# A Review on Linear Regression Comprehensive in Machine Learning

## Abstract

Perhaps one of the most common and comprehensive statistical and machine learning algorithms are linear regression. Linear regression is used to find a linear relationship between one or more predictors. The linear regression has two types: simple regression and multiple regression (MLR). This paper discusses various works by different researchers on linear regression and polynomial regression and compares their performance using the best approach to optimize prediction and precision. Almost all of the articles analyzed in this review is focused on datasets; in order to determine a model's efficiency, it must be correlated with the actual values obtained for the explanatory variables.

## Keywords

Regression, Simple Linear Regression, Multiple Linear Regression, polynomial Regression, least square method

## References

- S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: From theory to algorithms: Cambridge university press, 2014.
- K. P. Murphy, Machine learning: a probabilistic perspective: MIT press, 2012.
- P. Domingos, "A few useful things to know about machine learning," Communications of the ACM, vol. 55, pp. 78-87, 2012.
- D. Q. Zeebaree, H. Haron, A. M. Abdulazeez, and D. A. Zebari, "Machine learning and Region Growing for Breast Cancer Segmentation," in 2019 International Conference on Advanced Science and Engineering (ICOASE), 2019, pp. 88-93.
- Bargarai, F., Abdulazeez, A., Tiryaki, V., & Zeebaree, D. (2020). Management of Wireless Communication Systems Using Artificial Intelligence-Based Software Defined Radio.
- B. Akgun and S. G. Oguducu, "Streaming linear regression on Spark MLlib and MOA," in Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2015, 2015, pp. 1244-1247.
- M. H. Dehghan, F. Hamidi, and M. Salajegheh, "Study of linear regression based on least squares and fuzzy least absolutes deviations and its application in geography," in 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), 2015, pp. 1-6.
- D. M. Abdulqader, A. M. Abdulazeez, and D. Q. Zeebaree, "Machine Learning Supervised Algorithms of Gene Selection: A Review," Machine Learning, vol. 62, 2020.
- Zebari, D. A., Zeebaree, D. Q., Abdulazeez, A. M., Haron, H., & Hamed, H. N. A. (2020). Improved Threshold Based and Trainable Fully Automated Segmentation for Breast Cancer Boundary and Pectoral Muscle in Mammogram Images. IEEE Access, 8, 203097-203116..
- Abdulazeez, A, M. A. Sulaiman, and D. Q. Zeebaree "Evaluating Data Mining Classification Methods Performance in Internet of Things Applications," Journal of Soft Computing and Data Mining, vol. 1, pp. 11-25, 2020.
- H.-I. Lim, "A Linear Regression Approach to Modeling Software Characteristics for Classifying Similar Software," in 2019 IEEE 43rd Annual Computer Software and Applications Conference (COMPSAC), 2019, pp. 942-943.
- M. R. Sarkar, M. G. Rabbani, A. R. Khan, and M. M. Hossain, "Electricity demand forecasting of Rajshahi City in Bangladesh using fuzzy linear regression model," in 2015 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT), 2015, pp. 1-3.
- J. Wu, C. Liu, W. Cui, and Y. Zhang, "Personalized Collaborative Filtering Recommendation Algorithm based on Linear Regression," in 2019 IEEE International Conference on Power Data Science (ICPDS), 2019, pp. 139-142.
- H. Roopa and T. Asha, "A linear model based on principal component analysis for disease prediction," IEEE Access, vol. 7, pp. 105314-105318, 2019.
- G. A. Seber and A. J. Lee, Linear regression analysis vol. 329: John Wiley & Sons, 2012.
- D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis vol. 821: John Wiley & Sons, 2012.
- S. Kavitha, S. Varuna, and R. Ramya, "A comparative analysis on linear regression and support vector regression," in 2016 Online International Conference on Green Engineering and Technologies (IC-GET), 2016, pp. 1-5.
- Abdulazeez, A., Salim, B., Zeebaree, D., & Doghramachi, D. (2020). Comparison of VPN Protocols at Network Layer Focusing on Wire Guard Protocol..
