Formula: DFBETAS_ij = (b_j - b_(i)j) / (s_(i) sqrt(C_jj)), C = (X'X)^-1
References
Belsley, Kuh and Welsch (1980), Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley. The definitions and the cutoffs used here (2/sqrt(n) for DFBETAS, 2 sqrt(p/n) for DFFITS, scaling by the delete-one root mean square s_(i)) are as documented by the SAS and R reference implementations, which cite BKW for them.
Examples
V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Dfbetas(V, V)
#> $dfbetas
#> [,1] [,2]
#> [1,] -0.18370455 0.15461042
#> [2,] 0.00000000 0.00000000
#> [3,] 0.15042309 -0.09494992
#> [4,] 0.18497895 -0.06227319
#> [5,] 0.07399158 0.06227319
#> [6,] -0.03926958 0.19830164
#> [7,] -0.46864708 0.98606323
#> [8,] -1.16533692 1.96155433
#>
#> $cutoff
#> [1] 0.7071068
#>
#> $leverage
#> [1] 0.4166667 0.2738095 0.1785714 0.1309524 0.1309524 0.1785714 0.2738095
#> [8] 0.4166667
#>
#> $beta
#> [1] 6.097555e-16 1.000000e+00
#>
#> $sigma_i
#> [1] 1.329622e-15 1.335963e-15 1.317870e-15 1.266196e-15 1.266196e-15
#> [6] 1.262033e-15 9.569522e-16 8.384101e-16
#>
#> $n
#> [1] 8
#>
#> $p
#> [1] 2
#>
#> $method
#> [1] "DFBETAS (Belsley-Kuh-Welsch)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"