Regression Analysis Applying Percentage-Error-Based Cost Function

Regression analysis is a fundamental statistical tool for modeling relationships between variables and making predictions in fields such as economics, engineering, and data science.Traditional cost functions such as the mean squared error (MSE), mean absolute error, and Huber loss are widely used but focus only on absolute differences, ignoring the relative scale of target values.This limitation often results in inconsistent error evaluations when the target values vary significantly in scale.To address this issue, this study proposes a new percentageerror-based cost function that measures prediction errors relative to the target value, thereby improving the accuracy and stability across different scales.The research framework integrates the theoretical foundations of regression cost functions, experimental design using benchmark data, and performance evaluation using two representative models: linear regression and multilayer perceptron.The experimental dataset, consisting of 1,030 instances of concrete compressive strength, included eight input variables related to the material composition and one target variable.The models were trained using both the conventional and proposed cost functions, and their performances were compared in terms of mean error, percentage error, and variance.The results demonstrate that the proposed cost function reduces the percentage error variance by over 50% compared with the MSE-based models.This improvement shows that the percentage-error-based approach delivers a more consistent performance, particularly for datasets with heterogeneous value ranges.This study proposes both a mean squared percentage error (MSPE) and an importance-weighted MSPE-based cost function, demonstrating performance improvements over the conventional MSE.Future work could apply this framework to other machine learning models and real-world applications in the finance, manufacturing, and forecasting domains.