# How to report a multiple linear regression equation when the interaction makes lower order items non-significant [duplicate]

I've read a number of the other discussions I can find on here about lower order items and interaction terms in regression but either my statistical incompetence is preventing from seeing it or I could not find a clear answer to the specific question I have. Any help would be very much appreciated!

I have a regression model in which I use sex and a personality trait to predict a separate outcome. Both sex and the personality trait do predict the outcome variable. However, there is a clear interaction: the personality trait is only predictive of the outcome in men. In men the association is very clear, whereas it is completely insignificant in women. Hence, there is an interaction, and this is supported by a significant R2 change when you add the interaction term to the model. When you add the interaction term, both sex and the trait alone become insignificant, so the main effects are no longer meaningful.

My aim is not to predict new data but to understand the phenomenon I'm observing and it is clear that you would say 'if you are male, then this trait predicts this outcome, but not if you are female'. However, I am obliged to report a regression equation. Should I still include the coefficients for the main effects in the equation even though they are now non-significant and so, it seems to me, shouldn't be included in a model to predict the outcome? If I should only include the interaction term in the equation, then should I also report the actual regression model as just including the interaction term, without the lower order trait and sex predictors, given that they go straight to insignificance when the interaction is included?

Again, any help would be much appreciated, and apologies if this is answered in the other threads about lower order terms but I just did not understand it!

## marked as duplicate by Stephan Kolassa, kjetil b halvorsen, Maarten Buis, Peter Flom♦ regression StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 20 '18 at 13:16

• I understand that very similar questions have been asked before but they seem to either be about one where the main effects, or at least one main effect, remains significant and in the answers I do not see it clearly stated whether one should or should not include the non-significant main effects in a regression equation. I would be very happy if you can point me to an answer that has answered this question in a way that is understandable to someone who is not well versed in statistics (which I understand must be a little frustrating if the answers seem entirely clear to you) – Jamie Feb 20 '18 at 13:41