Implementation of linear regression, lasso/ridge regression, and kernel trick ridge regression in a real-life example

Zhiqiu Wang; Zhiren Xia; Hongru Ye; Taiming Xing; Zishen Liu; Zhengyu An

doi:10.1117/12.3036681

21 July 2024 Implementation of linear regression, lasso/ridge regression, and kernel trick ridge regression in a real-life example

Zhiqiu Wang, Zhiren Xia, Hongru Ye, Taiming Xing, Zishen Liu, Zhengyu An

Author Affiliations +

Proceedings Volume 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024); 132190X (2024) https://doi.org/10.1117/12.3036681
Event: 4th International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2024), 2024, Kaifeng, China

Abstract

Linear regressions are simple and convenient tools that are applicable in modeling the relationship of multiple variables; this regression can also extrapolate or interpolate based on given values to predict other values. To investigate how linear regressions, linear regressions with kernel trick, and linear regression with lasso and ridge regularizations are applicable in various real-life situations, this paper will discuss the distinctions between the regressions and assess each of their efficacy by implementing them in a couple of multi-variate datasets, one involving crime rates and Boston housing attributes, the other concerned with fuel efficiency and car features. We conclude that linear regression performs the best in MSE(40.316) and RMSE(6.349) metrics, while the Lasso regression performs best in MAE(2.804) and MAPE(19.689) metrics.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Zhiqiu Wang, Zhiren Xia, Hongru Ye, Taiming Xing, Zishen Liu, and Zhengyu An "Implementation of linear regression, lasso/ridge regression, and kernel trick ridge regression in a real-life example", Proc. SPIE 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024), 132190X (21 July 2024); https://doi.org/10.1117/12.3036681

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