Thank you so much for your time. I am running an analysis where I explore the association of the same predictors across multiple outcomes (these outcomes are correlated). My understanding is that when I run this in R:

lm.all <- lm(cbind(outcome1, outcome2, outcome3) ~ age + sex + education, data = df)

That when using summary(lm.all) the output is the same as running multiple univariate regressions (so per each outcome). How do I take into account the correlations between my outcomes?

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    $\begingroup$ Does this answer your question? Why do we need multivariate regression (as opposed to a bunch of univariate regressions)? The individual regression coefficients shown by summary() are the same as for a set of individual multiple regressions, but the multivariate regression takes the outcome correlations into account, in the coefficient covariances that are needed for accurate inference about their values. $\endgroup$
    – EdM
    Dec 9 '20 at 18:28
  • $\begingroup$ Unless you have a very large amount of data, you need to propose a model for those correlations in order to estimate them and exploit those estimates in the regression. lm won't do that for you. $\endgroup$
    – whuber
    Dec 9 '20 at 18:53
  • $\begingroup$ Thank you both for your responses. I have a correlation matrix of the outcome variables -- (only two outcomes have a sig. correlation, but biologically it is known that all outcomes are correlated to some extent). Is this what I would need to put into the regression? As a covariate? I'm a bit confused... $\endgroup$
    – Emma
    Dec 10 '20 at 8:07