figure 4: [PERSON]’s correlation matrix.  
Figure 3: Distribution of AI-generated assessments.  
To compare model performance, both the adjusted R-squared (R\({}^{2}\_\)adj) and the Mean Absolute Error (MAE) were used. The goal is to identify the model that best balances explanatory power (higher R\({}^{2}\_\)adj) and predictive accuracy (lower MAE). The results are presented in Table 2.  
The full model, which includes all variables, achieves the highest explanatory power (R\({}^{2}\_\)adj = 0.9245) and the lowest prediction error (MAE = 0.4265). However, the reduced model using only statistically significant variables performs almost identically, with a negligible drop of less than 1% in the explained variance (R\({}^{2}\_\)adj = 0.9156) and an increase of just 3.1 hundredths in MAE. This suggests that the removal of non-significant predictors does not meaningfully reduce model accuracy.  
Such a minor trade-off supports the preference for the reduced model due to its parsimony and interpretability, especially in practical contexts where a simpler implementation is beneficial.  
Among the individual models, the o3_mini variable stands out, achieving an adjusted R\({}^{2}\) of 0.8820 and an MAE of 0.5428, indicating solid predictive capability even in isolation. Meanwhile, DeepSeek and GPT 4o, though significant in the full model, perform less effectively when used alone, confirming the advantage of combining multiple informative predictors.  
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To assess whether the model's accuracy is statistically and pedagogically acceptable, the MAE was calculated, resulting in a value of 0.54. A one-sample \(t\)-test was performed to test the null hypothesis that the MAE was equal to the pedagogical threshold of 0.5. The test yielded a \(p\)-value = 0.3789, indicating that the average error was significantly equal to 0.5. This supports the model's validity within the context of educational evaluation, where small deviations (\(\leq\)0.5) are commonly considered negligible due to rounding conventions and qualitative grading interpretations.  
Additionally, a manual calculation of the prediction errors revealed that 90% of the observations had an absolute error less than or equal to 0.5 points, satisfying the pedagogical criterion established for acceptable grading accuracy. The remaining 10% of cases in which the error exceeded 0.5 points were examined further. Most of these corresponded to false negatives, where the model assigned failing grades to students who were passed by the instructor. While these instances were relatively few, they highlight a conservative bias in the model's predictions that warrants further investigation.