  This paper revisits the knockoff-based multiple testing setup considered in
Barber & Candes (2015) for variable selection applied to a linear regression
model with $n\ge 2d$, where $n$ is the sample size and $d$ is the number of
explanatory variables. The BH method based on ordinary least squares estimates
of the regressions coefficients is adjusted to this setup, making it a valid
$p$-value based FDR controlling method that does not rely on any specific
correlation structure of the explanatory variables. Simulations and real data
applications demonstrate that our proposed method in its original form and its
data-adaptive version incorporating estimated proportion of truly unimportant
explanatory variables are powerful competitors of the FDR controlling methods
in Barber & Candes (2015).
