问题 单项选择题

最小二乘法的原理是,当所有的测量数据的( )最小时,所拟合的直线最优。

A.误差

B.偏差的积

C.误差的和

D.偏差的平方和

答案

参考答案:D

解析: 一元线性回归是工程中经常遇到的配直线的问题。通过试验,可以得到若干组的对应数据,根据这些数据画出相关图,当点大致分布在一条直线附近时,说明两变量之间存在线性关系,即可以用一条适当的直线来表示这两变量的关系。此直线方程为:y=a+bx,a、b是回归系数,最小二乘法是根据偏差平方和最小的条件来选择常数a、b的方法,当所有数据偏差平方和最小时,所配的直线最优。

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