- M. S. Acharya, A. Armaan, and A. S. Antony, "A comparison of regression models for prediction of graduate admissions," in 2019 International Conference on Computational Intelligence in Data Science (ICCIDS), 2019, pp. 1-5.
- Z. Zhang, Y. Li, L. Li, Z. Li, and S. Liu, "Multiple linear regression for high efficiency video intra coding," in ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, pp. 1832-1836.
- Najat, N., & Abdulazeez, A. M. (2017, November). Gene clustering with partition around mediods algorithm based on weighted and normalized Mahalanobis distance. In 2017 International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS) (pp. 140-145). IEEE..
- M. C. Roziqin, A. Basuki, and T. Harsono, "A comparison of montecarlo linear and dynamic polynomial regression in predicting dengue fever case," in 2016 International Conference on Knowledge Creation and Intelligent Computing (KCIC), 2016, pp. 213-218.
- A. K. Prasad, M. Ahadi, B. S. Thakur, and S. Roy, "Accurate polynomial chaos expansion for variability analysis using optimal design of experiments," in 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015, pp. 1-4.
- Y. Chen, P. He, W. Chen, and F. Zhao, "A polynomial regression method based on Trans-dimensional Markov Chain Monte Carlo," in 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), 2018, pp. 1781-1786.
- G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, "Color correction using root-polynomial regression," IEEE Transactions on Image Processing, vol. 24, pp. 1460-1470, 2015.
- N. N. Mohammed and A. M. Abdulazeez, "Evaluation of partitioning around medoids algorithm with various distances on microarray data," in 2017 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), 2017, pp. 1011-1016.
- H. Jie and G. Zheng, "Calibration of Torque Error of Permanent Magnet Synchronous Motor Base on Polynomial Linear Regression Model," in IECON 2019-45th Annual Conference of the IEEE Industrial Electronics Society, 2019, pp. 318-323.
- H. Niu, Q. Lu, and C. Wang, "Color correction based on histogram matching and polynomial regression for image stitching," in 2018 IEEE 3rd International Conference on Image, Vision and Computing (ICIVC), 2018, pp. 257-261.
- X. Yan and X. Su, Linear regression analysis: theory and computing: World Scientific, 2009.
- Y. Fujita, S. Ikuno, T. Itoh, and H. Nakamura, "Modified Improved Interpolating Moving Least Squares Method for Meshless Approaches," IEEE Transactions on Magnetics, vol. 55, pp. 1-4, 2019.
- J. Wolberg, Data analysis using the method of least squares: extracting the most information from experiments: Springer Science & Business Media, 2006.
- J.-H. Xue and D. M. Titterington, "$ t $-Tests, $ F $-Tests and Otsu's Methods for Image Thresholding," IEEE Transactions on Image Processing, vol. 20, pp. 2392-2396, 2011.
- R. Zhang and J. Tian, "Multi-parameter ocean surface wind speed retrieval based on least square method," in 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2016, pp. 5835-5837.
- H. Chi, "A Discussions on the Least-Square Method in the Course of Error Theory and Data Processing," in 2015 International Conference on Computational Intelligence and Communication Networks (CICN), 2015, pp. 486-489.
- N. V. Sabnis, P. Patil, N. S. Desai, S. Hirikude, S. Ingale, and V. Kulkarni, "Outcome-Based Education—A Case Study on Project Based Learning," in 2019 IEEE Tenth International Conference on Technology for Education (T4E), 2019, pp. 248-249.
- G. Nnachi, A. Akumu, C. Richards, and D. Nicolae, "Application of statistical tools in power transformer FRA results interpretation: Transformer winding diagnosis based on frequency response analysis," in 2017 IEEE PES PowerAfrica, 2017, pp. 16-22.
- X. Wang and X. Sun, "An improved weighted naive bayesian classification algorithm based on multivariable linear regression model," in 2016 9th International Symposium on Computational Intelligence and Design (ISCID), 2016, pp. 219-222.
