How to interpret a significant moderation model with nonsignificant $X$, $W$, and $XW$, and only significant covariates?

Question

First time data analyst, working on my thesis.

Below is a portion of the PROCESS output for one of my moderation analyses. I have been trying to make sense of this.

Alcohol use = DV

JVQ = IV

PWB = Moderator 

Gender = Covariate 1

SU_7R = Covariate 2

How can it be that my summary is significant and the only significant variable in the model is SU_7R_pu (Likert type variable ranging 1-7)? Is this telling me that the 15.25% variance accounted for in the model is mostly accounted for by the covariate SU_7R_pu? Also, how do I interpret the conditional effect of the covariates impact of X->Y?

For $b_1$, $b_2$, and $b_3$ Hayes' book is quite clear, but when it comes to making sense of the output for the covariates, I'm a little lost. Does it even make sense to say that there was an conditional effect of the covariates on the model, or only to say that it was controlled for and the model was adjusted? Does the model still get adjusted if the covariate is nonsignificant?

Is it possible to have a significant model F statistic and no significant coefficients?

In an other case, with a different DV, the model is nonsignificant; however the same covariate is significant ... what is the difference between these two cases in terms of interpretability?

Answer 1

There is a lot of questions, let break them out.

Regarding the title itself, your models imply that the only good predictor is SU_7R_pu. Maybe it is related too much with other VIs so it is the one taking most of the variance in the DV. However, the models, as they stand, imply that your IV and moderator has no effect (statistically) when you control for SU_7R_pu.

How can it be that my summary is significant and the only significant variable in the model is SU_7R_pu (Likert type variable ranging 1-7)?

The model summary is about all the variables in the models. It is not specifically about a moderation model (or the IVs and moderators) being significant. So if a single variable is significant, then the model should, in most cases, also be.

Is this telling me that the 15.25% variance accounted for in the model is mostly accounted for by the covariate SU_7R_pu?

Like previous question, the 15.25% is about all the variables. But it is pretty fair to guess that most comes from SU_7R_pu.

Also, how do I interpret the conditional effect of the covariates impact of X->Y?

According to the results in OP, there is likely no moderation effects :Int_1 is not significant.

Does it even make sense to say that there was an conditional effect of the covariates on the model, or only to say that it was controlled for and the model was adjusted?

The statistical model do not care if the variable is "covariate" or an "IV", it is treated as an IV. You can say that there is relation between your covariate on the outcomes.

Does the model still get adjusted if the covariate is nonsignificant?

Yes.

Is it possible to have a significant model F statistic and no significant coefficients?

Yes it is. It is even possible to have R^2 near 100% with no regression coefficients being significant. You just need a lot of them.

In an other case, with a different DV, the model is nonsignificant; however the same covariate is significant...what is the difference between these two cases in terms of interpretability?

It is the exact same interpretation.