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Quantitative Essay Assessment Using Boosted Tree Regression and Linguistic Analytics in Matlab

Author : Waqas Javaid

Abstract

This paper presents the design and implementation of Automated Essay Scoring (AES) system developed in MATLAB using advanced machine learning techniques. The proposed system integrates linguistic feature engineering with ensemble regression modeling to evaluate essay quality objectively and consistently. A synthetic training corpus is generated to simulate diverse writing styles and score distributions, enabling robust supervised learning [1]. Twelve carefully selected features, including vocabulary richness, grammatical structure, coherence, readability index, lexical diversity, and syntactic complexity, are extracted to capture both structural and semantic characteristics of essays [2]. An LSBoost ensemble regression model is trained to predict scores within a standardized grading range. Comprehensive performance evaluation is conducted using R², RMSE, MAE, and Pearson correlation metrics [3]. The system further includes seven analytical visualization modules to interpret prediction accuracy, feature importance, residual distribution, and multidimensional feature-score relationships. Experimental results demonstrate strong predictive capability and statistical reliability [4]. The proposed framework provides an interpretable, scalable, and computationally efficient solution for intelligent essay assessment. This research contributes to AI-driven educational technology by offering a reproducible and extensible automated grading architecture.

  1. Introduction

The rapid advancement of Artificial Intelligence in education has transformed traditional assessment methodologies, particularly in the domain of written evaluation.

Figure 1: Automated Essay Scoring System highlighting AI-driven analysis of essay features and prediction scores.

Figure 1 presents the Automated Essay Scoring (AES) systems have emerged as intelligent tools capable of providing consistent, objective, and scalable grading solutions for academic institutions and online learning platforms. Manual essay evaluation is often time-consuming, subjective, and prone to inconsistency due to human bias and fatigue, creating a strong need for reliable computational alternatives [5]. In response to these challenges, machine learning–based essay scoring models have gained significant research attention. These systems leverage linguistic feature extraction, statistical modeling, and predictive analytics to estimate essay quality with high accuracy. The integration of Natural Language Processing (NLP) techniques enables deeper analysis of grammar, coherence, lexical richness, readability, and syntactic complexity [6]. Unlike rule-based grading systems, modern AES frameworks employ ensemble learning algorithms that can capture nonlinear relationships between textual features and holistic scores. Feature engineering plays a critical role in designing robust scoring systems, as carefully selected linguistic indicators directly influence prediction performance. Furthermore, the use of regression-based ensemble models improves generalization capability and minimizes overfitting [7]. Visualization and statistical evaluation techniques enhance interpretability, making the system more transparent and academically reliable. With the increasing adoption of digital examinations and e-learning platforms, automated grading systems are becoming essential components of smart educational ecosystems. Beyond efficiency, AES systems also support formative feedback and large-scale standardized testing environments [8]. However, achieving high predictive validity requires systematic dataset generation, normalization strategies, and rigorous performance analysis. This research focuses on developing a comprehensive MATLAB-based Automated Essay Scoring system that integrates twelve linguistic features with an LSBoost ensemble regression model. The proposed framework aims to deliver accurate score prediction, statistical robustness, and analytical interpretability [9]. By combining machine learning, linguistic intelligence, and performance visualization, the study contributes to advancing AI-driven educational assessment technologies.

1.1 Background of Automated Essay Scoring

The evaluation of written essays has traditionally relied on human judgment, which, although valuable, is often subjective and inconsistent. As educational systems expand and digital learning environments grow, the demand for scalable and objective assessment methods has significantly increased. Automated Essay Scoring (AES) systems were developed to address these challenges by leveraging computational intelligence to evaluate written content [10]. These systems aim to replicate human grading patterns using statistical and machine learning models. Over the past decade, AES has evolved from simple rule-based algorithms to advanced predictive systems powered by Artificial Intelligence. The integration of data-driven methodologies has improved grading consistency and efficiency. Educational institutions now recognize AES as a practical solution for large-scale testing. Additionally, automated systems reduce grading workload and turnaround time. This technological shift represents a major advancement in educational assessment. Consequently, AES research has become an important domain within AI in education.

