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Cook's distance, leverage, DFBETAS — define.

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Answer

  • Leverage hiih_{\mathrm{ii}}: diagonal of hat matrix H  =  X(XX)−1H\; = \;X(XX)^{-1}X'; measures how extreme xix_{i} is in X-space.
  • Cook's distance: how much β̂ changes if point i is removed; > 4/n is a flag.
  • DFBETASi\mathrm{DFBETAS}_{i},j: change in β̂_j (in SE units) after removing i; > 2/√n flag.
  • DFFITS: change in fitted value.
  • All identify points that unduly drive the fit — investigate before dropping (often signal of a real edge case or a bug in the data pipeline).
Check yourself — multiple choice
  • Random
  • Leverage hiih_{\mathrm{ii}} (X-space extremity), Cook's D (β̂ change on removal, > 4/n flag), DFBETAS (per-coef change), DFFITS (fitted-value change)
  • Only mean
  • Same as VIF

Influential-point diagnostics: leverage, Cook's D, DFBETAS, DFFITS.

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