The hat matrix in regression and ANOVA.¶
Hoaglin, D. C., & Welsch, R. E. (1978). The hat matrix in regression and ANOVA. The American Statistician, 32(1), 17-22.
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Primes¶
- Idempotence
- … Schröder (1890–1905) systematized); idempotent matrices `P² = P` are projection operators onto subspaces, central to linear algebra and statistics (the hat matrix `H = X(XᵀX)⁻¹Xᵀ` projecting observed `y` onto fitted `ŷ` is idempotent, as Hoaglin and Welsch (1978) develop in their treatment of regression diagnostics
This source(Originating treatment of the hat matrix as a regression-diagnostics tool; establishes the leverage interpretation of `h_ii` and the bound `h_ii ≤ 1` from the projection-matrix property.)
- … Schröder (1890–1905) systematized); idempotent matrices `P² = P` are projection operators onto subspaces, central to linear algebra and statistics (the hat matrix `H = X(XᵀX)⁻¹Xᵀ` projecting observed `y` onto fitted `ŷ` is idempotent, as Hoaglin and Welsch (1978) develop in their treatment of regression diagnostics
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