一种线性回归新模型

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英文篇名：A New Method for Solving Linear Regression 作者：赵茂先 ; 余阳 英文作者：Zhao Maoxian;Yu Yang;College of Mathematics and System Science,Shandong University of Science and Technology; 关键词：回归新模型 ; 最小二乘法 ; 总绝对误差 英文关键词：regression model;;least square method;;total absolute error 中文刊名：统计与决策 英文刊名：Statistics & Decision 机构：山东科技大学数学与系统科学学院; 出版日期：2019-09-24 14:00 出版单位：统计与决策 年：2019 期：18 基金：国家自然科学基金资助项目(61370207) 语种：中文; 页：23-27 页数：5 CN：42-1009/C ISSN：1002-6487 分类号：O212.1

摘要

文章针对一元线性回归的绝对误差提出了两种新模型,其中一种是求所有数据点连接平均值产生的斜率,然后求它们的平均值就可以得到斜率,最后利用均值点便可得到一元线性回归方程。另一种是利用经过均值的回归直线,每个点偏离回归直线的斜率再求平均值,即是回归直线的斜率,该方法有"抵抗"异常值的效果。最小二乘法对异常值敏感,所以在含异常值的情况下,新方法在一定情况下"抗"异常值的效果优于最小二乘法,并且在某些情况下绝对误差和预测值误差都优于最小二乘法。
        This paper proposes two new models for the absolute error of linear regression with one variable, one of which is to find the slope generated by the average of all data points connected, and then find the average to get the slope, and finally use the mean point to get the linear regression equation with one variable. The other method is to use the regression line passing through the mean, the slope of each point deviating from the regression line to calculate the average, which is the slope of the regression line. This method has the effect of "resisting" outliers. The least square method is sensitive to outliers. Therefore, when the outliers are included, the new method is better than the least square method under certain circumstances, and in some cases, both the absolute error and the predicted error are better than the least square method.

引文

[1]郭春贤.移动最小二乘法的快速算法及其应用[D].重庆:重庆大学学位论文,2016.
    [2]李蓓蕾.多次自适应最小二乘曲线拟合方法及其应用[D].湖北:长江大学学位论文,2014.
    [3]田垅,刘宗田.最小二乘法分段直线拟合[J].计算机科学,2012,(S1).
    [4]丁克良,欧吉坤,赵春梅.正交最小二乘法曲线拟合法[J].测绘科学,2007,32(3).
    [5]沈以淡.简明数学词典[M].北京:北京理工大学出版社,2007.