1.2 Limitations of Manual Essay Evaluation

Manual grading, despite its qualitative depth, presents several limitations in modern educational contexts. Human evaluators may experience fatigue, bias, and variability in scoring standards. Even trained examiners can differ in their interpretation of writing quality. Such inconsistencies may affect fairness and reliability in high-stakes examinations. Furthermore, grading large volumes of essays requires substantial time and institutional resources [11]. In online learning platforms, rapid feedback is essential, yet manual evaluation delays this process. The subjectivity involved in assessing coherence, grammar, and argument strength further complicates standardization. These challenges highlight the necessity of automated and objective evaluation mechanisms [12]. An intelligent system capable of consistent scoring can enhance transparency. Therefore, machine learning-based AES systems provide a promising alternative to traditional grading methods.

1.3 Role of Machine Learning in Essay Scoring

Machine learning has transformed automated assessment by enabling systems to learn scoring patterns from labeled datasets. Instead of relying solely on handcrafted rules, modern AES systems analyze statistical relationships between linguistic features and assigned scores. Supervised learning algorithms, particularly regression-based models, are widely used for continuous score prediction. Ensemble learning techniques further enhance predictive performance by combining multiple weak learners [13]. Boosting methods, such as LSBoost, iteratively reduce prediction error. These approaches capture nonlinear relationships within textual data. The adaptability of machine learning models improves generalization to unseen essays. Moreover, predictive analytics enables quantitative performance evaluation using statistical metrics. As a result, machine learning forms the foundation of intelligent essay grading systems. Its integration ensures scalability, adaptability, and analytical robustness [14].

1.4 Importance of Linguistic Feature Engineering

Feature engineering is a critical component in developing a reliable Automated Essay Scoring system. The quality of extracted features directly influences prediction accuracy. Linguistic indicators such as essay length, vocabulary richness, and sentence structure reflect writing proficiency [15]. Advanced features including coherence score, lexical diversity, and syntactic complexity provide deeper insight into textual quality. Grammar patterns and spelling accuracy further contribute to holistic assessment. Transition word density and punctuation usage indicate logical flow and organization. Readability indices help estimate comprehension difficulty levels. Carefully selected features allow the model to capture multiple dimensions of writing quality. Feature normalization ensures balanced contribution during training [16]. Thus, systematic feature extraction strengthens model interpretability and performance.

1.5 Synthetic Dataset Generation for Model Training

A robust AES model requires a diverse and representative dataset for training. In scenarios where real-world labeled data is limited, synthetic essay generation offers a practical alternative. By simulating varying writing qualities, score distributions can be systematically controlled. Synthetic datasets enable experimental validation of machine learning models. They allow researchers to analyze system behavior under different linguistic conditions. Controlled generation also ensures reproducibility of experiments [17]. Essays can be designed to reflect varying vocabulary complexity and structural depth. This approach supports algorithm benchmarking and performance comparison. Although synthetic data may not capture all real-world nuances, it provides foundational training support. Therefore, dataset engineering plays a fundamental role in AES system development.

1.6 Ensemble Regression Model for Score Prediction

Ensemble regression models have demonstrated superior predictive capabilities in complex learning tasks. In essay scoring, boosted regression trees can effectively model nonlinear relationships between features and scores. The LSBoost algorithm iteratively refines predictions by minimizing residual errors [18]. This process enhances overall accuracy and reduces bias. Ensemble models combine multiple decision trees to improve generalization performance. Compared to single learners, boosted methods offer higher stability and robustness. They also handle feature interactions more effectively.

Table 1: Performance Summary by Essay Quality Level

Quality LevelScore RangeMean Prediction ErrorRMSESample SizeReliability
Poor2.0 – 3.00.00870.28768High
Below Average3.0 – 3.50.00420.29546High
Average3.5 – 4.0-0.00180.30216High
Good4.0 – 4.5-0.00340.31248Moderate
Very Good4.5 – 5.00.00210.34566Moderate
Excellent5.0 – 6.00.00290.39566Lower

In the table 1, I have added performance metrics such as R², RMSE, and MAE provide quantitative evaluation of model quality. High correlation between predicted and actual scores indicates strong predictive validity. Consequently, ensemble regression serves as a powerful core component of modern AES systems.

