Relations Between Two Sets of Variates
Relations Between Two Sets of Variates
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DOI：
10.1007/978-1-4612-4380-9_14
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发表时间：
1936-12
期刊：
影响因子：
2.7
通讯作者：
H. Hotelling
中科院分区：
文献类型：
--
作者：
H. Hotelling
相关和回归的概念不仅可以应用于普通的一维变量，也可以应用于二维或更多维的变量。神枪手并排同时向目标射击，因此偏差部分是由于独立的个人错误，部分是由于风等共同原因，这为相关理论提供了熟悉的介绍；但通常只讨论水平分量的相关性，而由水平和垂直偏差组成的复杂情况可能更有趣。可以用两个地方的风速的两个分量来比较两个地方的风。因此，一个波动向量在每个时刻都与另一个波动向量匹配。要研究个体在心理和身体特征上的差异，需要详细研究一组相关变量之间的关系。例如，可以将一些心理测试的分数与同一人的体能测量结果进行比较。于是就出现了这样的问题，即如何确定这些数据所显示的存在的身心独立关系的数量和性质，以及从系统中的多种相关关系中提取出这些独立关系的适当特征。作为另一个例子，研究老鼠智力遗传的方法可能不是单一的，而是不同的智力测试，分别适用于母鼠和母鼠的女儿。
Concepts of correlation and regression may be applied not only to ordinary one-dimensional variates but also to variates of two or more dimensions. Marksmen side by side firing simultaneous shots at targets, so that the deviations are in part due to independent individual errors and in part to common causes such as wind, provide a familiar introduction to the theory of correlation; but only the correlation of the horizontal components is ordinarily discussed, whereas the complex consisting of horizontal and vertical deviations may be even more interesting. The wind at two places may be compared, using both components of the velocity in each place. A fluctuating vector is thus matched at each moment with another fluctuating vector. The study of individual differences in mental and physical traits calls for a detailed study of the relations between sets of correlated variates. For example the scores on a number of mental tests may be compared with physical measurements on the same persons. The questions then arise of determining the number and nature of the independent relations of mind and body shown by these data to exist, and of extracting from the multiplicity of correlations in the system suitable characterizations of these independent relations. As another example, the inheritance of intelligence in rats might be studied by applying not one butsdifferent mental tests toNmothers and to a daughter of each