I have conducted a moderation analysis as follows:

X (continuous independent variable, centered), M (continuous moderator, centered),

Y (dependent variable).

Standard deviation for X is 3.8, and for M is 2.

I first entered X and M into a multiple regression analysis, and both were significantly associated with Y (beta X=0.23, beta M=0.21, both significant at p less than 0.05), with the model significant as well (R-squared=0.14). For the next step, I entered X, M, and the product of X and M (X*M, interaction factor) into a regression analysis, and got a small but significant R-squared change (of 0.001), with significant regression coefficients for X (beta X=0.273), for M (beta M=0.215) and for X*M (beta X*M=-0.034), all p less than 0.05. The interaction factor did have a sign opposite the main effects. I understand that this means that M is a significant moderator of the relationship between X and Y.

However, when I try to plot simple slopes at high (+1SD) and low (-1SD) levels of M, both slopes are nonsignificant (unstandardized slope 0.029, t=0.314 and p=0.89 for high M, and unstandardized slope 0.1349, t=0.902 and p=0.37 for low M). I believe this means neither slope is different from zero.

My question is, does this invalidate my interaction? Should I therefore not consider M a significant moderator of Y on X, despite significant interaction coefficient and significant R-squared change? If the interaction is still valid, how do I report the results of the simple slope analysis?

Thanks in advance!