工程试验中直线回归分析之点到直线距离平方和最小法  

Minimum Quadratic Sum of Distance from Test Point to Line on Linear Regression Analysis in Engineering Test

作　　者：张师定 赵金环[2] 

机构地区：[1]青建集团股份公司,青岛266071 [2]青岛理工大学学报编辑部,青岛266033

出　　处：《青岛理工大学学报》2012年第1期126-130,共5页Journal of Qingdao University of Technology

摘　　要：工程试验中常需进行2个变量间的回归分析,现行最小二乘法通过函数值残差最小而求得拟合曲线,但是误差因素分析表明自变量往往也存在误差,因此提出点到直线距离平方和最小的拟合方法,并给出了数字例子,计算结果与最小二乘法相近.Regression analysis is often needed in engineering test. Fitted curve is got through current least square method as the residual function value is minimum. Error factor analysis shows that the error still exists in independent variables. This paper suggests a new curve fitting method that quadratic sum of the distance from test point to line is minimum. And a digital example is given and the result is quite near to current method.

关 键 词：线性回归分析 点到直线距离 残差 误差因素 

分 类 号：U445.47[建筑科学—桥梁与隧道工程] O212.1[交通运输工程—道路与铁道工程]