insignificant interaction term - should we still look at the marginal effects?

Dear Statalist,

I have a question that is maybe not so much about Stata as it is about statistics in general.


I run a multivariate regression model (prais) and include an interaction effect between two continuous variables. Let’s call them X and Z. (c.X#c.Z)
The output tells me the interaction term c.X#c.Z is not significant. P>(t) = 0.470

Can I/should I proclaim that there is no interaction, or should I still look at the marginal effects?

When I look at the margins, I get the following:
margins, dydx(X) at( Z=(0(1)10)) vsquish


------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
X |
_at |
1 | -.0272084 .0156325 -1.74 0.082 -.0578475 .0034307
2 | -.0252041 .0131056 -1.92 0.054 -.0508906 .0004824
3 | -.0231998 .0106948 -2.17 0.030 -.0441613 -.0022383
4 | -.0211955 .0084996 -2.49 0.013 -.0378544 -.0045366
5 | -.0191912 .0067341 -2.85 0.004 -.0323898 -.0059926
6 | -.0171869 .0058046 -2.96 0.003 -.0285638 -.00581
7 | -.0151826 .0061058 -2.49 0.013 -.0271497 -.0032156
8 | -.0131783 .0074905 -1.76 0.079 -.0278595 .0015028
9 | -.0111741 .0094961 -1.18 0.239 -.0297861 .007438
10 | -.0091698 .0118104 -0.78 0.438 -.0323177 .0139782
11 | -.0071655 .0142841 -0.50 0.616 -.0351618 .0208308
------------------------------------------------------------------------------

Or should I say, based on this, that the two variables actually interact; that at some values of Z (3-8), the effect of X on Y is actually moderated/influenced by Z.
I thought that after looking at the (insignificant) interaction term in the output, there is no need to investigate further.

Would the conclusion/interpretation change if _all 11_ values (not just 3-8 but 1-11) were significant, while the main interaction term in the multivariate regression remains insignificant?

Thank you,

Alex