Using Duncan’s regression of occupational prestige on the educational and income levels of occupations, verify that the influence vector for the deletion of ministers on the regression coefficients, d...

Using Duncan’s regression of occupational prestige on the educational and income levels of occupations, verify that the influence vector for the deletion of ministers on the regression coefficients, d_i
= b – b_(-i), can be written as

where x_i
is the ith row of the model matrix X (i.e., the row for ministers) written as a column. [A much more difficult problem is to show that this formula works in general; see, e.g., Belsley, et al. (1980, pp. 69–83) or Velleman and Welsch (1981).]