Relations between two sets of variates
Relations between two sets of variates
复制标题
DOI：
10.1093/biomet/28.3-4.321
复制
发表时间：
1936-12-01
期刊：
影响因子：
2.7
通讯作者：
Hotelling, H
中科院分区：
文献类型：
--
作者：
Hotelling, H
相关和回归的概念不仅可以应用于普通的一维变量，而且可以应用于二维或更多维的变量。射手并排向目标同时射击，因此偏差部分是由于独立的个人误差，部分是由于风等常见原因，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合体可能更有趣。可以使用每个地方的速度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相匹配。对心理和身体特征的个体差异的研究需要对相关变量组之间的关系进行详细研究。例如，可以将多个心理测试的分数与同一个人的身体测量结果进行比较。接下来的问题是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，以及从系统中的多重相关性中提取这些独立关系的适当特征。另一个例子，可以通过对 N 个母亲及其女儿进行不同的智力测试来研究老鼠的智力遗传。
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