基于直线加权平均的平均值法、逐差法和最小二乘法的等效假设研究  

STUDY OF EQUIVALENT HYPOTHESIS BASED ON THE WEIGHTED LINES AMONG THE ARITHMETIC MEAN METHOD,THE SUCCESSIVE DIFFERENCE METHOD AND THE LEAST SQUARE METHOD

作　　者：魏同利[1] 郝惠娟[2] 马天鹏[1] WEI Tongli;HAO Huijuan;MA Tianpeng(School of Electrical and Information Engineering,North Minzu University;School of Preparatory Education,Ningxia University,Yinchuan Ningxia 750021)

机构地区：[1]北方民族大学电气信息工程学院 [2]宁夏大学预科教育学院,宁夏银川750021

出　　处：《物理与工程》2018年第4期88-92,95,共6页Physics and Engineering

基　　金：北方民族大学2016年教育教学改革研究项目(项目批准号:2016JY1114)

摘　　要：从等间距线性数据所确定的直线出发,对算术平均值法、逐差法和最小二乘法的基本假设进行了研究。针对计算等间距线性数据最佳斜率的3种不同方法,基于直线加权平均研究了每条可能直线的权重。界定了3种不同类型的线性数据:在最小间隔等权的线性数据中,经算术平均值法计算的斜率,标准误差最小;在点等权的线性数据中,通过最小二乘法所得到的斜率,标准误差最小;最后,从不等精度的假设出发,定量给出了逐差法最优的条件:测量数据的标准误差由两端向中间区域以1/2次方的速率衰减。Based on the straight lines determined by the points of linear data with equal intervals,the fundamental hypothesis of the arithmetic mean method,the successive difference method and the least square method are studied.The weight of each possible line is settled in the three methods for calculating the optimal slope of the linear data with equal intervals.And three different types of linear date are defined.For the first type of data,the standard errors of the minimum intervals are equal,and the standard errors of the slope calculating by the arithmetic mean method have the minimum value.For the second type,the standard errors of the points are equal,and the standard errors of the slope calculating by the least square method have the minimum value.Finally,based on the assumption of unequal accuracy,the optimal condition of the successive difference method is given quantitatively,in which the standard errors decay by a rate of 1/2 from two sides to the middle region.

关 键 词：算术平均值法 逐差法 最小二乘法 加权直线 等效假设 

分 类 号：O241[理学—计算数学]