1.7 Statistical Validation and Performance Metrics

The reliability of an Automated Essay Scoring system must be validated using statistical performance indicators. Coefficient of determination (R²) measures how well predicted scores explain score variance. Root Mean Square Error (RMSE) quantifies average prediction deviation. Mean Absolute Error (MAE) evaluates overall prediction accuracy. Pearson correlation analysis examines linear association between actual and predicted scores [19]. Error distribution analysis identifies bias and variance patterns. Confidence intervals estimate prediction reliability across samples. Residual plots reveal systematic prediction trends or inconsistencies. Such statistical evaluations ensure transparency in system performance. Rigorous validation strengthens academic credibility. Therefore, quantitative assessment is essential for research-based AES development.

1.8 Visualization and Interpretability in AES

Interpretability is crucial for trust and academic acceptance of automated grading systems. Visualization techniques provide insight into model behavior and feature influence. Feature importance ranking identifies the most impactful linguistic attributes. Correlation matrices reveal relationships among extracted features. Predicted versus actual score plots demonstrate model accuracy. Residual analysis highlights overestimation and underestimation patterns [20]. Distribution comparisons show alignment between predicted and real score ranges. Three-dimensional feature-score visualization enhances multidimensional understanding. Analytical plots support transparent reporting of results. Visual interpretation bridges the gap between computational modeling and educational research. Hence, visualization strengthens system explainability and usability.

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1.9 Applications in Modern Educational Technology

Automated Essay Scoring systems have wide-ranging applications in contemporary education. Online learning platforms utilize AES for rapid formative feedback. Standardized testing agencies employ automated grading to manage large-scale examinations. Universities integrate intelligent assessment tools into digital classrooms [21]. AES systems support adaptive learning environments by identifying writing weaknesses. They also facilitate data-driven curriculum improvements. Intelligent grading systems reduce administrative workload and operational costs. Furthermore, they enable real-time evaluation in remote learning scenarios. Integration with Learning Management Systems enhances digital education ecosystems. As educational technology evolves, AES becomes increasingly indispensable.

1.10 Research Contribution and Study Objective

This study presents a comprehensive MATLAB-based Automated Essay Scoring system integrating twelve linguistic features with an ensemble regression model. The framework emphasizes feature engineering, statistical validation, and interpretability. By employing LSBoost regression, the system achieves accurate and consistent score prediction. Seven analytical visualization modules enhance performance transparency. The research demonstrates the feasibility of combining linguistic intelligence with machine learning techniques. It provides a reproducible architecture suitable for academic experimentation [22]. The proposed model offers scalability and adaptability for future enhancements. Its design supports further integration with advanced NLP methods. Ultimately, this work contributes to advancing AI-driven educational assessment technologies. The study establishes a foundation for future research in intelligent essay evaluation systems.

  1. Problem Statement

The evaluation of written essays remains a complex and resource-intensive task in modern educational systems, particularly in large-scale academic environments. Traditional manual grading methods are often time-consuming, inconsistent, and influenced by subjective human judgment. Variability among evaluators can lead to fairness concerns and reduced reliability in assessment outcomes. Additionally, providing timely feedback to students becomes increasingly difficult as the number of submissions grows. Existing automated grading approaches may lack interpretability, robustness, or the ability to capture multidimensional linguistic characteristics. Many systems rely on limited features, resulting in reduced predictive accuracy and generalization capability. There is also a need for transparent statistical validation to ensure academic credibility. Furthermore, integrating advanced machine learning techniques with comprehensive feature engineering remains a research challenge. Therefore, a scalable, interpretable, and statistically reliable Automated Essay Scoring system is required. The core problem addressed in this study is the development of an intelligent essay evaluation framework that ensures accuracy, objectivity, and analytical transparency using ensemble machine learning methods.

  1. Mathematical Approach

The proposed Automated Essay Scoring system is formulated as a supervised regression problem where each essay is represented by a feature vector extracted from linguistic analysis [31].

  • x: Feature vector representing an essay
  • x1,x2,…,xn: Extracted linguistic features (grammar, readability, vocabulary richness, coherence)
  • n: Total number of features

The objective is to learn a predictive function (f(x)) that maps feature space to a continuous score (y in [0,6] ) by minimizing the empirical loss [32].

  • L: Loss function (average prediction error)
  • n: Number of training samples
  • yi: Actual essay score
  • y^i: Predicted score

An ensemble boosting model iteratively constructs weak learners ( h_m(x) ) and combines them as to reduce residual error [33].

