  Principal loading analysis is a dimension reduction method that discards
variables which have only a small distorting effect on the covariance matrix.
As a special case, principal loading analysis discards variables that are not
correlated with the remaining ones. In multivariate linear regression on the
other hand, predictors that are neither correlated with both the remaining
predictors nor with the dependent variables have a regression coefficients
equal to zero. Hence, if the goal is to select a number of predictors,
variables that do not correlate are discarded as it is also done in principal
loading analysis. That both methods select the same variables occurs not only
for the special case of zero correlation however. We contribute conditions
under which both methods share the same variable selection. Further, we extend
those conditions to provide a choice for the threshold in principal loading
analysis which only follows recommendations based on simulation results so far.
