# What is the correct way to follow up a multivariate multiple regression?

tl;dr What is the appropriate follow-up test after a multivariate multiple regression to interpret the nature of the significant effects? I recently conducted a study in which I used a series of multiple linear regressions to predict different outcomes (y1-y6) using the same set of predictor variables (x1-x8). My hypotheses were that all of the predictors (barring x7 and x8, which were dummy variables) would be significantly associated with each outcome, and that x1 in particular would exert the strongest effect. To give an example of some of the results, the separate univariate regressions indicated that x1 and x2 were significant predictors of y1; that x1, x3 and x4 were significant predictors of y2; that there were no significant predictors of y3; and so on. Noting that the outcomes were relatively intercorrelated (r values ~= 0.15=0.35), a reviewer suggested it would be more appropriate to use a multivariate multiple regression instead. I’ve never been taught this technique before, but using advice I found online I ran the analysis using: mlm1