  • f(x): Final predicted score
  • M: Number of weak learners (trees)
  • αm: Weight of m-th learner
  • hm(x): m-th weak learner (decision tree)

Feature normalization ensures bounded input space, improving convergence and numerical stability during training. Model performance is quantitatively evaluated using statistical metrics such as ( R^2 ), RMSE, MAE, and Pearson correlation coefficient to validate predictive accuracy and generalization capability. The mathematical formulation of the Automated Essay Scoring system can be understood as a supervised learning regression problem where each essay is transformed into a structured numerical representation using twelve linguistic features. These features collectively form a feature vector that captures multiple dimensions of writing quality, including vocabulary richness, coherence, grammar, and readability. The goal of the model is to learn a mapping function that predicts a continuous essay score within a defined grading range. During training, the system minimizes the average squared difference between the actual scores and the predicted scores to reduce overall prediction error. This error minimization process ensures that the model gradually improves its scoring accuracy. An ensemble boosting strategy is employed, where multiple weak decision tree models are trained sequentially. Each subsequent model focuses on correcting the prediction errors made by the previous one. The final predicted score is obtained by combining the outputs of all individual learners in a weighted manner. Feature normalization is applied to maintain balanced influence among variables and enhance numerical stability. Overall, this mathematical framework ensures reliable, scalable, and statistically validated essay score prediction.

  1. Methodology

The methodology of the proposed Automated Essay Scoring system follows a structured and systematic machine learning pipeline designed to ensure accuracy, interpretability, and reproducibility. The process begins with system initialization and configuration of key parameters, including feature definitions and score range normalization [23]. A synthetic essay dataset is generated to simulate diverse writing qualities and score distributions, enabling controlled experimental analysis. Each essay undergoes preprocessing, including text normalization, tokenization, and sentence segmentation. Twelve linguistic features are extracted to represent structural, grammatical, lexical, and readability characteristics of the text. These features include essay length, vocabulary richness, coherence score, spelling accuracy, syntactic complexity, and transition word density. The extracted feature vectors are normalized to maintain balanced scaling across dimensions [24]. The dataset is then divided into training and testing subsets to evaluate generalization performance. An ensemble regression model based on boosting is trained using the feature matrix and corresponding scores. The boosting algorithm iteratively refines prediction accuracy by minimizing residual errors. After training, the model predicts scores for unseen test essays. Performance evaluation is conducted using statistical metrics such as coefficient of determination, root mean square error, and mean absolute error. Pearson correlation analysis is performed to assess the linear relationship between predicted and actual scores. Error distribution and residual analysis are examined to detect bias or variance patterns. Feature importance ranking is computed to identify the most influential linguistic attributes. Visualization modules generate analytical plots for interpretability and performance validation [25]. Confidence intervals are calculated to estimate prediction reliability. A sample essay analysis is conducted to demonstrate practical applicability. Finally, the trained model is prepared for export and future deployment, ensuring scalability and adaptability for real-world educational environments.

  1. Design Matlab Simulation and Analysis

The simulation of the Automated Essay Scoring system is designed to mimic real-world essay evaluation using a controlled synthetic dataset. Initially, the system generates a large set of training essays with randomized scores spanning the scoring range, ensuring a diverse representation of writing quality. Each essay undergoes preprocessing, including normalization, tokenization, and sentence segmentation, to prepare for feature extraction. Twelve linguistic and structural features are extracted, including essay length, vocabulary richness, grammar score, coherence, spelling accuracy, readability, syntactic complexity, transition word density, lexical diversity, and punctuation density. These features are normalized to maintain consistent scaling across all inputs. The normalized feature matrix is then used to train an ensemble regression model using a boosting algorithm, which iteratively minimizes prediction errors. After training, the model is evaluated on a separate test dataset of essays generated with similar statistical properties to the training set. Predicted scores are compared against actual scores to assess model accuracy. Performance metrics such as coefficient of determination, root mean square error, mean absolute error, and Pearson correlation are computed. Error distributions are analyzed to identify potential biases or systematic deviations. Feature importance is calculated to determine which attributes most strongly influence essay scores. Correlation matrices reveal relationships between features and highlight multicollinearity. Visualization plots, including predicted versus actual scores, error distributions, residual plots, and 3D feature-score relationships, are generated for interpretability. Confidence intervals are estimated to quantify prediction reliability. Sample essay analyses demonstrate practical applicability and highlight the contribution of each feature to the predicted score. The simulation ensures scalability, allowing extension to larger datasets or real essay collections. Overall, the system integrates synthetic data generation, feature engineering, ensemble modeling, and detailed visualization to provide a robust and interpretable framework for automated essay scoring.

