Revision 1
The explanation of the major differences between the first revision and the previously published version.
This updated version of the article includes several significant enhancements based on the reviewer's feedback.
Introduction: This paper highlights quadratic polynomials' unique advantages in capturing curvature and non-linear relationships. It also includes a brief comparison with other models, such as linear and cubic polynomials, emphasizing specific scenarios where quadratic polynomials are most effective.
Data Preprocessing Steps: A new subsection has been added detailing the preprocessing steps undertaken before fitting the quadratic model. This includes techniques for handling missing data, detecting and treating outliers, and applying data normalization or scaling. This addition aims to provide a clearer understanding of the steps taken to prepare the data for analysis.
Discussion of R-squared Limitations: The methods section now contains a paragraph discussing the limitations of using R-squared as the sole measure of model fit. It suggests additional metrics such as Adjusted R-squared, Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) to offer a more comprehensive evaluation of model performance.
Results: A new section has been included comparing the performance of quadratic polynomials with linear and cubic models using the same datasets. The comparison uses metrics like R-squared, Adjusted R-squared, and MSE to evaluate the fit and predictive accuracy, providing a broader perspective on the effectiveness of quadratic models.
Discussion: The discussion now delves deeper into the potential challenges and limitations of quadratic polynomials, such as overfitting and sensitivity to data variability. It addresses scenarios where quadratic polynomials might overfit, particularly with small or noisy datasets, and suggests methods for mitigating these issues, including regularization techniques and cross-validation methods. This addition aims to provide a more balanced view of the use of quadratic polynomials in data analysis.