A nice description of leverage in the sense that I am using it is given here so I will not repeat it.
Who originally defined leverage scores to be the diagonal elements of $X(X^TX)^{-1}X^T$?
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1$\begingroup$ This is not really the definition: it's a consequence of a definition. Belsley, Kuh, and Welsch (Regression Diagnostics, 1980) motivate it as follows. "The influence of the response value, $y_i,$ on the fit is most directly reflected in its impact on the corresponding fitted value, $\hat y_i,$ and this information is seen ... to be contained in $h_i$" (the diagonal element of the hat matrix). See BK&W pp 16 - 18 for the subsequent analysis. $\endgroup$– whuber ♦Mar 9, 2022 at 16:26
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1$\begingroup$ To the closevoter(s): I think this is perfectly on-topic here, and not opinion-based $\endgroup$– kjetil b halvorsen ♦Mar 9, 2022 at 17:02
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Hoaglin & Welsch (1978) say Thus we use the hat matrix to identify "high-leverage points." If this notion is to be really useful, we must make it more precise.
This suggests the term 'leverage' is not widely used at that point, and I don't have an earlier reference.
Tukey (who also coined the term 'hat matrix') uses 'leverage' in a related sense in a 1965 paper, talking about the amount of information in subsets of a sample, but not for regression. It's not used in the paper by Cook defining Cook's distance for measuring influence.
answered Mar 9, 2022 at 5:30
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4$\begingroup$ Sall (1990) includes a nice historical literature review doi.org/10.1080/00031305.1990.10475750 $\endgroup$ Mar 9, 2022 at 5:59