Fitting a Straight Line When Both Variables are Subject to Error
Fitting a Straight Line When Both Variables are Subject to Error
复制标题
当两个变量都有误差时拟合直线
DOI：
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发表时间：
1949
期刊：
影响因子：
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通讯作者：
M. Bartlett
中科院分区：
文献类型：
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作者：
M. Bartlett
(i)必须区分变量y关于第二变量x的线性回归方程和被误差掩盖的两个变量Y和X之间的线性函数关系。即使变量x有误差，前一个方程仍然可用于预测，但当函数关系存在时，前一个方程不一定适合于函数关系。(ii)对于第二个问题，可以建立最大似然方程，但是如果没有进一步的假设，例如关于x和y中误差的相对大小的假设，它们不会导致唯一的解。
(i) a distinction must be made between the linear regression equation of a variable y on a second variable x, and a linear functional relation between two variables Y and X masked by errors. The former equation is still available for prediction even if the variable x is subject to error, but is not necessarily appropriate for a functional relation when one exists. (ii) it is possible to set up maximum likelihood equations for the second problem, but they do not lead to a unique solution without further assumptions, such as an assumption about the relative magnitude of the errors in x and y.