Figure 2: Predicted vs Actual Essay Scores showing model accuracy and correlation.

This figure 2 visualizes the comparison between predicted and actual essay scores using a scatter plot with an overlaid ideal fit line. Each point represents a single essay in the test set, illustrating how closely the model’s prediction matches the true score. The correlation coefficient is displayed to quantify the linear relationship, and a p-value indicates statistical significance. Points clustered along the diagonal line indicate accurate predictions, while deviations reveal errors. The figure also allows identification of outliers where the model significantly overestimates or underestimates scores. This visual assessment complements numerical metrics like RMSE and MAE. Color, size, and markers enhance clarity and readability. Grid lines and axis limits provide a clear scale for interpretation. The use of text annotations highlights statistical significance and provides context for interpretation. Overall, this figure confirms the predictive strength of the ensemble regression model.

Figure 3: Feature Importance Ranking of linguistic and structural attributes in essay scoring.

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This figure 3 presents a bar chart ranking the importance of each extracted feature in predicting essay scores. Features with higher bars have a stronger influence on the regression model’s predictions. The visualization helps identify which linguistic characteristics, such as grammar or coherence, are most critical. Each bar is labeled with its corresponding numerical importance score for precise interpretation. Features are sorted in descending order to highlight top contributors. The figure allows educators or researchers to understand the model’s decision-making process. Color coding improves differentiation among features. The x-axis lists all 12 features, rotated for readability. By showing feature importance, the plot guides potential feature selection or dimensionality reduction in future model refinement. The figure also aids in interpreting model transparency and fairness.

Figure 4: Error Distribution Analysis of predicted essay scores against actual scores.

This figure 4 displays a histogram of prediction errors to assess the accuracy and consistency of the model. Positive errors indicate overprediction, while negative errors indicate underprediction. The mean, standard deviation, and skewness of errors are displayed in a statistics box for quantitative assessment. A vertical line at zero highlights perfect prediction. The distribution shape reveals bias or asymmetry in the model predictions. Outliers can be visually identified, allowing investigation into unusual essays. The histogram’s color and transparency enhance readability. Grid lines support easy comparison of error frequency. This figure complements the scatter plot by showing the aggregate prediction performance. It also helps evaluate whether errors are normally distributed or if systematic patterns exist.

Figure 5: Feature Correlation Matrix showing inter-feature relationships and multicollinearity.

This figure 5 uses a color-coded heatmap to visualize correlations among all extracted features. Positive correlations are shown in one color, negative correlations in another, with intensity indicating strength. Correlation values above a threshold are annotated for clarity. Strong correlations between features can indicate redundancy, guiding feature selection or dimensionality reduction. This matrix helps assess multicollinearity, which could affect model stability. It also provides insight into how different linguistic features interact within essays. Axes are labeled with feature names for easy identification. The use of color gradients helps in visually detecting patterns. The heatmap also serves as a diagnostic tool to ensure meaningful contributions from each feature. Researchers can use this figure to refine feature engineering for improved model performance.

Figure 6: Score Distribution Comparison between actual and predicted essay scores.

This figure 6 overlays histograms of actual and predicted scores to visualize how well the model replicates the score distribution. Differences in histogram peaks indicate areas where the model over or underpredicts. Probabilities are normalized for comparison. Mean and standard deviation values of each distribution are annotated for quantitative context. Transparency allows simultaneous comparison of the two distributions. The figure helps evaluate whether the model captures overall trends in essay scores. Misalignment of distributions may indicate bias or limited generalization. Grid lines and bin widths facilitate visual clarity. This comparison is essential to ensure that the model does not systematically favor certain score ranges. The figure supports model validation for both individual accuracy and overall distribution representation.

Figure 7:  Residual Analysis showing prediction errors relative to predicted scores.

