  This paper traces the historical and analytical development of what is known
in the econometrics literature as the Frisch-Waugh-Lovell theorem. This theorem
demonstrates that the coefficients on any subset of covariates in a multiple
regression is equal to the coefficients in a regression of the residualized
outcome variable on the residualized subset of covariates, where
residualization uses the complement of the subset of covariates of interest. In
this paper, I suggest that the theorem should be renamed as the
Yule-Frisch-Waugh-Lovell (YFWL) theorem to recognize the pioneering
contribution of the statistician G. Udny Yule in its development. Second, I
highlight recent work by the statistician, P. Ding, which has extended the YFWL
theorem to a comparison of estimated covariance matrices of coefficients from
multiple and partial, i.e. residualized regressions. Third, I show that, in
cases where Ding's results do not apply, one can still resort to a
computational method to conduct statistical inference about coefficients in
multiple regressions using information from partial regressions.
