Predictive modeling is one of the most important uses of mathematics and statistics in data science research. Among the several methods available, regression based mathematical models are still in use with advantages of interpretability, efficiency and adaptability to a range of data sets. A comparative analysis of the various publicly available data sets will be provided for predictive analysis of different regression-based mathematical models, and the results will be presented in this paper. The major goal is to determine the efficacy of these models in terms of their ability to predict with respect to various distributions and levels of noise in the data set. A few publicly available data sets for other areas such as economics, medicine, and environmental sciences have been used. The data used has been pre-treated for the typical pre-processing methods such as normalization, missing value imputation and feature selection to make the results more reliable. Evaluation of each regression model involves evaluation metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and coefficient of determination (R² Score). The results obtained seem to indicate that linear regression performs well for data which has a linear variation, and polynomial regression performs better for more complex data that needs some flexibility. Overall, the regularized regression methods make better predictions. The results from this analysis demonstrate the significance of adopting the right regression approach depending on the features of the data sets. This comparative assessment will help improve decision making when choosing regression models to make accurate predictions, which can be achieved using mathematics.
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Regression Models, Predictive Analysis, Machine Learning, Regularization Techniques, Mathematical Modeling.
