Hooker and Yule on Relative Importance: A Statistical Detective Story
本文重新审视了1906年胡克和尤尔关于多元回归中两个变量对第三个变量相对影响的方法,发现其公式与数值示例存在矛盾,最终推断他们实际意图是回归系数乘以自变量平均值,即经济学家偏好的“水平重要性”。
Summary In their 1906 J. R. Statist. Soc paper, R.H. Hooker and G.U. Yule present an approach to the relative influence of two variables upon a third in a multiple regression context. The primary formulas suggest that by 'relative influence' Hooker and Yule meant just the ratio of (partial) regression coefficients. Inspection of the numerical example and its text description, however, suggests something different, but not clearly described. Analysis strongly points toward regression coefficient times average (of independent variable) as the intended concept of relative importance. This sometimes-called 'level importance' is favored by economists because of its proportionality to elasticity. Hooker himself returned to the topic in 1907 and created fresh puzzles.