This scatter plot figure 7 displays residuals, which are the differences between predicted and actual scores, against predicted scores. It allows identification of patterns, such as heteroscedasticity, where error magnitude varies with score. A horizontal line at zero indicates perfect predictions. Color coding by residual magnitude enhances visual interpretation. Outliers can be quickly detected and analyzed for causes of extreme errors. The residual plot complements the error distribution histogram by showing relationships between errors and predicted values. Annotation boxes provide summary statistics like mean, standard deviation, and error range. Grid lines and axis labels support interpretation. This figure is useful for diagnosing systematic model errors. It confirms whether the model predictions are unbiased across the score range.

Figure 8: 3D Relationship between top three important features and essay scores.

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This figure 8 uses a 3D scatter plot to visualize the relationship between the three most influential features and essay scores. Each axis represents a different feature, while color indicates the actual essay score. It highlights how combinations of features influence scoring, revealing potential nonlinear interactions. Clusters in 3D space may indicate groups of essays with similar feature patterns. The plot allows inspection of complex relationships not visible in 2D. Rotating the figure provides multiple perspectives. The color gradient helps identify high and low scoring essays in feature space. This visualization aids interpretability, showing how top features jointly affect predictions. It also serves as a diagnostic tool for model behavior. Researchers can leverage this figure to understand feature contributions to essay quality in practical applications.

  1. Results and Discussion

The results of the automated essay scoring simulation demonstrate a high level of predictive accuracy and robust feature interpretability. The ensemble regression model achieved a strong coefficient of determination, indicating that a substantial portion of the variation in essay scores is captured by the extracted linguistic features [26]. Analysis of the predicted versus actual scores shows that the model can reliably estimate essay quality, with only minor deviations observed in certain outlier essays. Error distribution analysis reveals that most predictions fall within a narrow range of the actual scores, confirming model consistency. Feature importance analysis highlights that grammar, coherence, and vocabulary richness contribute most significantly to the predicted score, validating the relevance of these linguistic attributes. Correlation matrix analysis identifies moderate multicollinearity among certain features, such as sentence count and essay length, which is expected in natural language data [27]. Residual plots indicate no substantial systematic bias across the score spectrum, demonstrating that the model performs uniformly across low and high scoring essays. Score distribution comparisons between actual and predicted scores suggest that the model preserves the overall scoring trends without significant distortion. Confidence interval analysis further supports the reliability of predictions, showing that most errors fall within acceptable bounds. The 3D feature-score visualization illustrates complex interactions between top features, providing insight into the model’s decision-making process. Sample essay analysis demonstrates that the model can distinguish subtle differences in essay quality, accurately capturing nuances in writing style, sentence structure, and vocabulary usage. Spelling and punctuation metrics correlate moderately with predicted scores, confirming their secondary influence. Lexical diversity and transition word density appear as meaningful but less dominant predictors, reinforcing the importance of content coherence [28]. The model’s ability to generalize across synthetic test essays suggests potential applicability to real-world datasets. The discussion confirms that ensemble regression, combined with comprehensive linguistic feature extraction, is a suitable approach for automated essay scoring. Potential limitations include sensitivity to feature selection and the reliance on synthetic training data. Future improvements may involve incorporating semantic embeddings and advanced language models to enhance predictive power. Overall, the results indicate that the system provides a reliable, interpretable, and scalable solution for automated assessment of essay quality.

  1. Conclusion

In conclusion, the automated essay scoring system demonstrates effective and reliable performance in predicting essay quality using a comprehensive set of linguistic features. The ensemble regression model accurately captures the relationship between structural, lexical, and syntactic attributes of essays and their corresponding scores [29]. Feature importance analysis confirms that grammar, coherence, and vocabulary richness are the most influential predictors, providing interpretability to the model’s decisions. Error and residual analyses indicate minimal bias and consistent performance across different score ranges. Confidence interval evaluation further validates the reliability of predictions [30]. The system successfully models complex interactions among features, as seen in the 3D feature-score relationships. While trained on synthetic essays, the methodology provides a strong foundation for application to real-world datasets. Limitations include dependency on feature selection and potential variations in natural language. Future enhancements could incorporate semantic embeddings and deep learning-based linguistic representations. Overall, the system offers a scalable, transparent, and scientifically grounded solution for automated essay assessment.

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