- Z. Peng and X. Li, "Application of a multi-factor linear regression model for stock portfolio optimization," in 2018 International Conference on Virtual Reality and Intelligent Systems (ICVRIS), 2018, pp. 367-370.
- Q. Feng, C. Yuan, J. Huang, and W. Li, "Center-based weighted kernel linear regression for image classification," in 2015 IEEE International Conference on Image Processing (ICIP), 2015, pp. 3630-3634.
- X. Feng, Y. Zhou, T. Hua, Y. Zou, and J. Xiao, "Contact temperature prediction of high voltage switchgear based on multiple linear regression model," in 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), 2017, pp. 277-280.
- T. Maeda, S. Kiyoda, T. Kurashige, and Y. Miyataki, "Learning effects of automatic composition design software for human-equivalent phantoms from 1 GHz to 5 GHz with linear and exponential regression analysis," in 2015 IEEE MTT-S 2015 International Microwave Workshop Series on RF and Wireless Technologies for Biomedical and Healthcare Applications (IMWS-BIO), 2015, pp. 40-41.
- E. C. Jackson, J. A. Hughes, and M. Daley, "On the generalizability of linear and non-linear region of interest-based multivariate regression models for fmri data," in 2018 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), 2018, pp. 1-8.
- R. Harimurti, Y. Yamasari, and B. Asto, "Predicting student's psychomotor domain on the vocational senior high school using linear regression," in 2018 International Conference on Information and Communications Technology (ICOIACT), 2018, pp. 448-453.
- Y. Yang, "Prediction and analysis of aero-material consumption based on multivariate linear regression model," in 2018 IEEE 3rd International Conference on Cloud Computing and Big Data Analysis (ICCCBDA), 2018, pp. 628-632.
- D. Wei, M. Xing, J. Zhang, C. Zhang, and H. Cao, "Applied Research of Multiple Linear Regression in the Information Quantification of Chinese Medicine Bone-setting Manipulation," in 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2018, pp. 1912-1916.
- E. Sreehari and S. Srivastava, "Prediction of Climate Variable using Multiple Linear Regression," in 2018 4th International Conference on Computing Communication and Automation (ICCCA), 2018, pp. 1-4.
- T. Gopalakrishnan, R. Choudhary, and S. Prasad, "Prediction of Sales Value in Online shopping using Linear Regression," in 2018 4th International Conference on Computing Communication and Automation (ICCCA), 2018, pp. 1-6.
- H. Luminto, "Weather analysis to predict rice cultivation time using multiple linear regression to escalate farmer's exchange rate," in 2017 International Conference on Advanced Informatics, Concepts, Theory, and Applications (ICAICTA), Denpasar, Indonesia, 2017, pp. 16-18.
- D. Wang, Y. Gao, and Z. Tian, "One-Variable Linear Regression Mathematical Model of Color Reading and Material Concentration Identification," in 2017 International Conference on Smart City and Systems Engineering (ICSCSE), 2017, pp. 119-122.
- T. Bakibayev and A. Kulzhanova, "Common Movement Prediction using Polynomial Regression," in 2018 IEEE 12th International Conference on Application of Information and Communication Technologies (AICT), 2018, pp. 1-4.
- F. Grondin, H. Tang, and J. Glass, "Audio-Visual Calibration with Polynomial Regression for 2-D Projection Using SVD-PHAT," in ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, pp. 4856-4860.
- S.-J. Kwon, J. Park, J. H. Choi, J.-H. Lim, S.-E. Lee, and J. Kim, "Polynomial Regression method-based Remaining Useful Life Prediction and Comparative Analysis of Two Lithium Nickel Cobalt Manganese Oxide Batteries," in 2019 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 2510-2515.
- I. El Kafazi, R. Bannari, A. Abouabdellah, M. O. Aboutafail, and J. M. Guerrero, "Energy Production: A Comparison of Forecasting Methods using the Polynomial Curve Fitting and Linear Regression," in 2017 International Renewable and Sustainable Energy Conference (IRSEC), 2017, pp. 1-5.
- A. Al-Imam, "A Novel Method for Computationally Efficacious Linear and Polynomial Regression Analytics of Big Data in Medicine," Modern Applied Science, vol. 14, pp. 1-10, 2020.