Comparison between fuzzy bootstrap weighted multiple linear regression and multiple linear regression: a case study for oral cancer modelling

• Main Authors: Mohd Ibrahim, Mohamad Shafiq, Wan Ahmad, Wan Muhamad Amir, Hasan, Ruhaya, Harun, Masitah Hayati
• Format: Conference or Workshop Item
• Language: English
• Published: 2018
• Subjects: QA Mathematics; QA276 Mathematical Statistics
• Online Access: http://irep.iium.edu.my/72217/7/72217%20Comparison%20between%20Fuzzy.pdf; http://irep.iium.edu.my/72217/

(MLR) is the most common type of linear regression analysis. Current technology advancement and increasing of development of the new or modified methodology building leads to the development of an alternative method for multiple linear regression model calculation. Objectives: In this study, multiple linear regression model was calculated by using SAS programming language based on computational statistics which considered combination of robust regression, bootstrap, weighted data, Bayesian, and fuzzy regression method. Methodology: Methodology building is based on the SAS algorithm (SAS 9.4 software) which is a robust computational statistic that consists the combination of robust regression, bootstrap, weighted data, Bayesian, and fuzzy regression method. Three different SAS algorithms (i) bootstrap multiple linear regression (BMLR), (ii) bootstrap weighted Bayesian multiple linear regression (BWBMLR), and (iii) fuzzy bootstrap weighted multiple linear regression (FBWMLR) were compared separately according to their average width of prediction. To illustrate the potential of built-in algorithm, a case study which emphasized on tumour was used. The average width of prediction interval results for all models have been computed and compared. The smallest width was indicated as the best fitting model. Results: The result showed that the former MLR model has an average width of 7.4816 and BMLR model has an average width of 3.7098. Meanwhile, the BWBMLR model has an average width of 3.5279 and FBWMLR model has an average width of 0.0058. Conclusion: It is shown that the most efficient method to obtain a relationship between response and explanatory variable is to apply FBWMLR method compared to other methods because of the small average width prediction interval.